Orderings.isa revision d31090850b029162859d0aedf45bae2a83d7b673
<IsaExport file="Orderings"><Imports><Import name="HOL"/></Imports><Consts><ConstDecl name="bot_bool"><Type name="HOL.bool"/><NoTerm/></ConstDecl><ConstDecl name="bot_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type><NoTerm/></ConstDecl><ConstDecl name="bot"><TVar name="'a"/><NoTerm/></ConstDecl><ConstDecl name="bot_fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><NoTerm/></ConstDecl><ConstDecl name="bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type><NoTerm/></ConstDecl><ConstDecl name="bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type><NoTerm/></ConstDecl><ConstDecl name="linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type><NoTerm/></ConstDecl><ConstDecl name="order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type><NoTerm/></ConstDecl><ConstDecl name="preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type><NoTerm/></ConstDecl><ConstDecl name="top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type><NoTerm/></ConstDecl><ConstDecl name="dense_linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type><NoTerm/></ConstDecl><ConstDecl name="linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type><NoTerm/></ConstDecl><ConstDecl name="Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type><NoTerm/></ConstDecl><ConstDecl name="greater"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Term name="greater"><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></Term></ConstDecl><ConstDecl name="greater_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Term name="greater_eq"><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></Term></ConstDecl><ConstDecl name="max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type><NoTerm/></ConstDecl><ConstDecl name="min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type><NoTerm/></ConstDecl><ConstDecl name="less_bool"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="less_eq_bool"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="ord_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type><NoTerm/></ConstDecl><ConstDecl name="Least"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type><TVar name="'a"/></Type><NoTerm/></ConstDecl><ConstDecl name="greater"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Term name="greater"><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></Term></ConstDecl><ConstDecl name="greater_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Term name="greater_eq"><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></Term></ConstDecl><ConstDecl name="less"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="less_eq"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="max"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="min"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="less_eq_fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="less_fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type><NoTerm/></ConstDecl><ConstDecl name="order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type><NoTerm/></ConstDecl><ConstDecl name="mono"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type><NoTerm/></ConstDecl><ConstDecl name="strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type><NoTerm/></ConstDecl><ConstDecl name="preorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type><NoTerm/></ConstDecl><ConstDecl name="top_bool"><Type name="HOL.bool"/><NoTerm/></ConstDecl><ConstDecl name="top_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type><NoTerm/></ConstDecl><ConstDecl name="top"><TVar name="'a"/><NoTerm/></ConstDecl><ConstDecl name="top_fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><NoTerm/></ConstDecl><ConstDecl name="wellorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type><NoTerm/></ConstDecl></Consts><Axioms><Term name="bot_bool_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="HOL.bool"/></Const></App><Const name="Orderings.bot_bool_inst.bot_bool"><Type name="HOL.bool"/></Const></App></Term><Term name="bot_fun_def"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type></Const></App><Const name="Orderings.bot_fun_inst.bot_fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type></Const></App></Term><Term name="less_bool_def"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_bool_inst.less_bool"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="less_eq_bool_def"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_bool_inst.less_eq_bool"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="less_eq_fun_def"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_fun_inst.less_eq_fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="less_fun_def"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_fun_inst.less_fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="top_bool_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><Const name="Orderings.top_class.top"><Type name="HOL.bool"/></Const></App><Const name="Orderings.top_bool_inst.top_bool"><Type name="HOL.bool"/></Const></App></Term><Term name="top_fun_def"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.top_class.top"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type></Const></App><Const name="Orderings.top_fun_inst.top_fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type></Const></App></Term></Axioms><Theorems><Term name="arity_bot_bool"><App><Const name="Orderings.bot_class"><Type name="fun"><Type name="itself"><Type name="HOL.bool"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><Type name="HOL.bool"/></Type></Const></App></Term><Term name="arity_bot_fun"><App><Const name="Orderings.bot_class"><Type name="fun"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type></Type></Const></App></Term><Term name="arity_ord_fun"><App><Const name="Orderings.ord_class"><Type name="fun"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Type></Const></App></Term><Term name="arity_order_fun"><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Type></Const></App></Term><Term name="arity_preorder_fun"><App><Const name="Orderings.preorder_class"><Type name="fun"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.preorder"/></TVar></Type></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.preorder"/></TVar></Type></Type></Const></App></Term><Term name="arity_top_bool"><App><Const name="Orderings.top_class"><Type name="fun"><Type name="itself"><Type name="HOL.bool"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><Type name="HOL.bool"/></Type></Const></App></Term><Term name="arity_top_fun"><App><Const name="Orderings.top_class"><Type name="fun"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type></Type></Const></App></Term><Term name="bot_least"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="bot_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="bot_unique"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="le_bot"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="not_less_bot"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="bot_apply"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Const name="Orderings.bot_class.bot"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Const name="Orderings.bot_class.bot"><TVar name="'b"><class name="Orderings.bot"/></TVar></Const></App></Term><Term name="bot_boolE"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="HOL.bool"/></Const></App><Var name="P"><Type name="HOL.bool"/></Var></App></Term><Term name="bot_bool_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="HOL.bool"/></Const></App><Const name="HOL.False"><Type name="HOL.bool"/></Const></App></Term><Term name="bot_bool_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="HOL.bool"/></Const></App><Const name="HOL.False"><Type name="HOL.bool"/></Const></App></Term><Term name="bot_bool"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="HOL.bool"/></Const></App><Const name="Orderings.bot_bool_inst.bot_bool"><Type name="HOL.bool"/></Const></App></Term><Term name="axioms"><App><App><Const name="Orderings.class.bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App></Term><Term name="bot_axioms"><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App></Term><Term name="bot_least"><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App><Var name="a"><TVar name="'a"><class name="Orderings.bot"/></TVar></Var></App></Term><Term name="bot_less"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.bot"/></TVar></Var></App><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App><Var name="a"><TVar name="'a"><class name="Orderings.bot"/></TVar></Var></App></App></Term><Term name="bot_unique"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.bot"/></TVar></Var></App><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.bot"/></TVar></Var></App><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.bot_class.bot"><TVar name="'a"/></Const></App></App><App><Const name="Orderings.bot_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></App></Term><Term name="le_bot"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.bot"/></TVar></Var></App><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.bot"/></TVar></Var></App><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App></App></Term><Term name="not_less_bot"><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.bot"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.bot"/></TVar></Var></App><Const name="Orderings.bot_class.bot"><TVar name="'a"><class name="Orderings.bot"/></TVar></Const></App></App></Term><Term name="super"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.bot_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="bot_class_def"><App><App><Const name="=="><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.bot_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Pure.conjunction"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Orderings.class.bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.bot_class.bot"><TVar name="'a"/></Const></App></App></App></Term><Term name="bot_fun_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type></Const></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Const name="Orderings.bot_class.bot"><TVar name="'b"><class name="Orderings.bot"/></TVar></Const></Abs></App></Term><Term name="bot_fun_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.bot"/></TVar></Type></Const></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Const name="Orderings.bot_class.bot"><TVar name="'b"><class name="Orderings.bot"/></TVar></Const></Abs></App></Term><Term name="bot_fun"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.bot_class.bot"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type></Const></App><Const name="Orderings.bot_fun_inst.bot_fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type></Const></App></Term><Term name="axioms_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="axioms_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="Orderings.class.bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Bound index="0"/></App></Abs></App></App><App><App><Const name="Orderings.class.bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="bot_axioms_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Bound index="0"/></App></Abs></App></App></Term><Term name="bot_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.bot"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.bot_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="bot"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="axioms_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="axioms_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="Orderings.class.dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></Abs></App></Abs></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></Abs></App></Abs></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="z"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="2"/></App><Bound index="0"/></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App></Abs></App></App></Abs></App></Abs></App></App><App><Const name="Orderings.class.dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></App></Term><Term name="dense_linorder_axioms_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></Abs></App></Abs></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></Abs></App></Abs></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="z"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="2"/></App><Bound index="0"/></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App></Abs></App></App></Abs></App></Abs></App></App></App></App></Term><Term name="dense_linorder_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="Orderings.class.dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></Term><Term name="axioms_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="axioms_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="Orderings.class.linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App></Abs></App></Abs></App></App><App><Const name="Orderings.class.linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="linorder_axioms_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App></Abs></App></Abs></App></App></Term><Term name="linorder_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="Orderings.class.linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></Term><Term name="axioms_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="axioms_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="Orderings.class.order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><Const name="Orderings.class.order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="order_axioms_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App></App></Abs></App></Abs></App></App></Term><Term name="order_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="Orderings.class.order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App></App></App></Abs></App></Abs></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="0"/></App></Abs></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="z"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="2"/></App><Bound index="1"/></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="2"/></App><Bound index="0"/></App></App></App></Abs></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></App></Term><Term name="preorder_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App></App></App></Abs></App></Abs></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="0"/></App></Abs></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="z"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="2"/></App><Bound index="1"/></App></App><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="2"/></App><Bound index="0"/></App></App></App></Abs></App></Abs></App></Abs></App></App></App></App></Term><Term name="axioms_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="axioms_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="Orderings.class.top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></Abs></App></App><App><App><Const name="Orderings.class.top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="top_axioms_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></Abs></App></App></Term><Term name="top_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="axioms_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="axioms_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="Orderings.class.wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App><App><Bound index="3"/><Bound index="0"/></App></App></Abs></App></App><App><Bound index="2"/><Bound index="0"/></App></App></Abs></App></App><App><Bound index="1"/><Bound index="0"/></App></App></Abs></App></Abs></App></App><App><Const name="Orderings.class.wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></Term><Term name="wellorder_axioms_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App><App><Bound index="3"/><Bound index="0"/></App></App></Abs></App></App><App><Bound index="2"/><Bound index="0"/></App></App></Abs></App></App><App><Bound index="1"/><Bound index="0"/></App></App></Abs></App></Abs></App></App></Term><Term name="wellorder_def"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="Orderings.class.wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App></App></Term><Term name="dense"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="z"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Bound index="0"/></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Abs></App></App></App></Term><Term name="dense_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Abs></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="dense_le_bounded"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="w"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Bound index="0"/></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Abs></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="gt_ex"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Bound index="0"/></App></Abs></App></App></Term><Term name="lt_ex"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></Abs></App></App></Term><Term name="axioms"><App><Const name="Orderings.class.dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="dense"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="z"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Var name="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App></Abs></App></App></Term><Term name="dense_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Var name="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Var name="z"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App></Term><Term name="dense_le_bounded"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="w"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App><Bound index="0"/></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Var name="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Var name="z"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></App></App></Term><Term name="dense_linorder_axioms"><App><App><Const name="Orderings.class.dense_linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="gt_ex"><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App><Bound index="0"/></App></Abs></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App><App><Const name="Orderings.dense_linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></App></Term><Term name="lt_ex"><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Var name="x"><TVar name="'a"><class name="Orderings.dense_linorder"/></TVar></Var></App></Abs></App></Term><Term name="super"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.dense_linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="dense_linorder_class_def"><App><App><Const name="=="><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.dense_linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Pure.conjunction"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.class.dense_linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></App></Term><Term name="le_boolD"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App></Term><Term name="le_boolE"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><Var name="Q"><Type name="HOL.bool"/></Var></App><Var name="R"><Type name="HOL.bool"/></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App></App></Term><Term name="le_boolI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App></Term><Term name="le_boolI'"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App></Term><Term name="le_bool_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App></Term><Term name="le_bool_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App><Abs vname="P"><Type name="HOL.bool"/><Abs vname="Q"><Type name="HOL.bool"/><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></Abs></Abs></App></Term><Term name="le_funD"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="le_funE"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="le_funI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App></App></Term><Term name="le_fun_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></Abs></App></App></Term><Term name="le_fun_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const></App><Abs vname="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Abs vname="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="2"/><Bound index="0"/></App></App><App><Bound index="1"/><Bound index="0"/></App></App></Abs></App></Abs></Abs></App></Term><Term name="less_bool_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App></Term><Term name="less_bool_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App><Abs vname="P"><Type name="HOL.bool"/><Abs vname="Q"><Type name="HOL.bool"/><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><Bound index="1"/></App></App><Bound index="0"/></App></Abs></Abs></App></Term><Term name="less_fun_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var></App></App></App></App></Term><Term name="less_fun_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const></App><Abs vname="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Abs vname="g"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App></App></Abs></Abs></App></Term><Term name="antisym_conv1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="antisym_conv2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="antisym_conv3"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="dual_linorder"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App></App></Term><Term name="leD"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="leI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="le_cases"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></App></Term><Term name="le_less_linear"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="le_max_iff_disj"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><App><App><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="less_linear"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="less_max_iff_disj"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><App><App><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="linear"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="linorder_cases"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></App></App></Term><Term name="max_less_iff_conj"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><App><App><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="max_of_mono"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.order.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><Var name="m"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><Var name="n"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><App><App><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="m"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="n"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></App></Term><Term name="min_le_iff_disj"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><App><App><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="min_less_iff_conj"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><App><App><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="min_less_iff_disj"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><App><App><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="min_of_mono"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.order.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><Var name="m"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><Var name="n"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><App><App><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="m"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="n"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></App></Term><Term name="neqE"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App></App></App></Term><Term name="neq_iff"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="not_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="not_leE"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="not_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="not_less_iff_gr_or_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="split_max"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="i"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="i"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="j"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="i"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="i"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></App></Term><Term name="split_min"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="i"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="i"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="i"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="i"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="j"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></App></Term><Term name="strict_mono_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="strict_mono_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="strict_mono_less_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="linorder_antisym_conv1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="linorder_antisym_conv2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="linorder_antisym_conv3"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="antisym_conv1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="antisym_conv2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="antisym_conv3"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="axioms"><App><Const name="Orderings.class.linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="dual_linorder"><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Abs vname="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App><Abs vname="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Abs vname="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></App></Term><Term name="leD"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="leI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="le_cases"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="le_less_linear"><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="le_max_iff_disj"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="less_linear"><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="less_max_iff_disj"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="linear"><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="linorder_axioms"><App><App><Const name="Orderings.class.linorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="linorder_cases"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></App></Term><Term name="max_less_iff_conj"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="max_of_mono"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><Var name="m"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><Var name="n"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="m"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="n"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></App></Term><Term name="min_le_iff_disj"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="min_less_iff_conj"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="min_less_iff_disj"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="min_of_mono"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><Var name="m"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><Var name="n"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.linorder"/></TVar></Type></Var><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="m"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="n"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></App></Term><Term name="neqE"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App></App></Term><Term name="neq_iff"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="not_le"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="not_leE"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="not_less"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="not_less_iff_gr_or_eq"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="split_max"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="i"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="i"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="j"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="i"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="i"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></App></Term><Term name="split_min"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'a"><class name="Orderings.linorder"/></TVar></Type></Type></Const><Var name="i"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="i"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="i"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="i"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="j"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="j"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></App></Term><Term name="strict_mono_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="strict_mono_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="strict_mono_less_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="super"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="linorder_class_def"><App><App><Const name="=="><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Pure.conjunction"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.class.linorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></App></Term><Term name="linorder_le_cases"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="linorder_le_less_linear"><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="linorder_less_linear"><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="linorder_linear"><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="linorder_neqE"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App><Var name="R"><Type name="HOL.bool"/></Var></App></App></App></Term><Term name="linorder_neq_iff"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App></Term><Term name="linorder_not_le"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="linorder_not_less"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.linorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.linorder"/></TVar></Var></App></App></Term><Term name="max_leastL"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="least"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Bound index="0"/></App></Abs></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Const><Var name="least"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="x"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></Term><Term name="max_leastR"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="least"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Bound index="0"/></App></Abs></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="least"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></Term><Term name="max_ord_max"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Const></App><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></App></Term><Term name="min_leastL"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="least"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Bound index="0"/></App></Abs></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Const><Var name="least"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="least"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></Term><Term name="min_leastR"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="least"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Bound index="0"/></App></Abs></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="least"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="least"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></Term><Term name="min_ord_min"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Const></App><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></App></Term><Term name="Least_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var></App></App><App><Const name="HOL.The"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App></Abs></App></App></Abs></App></App></Term><Term name="Least_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><Abs vname="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><App><Const name="HOL.The"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="1"/><Bound index="0"/></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="2"/><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App></Abs></App></App></Abs></App></Abs></App></Term><Term name="max_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><App><Const name="HOL.If"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="max_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="b"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><App><Const name="HOL.If"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App></Term><Term name="min_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><App><Const name="HOL.If"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="min_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="b"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><App><Const name="HOL.If"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><Bound index="1"/></App><Bound index="0"/></App></Abs></Abs></App></Term><Term name="ord_eq_le_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="ord_eq_less_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="ord_le_eq_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="ord_less_eq_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="less_bool"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_bool_inst.less_bool"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="less_eq_bool"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_bool_inst.less_eq_bool"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="Least_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Const><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Var></App></App><App><Const name="HOL.The"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App></Abs></App></App></Abs></App></App></Term><Term name="Least_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.ord"/></TVar></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.ord"/></TVar></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Const></App><Abs vname="P"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><App><Const name="HOL.The"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="1"/><Bound index="0"/></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="2"/><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App></Abs></App></App></Abs></App></Abs></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.type_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.ord_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="max_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><App><Const name="HOL.If"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></Term><Term name="max_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Const></App><Abs vname="a"><TVar name="'a"><class name="Orderings.ord"/></TVar><Abs vname="b"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><App><Const name="HOL.If"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App></Term><Term name="min_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><App><Const name="HOL.If"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></Term><Term name="min_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Const></App><Abs vname="a"><TVar name="'a"><class name="Orderings.ord"/></TVar><Abs vname="b"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><App><Const name="HOL.If"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><Bound index="1"/></App><Bound index="0"/></App></Abs></Abs></App></Term><Term name="Least_dict"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type><TVar name="'a"/></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type><TVar name="'a"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type><TVar name="'a"/></Type></Const></App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type><TVar name="'a"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></Term><Term name="max_dict"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.max"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type></Const></App><App><Const name="Orderings.ord.max"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></Term><Term name="min_dict"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.min"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type></Const></App><App><Const name="Orderings.ord.min"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><TVar name="'a"/></Type></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></Term><Term name="ord_eq_le_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></App></Term><Term name="ord_eq_less_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></App></Term><Term name="ord_le_eq_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></App></Term><Term name="ord_less_eq_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></App></Term><Term name="super"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.ord_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="HOL.type_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="ord_class_def"><App><App><Const name="=="><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.ord_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="HOL.type_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="ord_eq_le_subst"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App></App></App></Term><Term name="ord_eq_less_subst"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App></App></App></Term><Term name="less_eq_fun"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_fun_inst.less_eq_fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="less_fun"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_fun_inst.less_fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="ord_le_eq_subst"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App></App></Term><Term name="ord_less_eq_subst"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App></App></Term><Term name="LeastI2_order"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Bound index="0"/></App></App></Abs></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></App></App></Term><Term name="Least_equality"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Bound index="0"/></App></App></Abs></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var></App></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="antisym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="antisym_conv"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="dual_order"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App></App></Term><Term name="eq_iff"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="le_imp_less_or_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="le_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="le_neq_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="less_imp_neq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="less_imp_not_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Const name="HOL.False"><Type name="HOL.bool"/></Const></App></App></App></Term><Term name="less_imp_not_eq2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Const name="HOL.False"><Type name="HOL.bool"/></Const></App></App></App></Term><Term name="less_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></App></Term><Term name="monoD"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.order.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></App></Term><Term name="monoI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.order.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App></App></Term><Term name="mono_def"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.order.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App></App></Term><Term name="mono_def_raw"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><Abs vname="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="2"/><Bound index="1"/></App></App><App><Bound index="2"/><Bound index="0"/></App></App></App></Abs></App></Abs></App></Abs></App></App></Term><Term name="neq_le_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="strict_monoD"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></App></Term><Term name="strict_monoI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App></App></Term><Term name="strict_mono_def"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App></App></Term><Term name="strict_mono_def_raw"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><Abs vname="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="2"/><Bound index="1"/></App></App><App><Bound index="2"/><Bound index="0"/></App></App></App></Abs></App></Abs></App></Abs></App></App></Term><Term name="strict_mono_mono"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="Orderings.order.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="f"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App></App></Term><Term name="order_antisym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_antisym_conv"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="LeastI2_order"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Bound index="0"/></App></App></Abs></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Const><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></App></Term><Term name="Least_equality"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Bound index="0"/></App></App></Abs></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Const><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Var></App></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="antisym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="antisym_conv"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="axioms"><App><Const name="Orderings.class.order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="dual_order"><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App></Term><Term name="eq_iff"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.preorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></App></Term><Term name="le_imp_less_or_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="le_less"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="le_neq_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="less_imp_neq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="less_imp_not_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Const name="HOL.False"><Type name="HOL.bool"/></Const></App></App></Term><Term name="less_imp_not_eq2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Const name="HOL.False"><Type name="HOL.bool"/></Const></App></App></Term><Term name="less_le"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="monoD"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="monoI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><Const name="Orderings.order_class.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App></Term><Term name="mono_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="Orderings.order_class.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App></Term><Term name="mono_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.order_class.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const></App><Abs vname="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="2"/><Bound index="1"/></App></App><App><Bound index="2"/><Bound index="0"/></App></App></App></Abs></App></Abs></App></Abs></App></Term><Term name="neq_le_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_axioms"><App><App><Const name="Orderings.class.order"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="mono_dict"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.order_class.mono"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Const></App><App><Const name="Orderings.order.mono"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></Term><Term name="strict_mono_dict"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Const></App><App><Const name="Orderings.order.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></Term><Term name="strict_monoD"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="strict_monoI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App></Term><Term name="strict_mono_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App></Term><Term name="strict_mono_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type><Type name="fun"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const></App><Abs vname="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Bound index="2"/><Bound index="1"/></App></App><App><Bound index="2"/><Bound index="0"/></App></App></App></Abs></App></Abs></App></Abs></App></Term><Term name="strict_mono_mono"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class.strict_mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App><App><Const name="Orderings.order_class.mono"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type><Type name="HOL.bool"/></Type></Const><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var></App></App></Term><Term name="super"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.preorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="order_class_def"><App><App><Const name="=="><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Pure.conjunction"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.preorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.class.order_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></App></Term><Term name="order_eq_iff"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_eq_refl"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></Term><Term name="order_le_imp_less_or_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_le_less"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.disj" infixr="|" mixfix_i="30"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_le_less_subst1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="order_le_less_subst2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_le_less_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_le_neq_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_less_asym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="order_less_asym'"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="order_less_imp_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></Term><Term name="order_less_imp_not_eq"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Const name="HOL.False"><Type name="HOL.bool"/></Const></App></App></Term><Term name="order_less_imp_not_eq2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Const name="HOL.False"><Type name="HOL.bool"/></Const></App></App></Term><Term name="order_less_imp_not_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App><Const name="HOL.True"><Type name="HOL.bool"/></Const></App></App></Term><Term name="order_less_imp_triv"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Const name="HOL.True"><Type name="HOL.bool"/></Const></App></App></Term><Term name="order_less_irrefl"><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></Term><Term name="order_less_le"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_less_le_subst1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="order_less_le_subst2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_less_le_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_less_not_sym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_less_subst1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="order_less_subst2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_less_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_neq_le_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_subst1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="order_subst2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_trans_rules_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_trans_rules_10"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App></App></App></Term><Term name="order_trans_rules_11"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App></App></Term><Term name="order_trans_rules_12"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.ord"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App></App></App></Term><Term name="order_trans_rules_13"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_14"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_15"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App></Term><Term name="order_trans_rules_16"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App><Var name="Q"><Type name="HOL.bool"/></Var></App></App></Term><Term name="order_trans_rules_17"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_18"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_19"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="order_trans_rules_20"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="order_trans_rules_21"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_22"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_23"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_24"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_25"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_26"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_27"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_28"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_29"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="r"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="s"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="s"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="t"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="r"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="t"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="order_trans_rules_3"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_trans_rules_4"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="order_trans_rules_5"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_trans_rules_6"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="order_trans_rules_7"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'c"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'c"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'c"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="order_trans_rules_8"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="order_trans_rules_9"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="1"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Bound index="0"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.ord"/></TVar><TVar name="'b"><class name="Orderings.ord"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App></App></App></Term><Term name="dual_preorder"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App></App></Term><Term name="eq_refl"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="le_less_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="less_asym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></App></Term><Term name="less_asym'"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="b"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></App></Term><Term name="less_imp_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="less_imp_not_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><Const name="HOL.True"><Type name="HOL.bool"/></Const></App></App></App></Term><Term name="less_imp_triv"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Const name="HOL.True"><Type name="HOL.bool"/></Const></App></App></App></Term><Term name="less_irrefl"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="less_le_not_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></App></Term><Term name="less_le_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="less_not_sym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="less_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="order_refl"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="order_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="y"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="axioms"><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="dual_preorder"><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Abs vname="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App><Abs vname="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Abs vname="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></Abs></Abs></App></Term><Term name="eq_refl"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.ord_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App><App><Const name="Orderings.preorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></App></Term><Term name="le_less_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="less_asym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><Var name="P"><Type name="HOL.bool"/></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="less_asym'"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="less_imp_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></Term><Term name="less_imp_not_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App><Const name="HOL.True"><Type name="HOL.bool"/></Const></App></App></Term><Term name="less_imp_triv"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App><Const name="HOL.True"><Type name="HOL.bool"/></Const></App></App></Term><Term name="less_irrefl"><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></Term><Term name="less_le_not_le"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="HOL.conj" infixr="&" mixfix_i="35"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></App></Term><Term name="less_le_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="less_not_sym"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="less_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="order_refl"><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></Term><Term name="order_trans"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App><Var name="z"><TVar name="'a"><class name="Orderings.preorder"/></TVar></Var></App></App></App></Term><Term name="preorder_axioms"><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.preorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="super"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.preorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.ord_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="preorder_class_def"><App><App><Const name="=="><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.preorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Pure.conjunction"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.ord_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Orderings.class.preorder"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></App></Term><Term name="less_top"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="not_top_less"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="top_greatest"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></Term><Term name="top_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="top_unique"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><Var name="top"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="top_apply"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Const name="Orderings.top_class.top"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type></Const><Var name="x"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><Const name="Orderings.top_class.top"><TVar name="'b"><class name="Orderings.top"/></TVar></Const></App></Term><Term name="top_boolI"><Const name="Orderings.top_class.top"><Type name="HOL.bool"/></Const></Term><Term name="top_bool_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.top_class.top"><Type name="HOL.bool"/></Const></App><Const name="HOL.True"><Type name="HOL.bool"/></Const></App></Term><Term name="top_bool_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><Const name="Orderings.top_class.top"><Type name="HOL.bool"/></Const></App><Const name="HOL.True"><Type name="HOL.bool"/></Const></App></Term><Term name="top_bool"><App><App><Const name="=="><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="prop"/></Type></Type></Const><Const name="Orderings.top_class.top"><Type name="HOL.bool"/></Const></App><Const name="Orderings.top_bool_inst.top_bool"><Type name="HOL.bool"/></Const></App></Term><Term name="axioms"><App><App><Const name="Orderings.class.top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.top_class.top"><TVar name="'a"/></Const></App></App><App><Const name="Orderings.top_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></App></Term><Term name="less_top"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.top"/></TVar></Var></App><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.top"/></TVar></Var></App><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App></App></Term><Term name="not_top_less"><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App><Var name="a"><TVar name="'a"><class name="Orderings.top"/></TVar></Var></App></App></Term><Term name="super"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.top_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="top_axioms"><App><App><App><Const name="Orderings.class.top"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App></Term><Term name="top_greatest"><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.top"/></TVar></Var></App><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App></Term><Term name="top_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App><Var name="a"><TVar name="'a"><class name="Orderings.top"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.top"/></TVar></Var></App><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App></App></Term><Term name="top_unique"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App><Var name="a"><TVar name="'a"><class name="Orderings.top"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.top"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.top"/></TVar></Var></App><Const name="Orderings.top_class.top"><TVar name="'a"><class name="Orderings.top"/></TVar></Const></App></App></Term><Term name="top_class_def"><App><App><Const name="=="><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.top_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Pure.conjunction"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.order_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Orderings.class.top_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.top_class.top"><TVar name="'a"/></Const></App></App></App></Term><Term name="top_fun_def"><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.top_class.top"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type></Const></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Const name="Orderings.top_class.top"><TVar name="'b"><class name="Orderings.top"/></TVar></Const></Abs></App></Term><Term name="top_fun_def_raw"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.top_class.top"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><TVar name="'b"><class name="Orderings.top"/></TVar></Type></Const></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><Const name="Orderings.top_class.top"><TVar name="'b"><class name="Orderings.top"/></TVar></Const></Abs></App></Term><Term name="top_fun"><App><App><Const name="=="><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type><Type name="prop"/></Type></Type></Const><Const name="Orderings.top_class.top"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type></Const></App><Const name="Orderings.top_fun_inst.top_fun"><Type name="fun"><TVar name="'a"/><TVar name="'b"/></Type></Const></App></Term><Term name="LeastI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App></App></App></Term><Term name="LeastI2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></App></Term><Term name="LeastI2_ex"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></App></Term><Term name="LeastI2_wellorder"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="b"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="1"/></App><Bound index="0"/></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></App></Term><Term name="LeastI_ex"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></Term><Term name="Least_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App><Var name="k"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="less_induct"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="HOL.type"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Bound index="0"/></App><Bound index="1"/></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="a"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="not_less_Least"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><Var name="k"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></App></Term><Term name="wellorder_Least_lemma_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App></App></App></Term><Term name="wellorder_Least_lemma_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Var name="less"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App><App><App><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var><App><App><Const name="Orderings.ord.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="HOL.type"/></TVar></Type></Type></Const><Var name="less_eq"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Type></Var></App><Abs vname="x"><TVar name="'a"><class name="HOL.type"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="HOL.type"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App><Var name="k"><TVar name="'a"><class name="HOL.type"/></TVar></Var></App></App></App></Term><Term name="LeastI"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App></App></Term><Term name="LeastI2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></Term><Term name="LeastI2_ex"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></Term><Term name="LeastI2_wellorder"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="a"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.All"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="b"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><App><Const name="HOL.implies" infixr="-->" mixfix_i="25"><Type name="fun"><Type name="HOL.bool"/><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="1"/></App><Bound index="0"/></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></App></Abs></App></App><App><Var name="Q"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></App></Term><Term name="LeastI_ex"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Ex"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><Type name="HOL.bool"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var></App></App></App></Term><Term name="Least_le"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App><Var name="k"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App></Term><Term name="axioms"><App><Const name="Orderings.class.wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="intro"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.class.wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App><App><Const name="Orderings.wellorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></App></Term><Term name="less_induct"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></App></Abs></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App></Term><Term name="not_less_Least"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="k"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App></App><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App></App></Term><Term name="super"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.wellorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App></Term><Term name="wellorder_Least_lemma_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App></App></Term><Term name="wellorder_Least_lemma_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Var name="k"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Const name="Orderings.ord_class.Least"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><App><Var name="P"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Var><Bound index="0"/></App></Abs></App></App><Var name="k"><TVar name="'a"><class name="Orderings.wellorder"/></TVar></Var></App></App></Term><Term name="wellorder_axioms"><App><App><Const name="Orderings.class.wellorder"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Type></Const><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.wellorder"/></TVar><Type name="HOL.bool"/></Type></Type></Const></App></Term><Term name="wellorder_class_def"><App><App><Const name="=="><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.wellorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><App><Const name="Pure.conjunction"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="Orderings.linorder_class"><Type name="fun"><Type name="itself"><TVar name="'a"/></Type><Type name="prop"/></Type></Const><Const name="TYPE"><Type name="itself"><TVar name="'a"/></Type></Const></App></App><App><Const name="Orderings.class.wellorder_axioms"><Type name="fun"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type><Type name="HOL.bool"/></Type></Const><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"/><Type name="fun"><TVar name="'a"/><Type name="HOL.bool"/></Type></Type></Const></App></App></App></Term><Term name="xt1_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_10"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_11"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_12"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_13"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xt1_14"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xt1_15"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xt1_16"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xt1_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_3"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_4"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_5"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_6"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_7"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_8"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xt1_9"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term><Term name="xt2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xt3"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xt4"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xt5"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xt6"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xt7"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xt8"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xt9"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xtrans_1"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_10"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_11"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_12"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="HOL.Not"><Type name="fun"><Type name="HOL.bool"/><Type name="HOL.bool"/></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_13"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xtrans_14"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xtrans_15"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xtrans_16"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xtrans_17"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xtrans_18"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xtrans_19"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xtrans_2"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_20"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xtrans_21"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App><Var name="b"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.ord"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.ord"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.ord"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xtrans_22"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xtrans_23"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'b"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'b"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><TVar name="'a"><class name="Orderings.order"/></TVar></Type></Var><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></Term><Term name="xtrans_24"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="x"><TVar name="'a"><class name="Orderings.order"/></TVar><App><Const name="all"><Type name="fun"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="prop"/></Type><Type name="prop"/></Type></Const><Abs vname="y"><TVar name="'a"><class name="Orderings.order"/></TVar><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Bound index="0"/></App><Bound index="1"/></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="0"/></App></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Bound index="1"/></App></App></App></Abs></App></Abs></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'b"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'b"><class name="Orderings.order"/></TVar></Var></App><App><Var name="f"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><TVar name="'b"><class name="Orderings.order"/></TVar></Type></Var><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></App></App></Term><Term name="xtrans_3"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_4"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="c"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_5"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="HOL.eq" infixl="=" mixfix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_6"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_7"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_8"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less_eq" infix="<=" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="y"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="z"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="x"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App></App></Term><Term name="xtrans_9"><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><App><App><Const name="==>"><Type name="fun"><Type name="prop"/><Type name="fun"><Type name="prop"/><Type name="prop"/></Type></Type></Const><App><App><Const name="Orderings.ord_class.less" infix="<" mixifix_i="50"><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="fun"><TVar name="'a"><class name="Orderings.order"/></TVar><Type name="HOL.bool"/></Type></Type></Const><Var name="a"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App><Var name="b"><TVar name="'a"><class name="Orderings.order"/></TVar></Var></App></App><Var name="P"><Type name="HOL.bool"/></Var></App></App></Term></Theorems><Types/></IsaExport>