sttifol.omdoc revision 239352d9aec4bc3823511873533fa812cbe259c7
<?xml version="1.0" encoding="UTF-8"?>
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath" >
<!-- generated from Twelf sources by Florian Rabe -->
<view name="IntExt" from="/type_theories/base.omdoc?Level" to="/first-order/proof_theory/sorted_modules.omdoc?SEqualPF">
<conass name="cl">
<om:OMOBJ>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMOBJ>
</conass>
<conass name="exp">
<om:OMOBJ>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMATP><om:OMV name="A"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMBIND>
</om:OMOBJ>
</conass>
<conass name="==">
<om:OMOBJ>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMATP><om:OMV name="A"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="X"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="Y"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMA>
<om:OMS base="/propositional/syntax/base.omdoc" module="Base" name="ded"/>
<om:OMA>
<om:OMS base="/syntax/sorted_modules.omdoc" module="SEqual" name="eq"/>
<om:OMV name="A"/>
<om:OMV name="X"/>
<om:OMV name="Y"/>
</om:OMA>
</om:OMA>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMOBJ>
</conass>
<conass name="refl">
<om:OMOBJ>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMATP><om:OMV name="A"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="X"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMA>
<om:OMS name="refl"/>
<om:OMV name="A"/>
<om:OMV name="X"/>
</om:OMA>
</om:OMBIND>
</om:OMBIND>
</om:OMOBJ>
</conass>
<conass name="sym">
<om:OMOBJ>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMATP><om:OMV name="A"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="X"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="Y"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/propositional/syntax/base.omdoc" module="Base" name="ded"/>
<om:OMA>
<om:OMS base="/syntax/sorted_modules.omdoc" module="SEqual" name="eq"/>
<om:OMV name="A"/>
<om:OMV name="X"/>
<om:OMV name="Y"/>
</om:OMA>
</om:OMA>
</om:OMATP><om:OMV name="p"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMA>
<om:OMS name="sym"/>
<om:OMV name="A"/>
<om:OMV name="X"/>
<om:OMV name="Y"/>
<om:OMV name="p"/>
</om:OMA>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMOBJ>
</conass>
<conass name="trans">
<om:OMOBJ>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMATP><om:OMV name="A"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="X"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="Y"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="Z"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/propositional/syntax/base.omdoc" module="Base" name="ded"/>
<om:OMA>
<om:OMS base="/syntax/sorted_modules.omdoc" module="SEqual" name="eq"/>
<om:OMV name="A"/>
<om:OMV name="X"/>
<om:OMV name="Y"/>
</om:OMA>
</om:OMA>
</om:OMATP><om:OMV name="p"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/propositional/syntax/base.omdoc" module="Base" name="ded"/>
<om:OMA>
<om:OMS base="/syntax/sorted_modules.omdoc" module="SEqual" name="eq"/>
<om:OMV name="A"/>
<om:OMV name="Y"/>
<om:OMV name="Z"/>
</om:OMA>
</om:OMA>
</om:OMATP><om:OMV name="q"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMA>
<om:OMS name="trans"/>
<om:OMV name="A"/>
<om:OMV name="X"/>
<om:OMV name="Y"/>
<om:OMV name="Z"/>
<om:OMV name="p"/>
<om:OMV name="q"/>
</om:OMA>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMOBJ>
</conass>
<conass name="cong">
<om:OMOBJ>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMATP><om:OMV name="A"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="X"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="Y"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMATP><om:OMV name="B"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/propositional/syntax/base.omdoc" module="Base" name="ded"/>
<om:OMA>
<om:OMS base="/syntax/sorted_modules.omdoc" module="SEqual" name="eq"/>
<om:OMV name="A"/>
<om:OMV name="X"/>
<om:OMV name="Y"/>
</om:OMA>
</om:OMA>
</om:OMATP><om:OMV name="F"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="arrow"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="B"/>
</om:OMA>
</om:OMA>
</om:OMATP><om:OMV name="p"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMA>
<om:OMS name="congF"/>
<om:OMV name="A"/>
<om:OMV name="X"/>
<om:OMV name="Y"/>
<om:OMV name="B"/>
<om:OMV name="F"/>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMA>
<om:OMS base="/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="A"/>
</om:OMA>
</om:OMATP><om:OMV name="x"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMA>
<om:OMV name="p"/>
<om:OMV name="x"/>
</om:OMA>
</om:OMBIND>
</om:OMA>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMBIND>
</om:OMOBJ>
</conass>
</view>
<theory name="STTIFOLEQ">
<include from="/first-order/proof_theory/sifol.omdoc?SIFOLEQPF"/>
<include from="/propositional/proof_theory/derived.omdoc?PLPFExt"/>
<structure name="fun" from="/type_theories/modules-lambda.omdoc?SimpFun">
<strass name="level">
<OMMOR ><om:OMS module="IntExt"/></OMMOR>
</strass>
</structure><alias name="→" for="??fun/→"/><alias name="λ" for="??fun/λ"/><alias name="@" for="??fun/@"/><alias name=";" for="??fun/;"/><alias name="∘" for="??fun/∘"/><alias name="beta" for="??fun/beta"/>
<constant name="set">
<type>
<om:OMOBJ>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="type"/>
</om:OMOBJ>
</type>
<definition>
<om:OMOBJ>
<om:OMS base="/first-order/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMOBJ>
</definition>
</constant>
<constant name="elem">
<type>
<om:OMOBJ>
<om:OMA>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="arrow"/>
<om:OMS base="/first-order/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="type"/>
</om:OMA>
</om:OMOBJ>
</type>
<definition>
<om:OMOBJ>
<om:OMBIND>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="lambda"/>
<om:OMBVAR>
<om:OMATTR><om:OMATP>
<om:OMS base="http://cds.omdoc.org/foundations/lf/lf.omdoc" module="lf" name="oftype"/>
<om:OMS base="/first-order/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/cl"/>
</om:OMATP><om:OMV name="x"/>
</om:OMATTR>
</om:OMBVAR>
<om:OMA>
<om:OMS base="/first-order/syntax/sorted_base.omdoc" module="BaseSFOL" name="sorts/exp"/>
<om:OMV name="x"/>
</om:OMA>
</om:OMBIND>
</om:OMOBJ>
</definition>
</constant>
</theory>
</omdoc>