var S : Type; N : Type; E : Type

type Set : Type -> Type := \ S : Type . S_v-1 ->? Unit

type Graph : Type -> Type -> Type := \ (N : Type)

(E : Type) . Set N_v-1@(N_v-1 ->? Unit) * (E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)

op __union__ : Graph N E * Graph N E -> Graph N E;

__union__, __intersection__, __\\__ : Set S * Set S -> Set S

forall g : Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N));

g' : Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N))

. (fun __=__[Set N@(N ->? Unit) * (E ->? N) * (E ->? N)]

: forall a : Type . a_v-1 * a_v-1 ->? Unit)

((op __union__[N; E]

: forall N : Type; E : Type .

Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) * (E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)) *

Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) * (E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)) -> Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) *

(E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)))

(var g : Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N)),

var g' : Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N))),

var g : Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N)))

%% Type Constructors -----------------------------------------------------

E : Type %(var_3)%

Graph

: Type -> Type -> Type

:= \ (N : Type)(E : Type) . Set N_v-1@(N_v-1 ->? Unit) *

(E_v-2 ->? N_v-1) * (E_v-2 ->? N_v-1)

Logical : Type := Unit ->? Unit

N : Type %(var_2)%

Pred : Type -> Type := \ a : Type . a_v-1 ->? Unit

S : Type %(var_1)%

Set : Type -> Type := \ S : Type . S_v-1 ->? Unit

Unit : Type := Unit

__*__ : Type+ -> Type+ -> Type

__-->__ : Type- -> Type+ -> Type

__-->?__ : Type- -> Type+ -> Type

__->__ : Type- -> Type+ -> Type

__->?__ : Type- -> Type+ -> Type

%% Assumptions -----------------------------------------------------------

__/\__ : ? Unit * ? Unit ->? Unit %(fun)%

__<=>__ : ? Unit * ? Unit ->? Unit %(fun)%

__=__ : forall a : Type . a_v-1 * a_v-1 ->? Unit %(fun)%

__=>__ : ? Unit * ? Unit ->? Unit %(fun)%

__=e=__ : forall a : Type . a_v-1 * a_v-1 ->? Unit %(fun)%

__\/__ : ? Unit * ? Unit ->? Unit %(fun)%

__\\__

: forall S : Type .

Set S_v-1@(S_v-1 ->? Unit) *

Set S_v-1@(S_v-1 ->? Unit) -> Set S_v-1@(S_v-1 ->? Unit)

%(op)%

__if__ : ? Unit * ? Unit ->? Unit %(fun)%

__intersection__

: forall S : Type .

Set S_v-1@(S_v-1 ->? Unit) *

Set S_v-1@(S_v-1 ->? Unit) -> Set S_v-1@(S_v-1 ->? Unit)

%(op)%

__union__

: forall S : Type .

Set S_v-1@(S_v-1 ->? Unit) *

Set S_v-1@(S_v-1 ->? Unit) -> Set S_v-1@(S_v-1 ->? Unit)

%(op)%

: forall N : Type; E : Type .

Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) * (E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)) *

Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) * (E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)) -> Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) *

(E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1))

%(op)%

__when__else__

: forall a : Type . a_v-1 * ? Unit * a_v-1 ->? a_v-1 %(fun)%

bottom : forall a : Type . a_v-1 %(fun)%

def__ : forall a : Type . a_v-1 ->? Unit %(fun)%

false : Unit %(fun)%

not__ : ? Unit ->? Unit %(fun)%

true : Unit %(fun)%

�__ : ? Unit ->? Unit %(fun)%

%% Sentences -------------------------------------------------------------

(fun __=__[Set N@(N ->? Unit) * (E ->? N) * (E ->? N)]

: forall a : Type . a_v-1 * a_v-1 ->? Unit)

((op __union__[N; E]

: forall N : Type; E : Type .

Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) * (E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)) *

Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) * (E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)) -> Graph N_v-1 E_v-2@(Set N_v-1@(N_v-1 ->? Unit) *

(E_v-2 ->? N_v-1) *

(E_v-2 ->? N_v-1)))

(var g : Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N)),

var g' : Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N))),

var g : Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N)))

%% Diagnostics -----------------------------------------------------------

*** Hint 1.7, is type variable 'S'

*** Hint 1.9, is type variable 'N'

*** Hint 1.11, is type variable 'E'