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

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

((N ->? Unit) * (E ->? N) * (E ->? N)) *

((N ->? Unit) * (E ->? N) * (E ->? N)) ->? 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))) :

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

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

(E ->? N)) -> 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))) :

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

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

Unit

%% 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

__*__ : 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 __=__[(N ->? Unit) * (E ->? N) * (E ->? N)]

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

((N ->? Unit) * (E ->? N) * (E ->? N)) *

((N ->? Unit) * (E ->? N) * (E ->? N)) ->? 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))) :

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

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

(E ->? N)) -> 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))) :

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

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

Unit

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

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

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

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

*** Hint, in type of '(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 'Set N@(N ->? Unit) * (E ->? N) * (E ->? N)' (3.37)

is not unifiable with type '_var_10_v10 ->? Unit' (2.19)

*** Hint, in type of '(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 'Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N)) *

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

is not unifiable with type 'Unit ->? Set _var_10_v10@(_var_10_v10 ->? Unit) *

Set _var_10_v10@(_var_10_v10 ->? Unit)'

*** Hint, in type of '(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 'Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N)) *

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

is not unifiable with type 'Unit ->? Graph _var_11_v11 _var_12_v12@(Set _var_11_v11@(_var_11_v11 ->? Unit) *

(_var_12_v12 ->? _var_11_v11) *

(_var_12_v12 ->? _var_11_v11)) *

Graph _var_11_v11 _var_12_v12@(Set _var_11_v11@(_var_11_v11 ->? Unit) *

(_var_12_v12 ->? _var_11_v11) *

(_var_12_v12 ->? _var_11_v11))'

*** Hint, in type of '(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 'Set N@(N ->? Unit) * (E ->? N) * (E ->? N)' (3.37)

is not unifiable with type '_var_61_v61 ->? Unit' (2.19)

*** Hint, in type of '(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 'Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N)) *

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

is not unifiable with type 'Unit ->? Set _var_61_v61@(_var_61_v61 ->? Unit) *

Set _var_61_v61@(_var_61_v61 ->? Unit)'

*** Hint, in type of '(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 'Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N)) *

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

is not unifiable with type 'Unit ->? Graph _var_62_v62 _var_63_v63@(Set _var_62_v62@(_var_62_v62 ->? Unit) *

(_var_63_v63 ->? _var_62_v62) *

(_var_63_v63 ->? _var_62_v62)) *

Graph _var_62_v62 _var_63_v63@(Set _var_62_v62@(_var_62_v62 ->? Unit) *

(_var_63_v63 ->? _var_62_v62) *

(_var_63_v63 ->? _var_62_v62))'

*** Hint 9.5-9.21, in type of '(((op __union__[N; _var_63_v63]

: 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))) :

Graph N _var_63_v63@(Set N@(N ->? Unit) * (_var_63_v63 ->? N) *

(_var_63_v63 ->? N)) *

Graph N _var_63_v63@(Set N@(N ->? Unit) * (_var_63_v63 ->? N) *

(_var_63_v63 ->? N)) -> Graph N _var_63_v63@(Set N@(N ->? Unit) *

(_var_63_v63 ->? N) *

(_var_63_v63 ->? 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))) :

Graph N _var_63_v63@(Set N@(N ->? Unit) * (_var_63_v63 ->? N) *

(_var_63_v63 ->? N)),

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

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

Graph N E@(Set N@(N ->? Unit) * (E ->? N) * (E ->? N))' (9.21)

is not unifiable with type 'Unit ->? _var_5_v5 * _var_5_v5' (9.21)