begin
definition
let A,
B,
C be ( ( non
empty ) ( non
empty )
set ) ;
let f be ( (
Function-like quasi_total ) ( non
empty Relation-like A : ( ( non
empty ) ( non
empty )
set )
-defined Funcs (
B : ( ( non
empty ) ( non
empty )
set ) ,
C : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
B : ( ( non
empty ) ( non
empty )
set ) ,
C : ( ( non
empty ) ( non
empty )
set ) )
-valued Function-like total quasi_total )
Function of
A : ( ( non
empty ) ( non
empty )
set ) ,
Funcs (
B : ( ( non
empty ) ( non
empty )
set ) ,
C : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
B : ( ( non
empty ) ( non
empty )
set ) ,
C : ( ( non
empty ) ( non
empty )
set ) ) ) ;
uncurryredefine func uncurry f -> ( (
Function-like quasi_total ) ( non
empty Relation-like [:A : ( ( ) ( ) CatStr ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like total quasi_total )
Function of
[:A : ( ( ) ( ) CatStr ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) ;
end;
theorem
for
A,
B,
C being ( ( non
empty ) ( non
empty )
set )
for
f being ( (
Function-like quasi_total ) ( non
empty Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined Funcs (
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
-valued Function-like total quasi_total )
Function of
A : ( ( non
empty ) ( non
empty )
set ) ,
Funcs (
B : ( ( non
empty ) ( non
empty )
set ) ,
C : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) holds
curry (uncurry f : ( ( Function-like quasi_total ) ( non empty Relation-like b1 : ( ( non empty ) ( non empty ) set ) -defined Funcs (b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like total quasi_total ) Function of b1 : ( ( non empty ) ( non empty ) set ) , Funcs (b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( (
Function-like quasi_total ) ( non
empty Relation-like [:b1 : ( ( non empty ) ( non empty ) set ) ,b2 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like total quasi_total )
Function of
[:b1 : ( ( non empty ) ( non empty ) set ) ,b2 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) : ( (
Function-like quasi_total ) ( non
empty Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined Funcs (
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
-valued Function-like total quasi_total )
Element of
bool [:b1 : ( ( non empty ) ( non empty ) set ) ,(Funcs (b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) )) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) :] : ( ( ) ( non
empty Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
= f : ( (
Function-like quasi_total ) ( non
empty Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined Funcs (
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
-valued Function-like total quasi_total )
Function of
b1 : ( ( non
empty ) ( non
empty )
set ) ,
Funcs (
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) ;
theorem
for
A,
B,
C being ( ( non
empty ) ( non
empty )
set )
for
f being ( (
Function-like quasi_total ) ( non
empty Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined Funcs (
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
-valued Function-like total quasi_total )
Function of
A : ( ( non
empty ) ( non
empty )
set ) ,
Funcs (
B : ( ( non
empty ) ( non
empty )
set ) ,
C : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
for
a being ( ( ) ( )
Element of
A : ( ( non
empty ) ( non
empty )
set ) )
for
b being ( ( ) ( )
Element of
B : ( ( non
empty ) ( non
empty )
set ) ) holds
(uncurry f : ( ( Function-like quasi_total ) ( non empty Relation-like b1 : ( ( non empty ) ( non empty ) set ) -defined Funcs (b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like total quasi_total ) Function of b1 : ( ( non empty ) ( non empty ) set ) , Funcs (b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( (
Function-like quasi_total ) ( non
empty Relation-like [:b1 : ( ( non empty ) ( non empty ) set ) ,b2 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like total quasi_total )
Function of
[:b1 : ( ( non empty ) ( non empty ) set ) ,b2 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
. (
a : ( ( ) ( )
Element of
b1 : ( ( non
empty ) ( non
empty )
set ) ) ,
b : ( ( ) ( )
Element of
b2 : ( ( non
empty ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
b3 : ( ( non
empty ) ( non
empty )
set ) )
= (f : ( ( Function-like quasi_total ) ( non empty Relation-like b1 : ( ( non empty ) ( non empty ) set ) -defined Funcs (b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like total quasi_total ) Function of b1 : ( ( non empty ) ( non empty ) set ) , Funcs (b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of b2 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) ) ) . a : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like total quasi_total )
Element of
Funcs (
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( non
empty functional )
FUNCTION_DOMAIN of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
. b : ( ( ) ( )
Element of
b2 : ( ( non
empty ) ( non
empty )
set ) ) : ( ( ) ( )
Element of
b3 : ( ( non
empty ) ( non
empty )
set ) ) ;
theorem
for
A,
B being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
f being ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) ex
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ex
t being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) st
(
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
dom f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
(Functors (b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) )
= F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
cod f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
(Functors (b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) )
= F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) )
= [[F1 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ] : ( ( ) ( ) set ) ,t : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ] : ( ( ) ( )
set ) ) ;
begin
definition
let A,
B be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
let a be ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ;
func a |-> B -> ( ( ) ( non
empty Relation-like the
carrier' of
(Functors (A : ( ( ) ( ) CatStr ) ,B : ( ( ) ( ) set ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
Functors (
A : ( ( ) ( )
CatStr ) ,
B : ( ( ) ( )
set ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
B : ( ( ) ( )
set ) )
means
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
CatStr ) ,
B : ( ( ) ( )
set ) )
for
t being ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
it : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
. [[F1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ] : ( ( ) ( ) set ) ,t : ( ( ) ( non empty Relation-like the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ] : ( ( ) ( )
set ) : ( ( ) ( )
set )
= t : ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
. a : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Morphism of
b1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
. a : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
B : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
. a : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
B : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ) ;
end;
begin
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
a being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) )
for
b being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
(F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ?- a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
. b : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) )
= F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
. [a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
A,
B being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
a1,
a2 being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) )
for
b1,
b2 being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
( (
Hom (
a1 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
a2 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
<> {} : ( ( ) (
empty Relation-like non-empty empty-yielding )
set ) &
Hom (
b1 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b2 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
<> {} : ( ( ) (
empty Relation-like non-empty empty-yielding )
set ) ) iff
Hom (
[a1 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b1 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ,
[a2 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b2 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
<> {} : ( ( ) (
empty Relation-like non-empty empty-yielding )
set ) ) ;
theorem
for
A,
B being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
a1,
a2 being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) )
for
b1,
b2 being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) st
Hom (
[a1 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b1 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ,
[a2 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b2 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
<> {} : ( ( ) (
empty Relation-like non-empty empty-yielding )
set ) holds
for
f being ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) )
for
g being ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) holds
(
[f : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ,g : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) is ( ( ) ( )
Morphism of
[a1 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b1 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ,
[a2 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b2 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ) iff (
f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) is ( ( ) ( )
Morphism of
a1 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
a2 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) &
g : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) is ( ( ) ( )
Morphism of
b1 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b2 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
for
t being ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
for
a being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
(
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
(curry t : ( ( ) ( non empty Relation-like the carrier of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b4 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ) : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
. a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) is ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ) ;
theorem
for
A,
B being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
a1,
a2 being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) )
for
b1,
b2 being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) )
for
f being ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) )
for
g being ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) st
f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) )
in Hom (
a1 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
a2 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) &
g : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) )
in Hom (
b1 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b2 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) holds
[f : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ,g : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) )
in Hom (
[a1 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b1 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ,
[a2 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b2 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
a,
b being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) st
Hom (
a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
<> {} : ( ( ) (
empty Relation-like non-empty empty-yielding )
set ) holds
for
f being ( ( ) ( )
Morphism of
a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) holds
(
F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- b : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
(curry (F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,f : ( ( ) ( ) Morphism of b5 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b6 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) )) : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Function of the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) , the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) )
* (IdMap B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Element of
bool [: the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( (
Function-like ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Element of
bool [: the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) is ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- b : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ) ;
definition
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
let F be ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
let f be ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) ;
func F ?- f -> ( ( ) ( non
empty Relation-like the
carrier of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
natural_transformation of
F : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
?- (dom f : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
B : ( ( ) ( )
set ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) ,
F : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
?- (cod f : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
B : ( ( ) ( )
set ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) )
equals
(curry (F : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,f : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Function of the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set ) , the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) )
* (IdMap B : ( ( ) ( ) set ) ) : ( (
Function-like quasi_total ) ( non
empty Relation-like the
carrier of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Element of
bool [: the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( (
Function-like ) (
Relation-like the
carrier of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like )
Element of
bool [: the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ;
end;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
g being ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) holds
F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom g : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (cod g : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
f being ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) )
for
b being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
(F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ?- f : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (cod b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
. b : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Morphism of
(b4 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ?- (dom b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
. b6 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) ,
(b4 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ?- (cod b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
. b6 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) )
= F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
. (
f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) ,
(id b : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Morphism of
b6 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b6 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) ( )
Element of the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
a being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
id (F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ?- a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- b5 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- b5 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (id a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Morphism of
b5 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b5 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom (id b5 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Morphism of b5 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b5 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (cod (id b5 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Morphism of b5 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b5 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
g,
f being ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) st
dom g : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) )
= cod f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) holds
for
t being ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom f : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom g : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) st
t : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom b6 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom b6 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (cod b6 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) holds
F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (g : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) (*) f : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom (b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) (*) b6 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (cod (b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) (*) b6 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= (F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ?- g : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (cod b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
`*` t : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom b6 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (dom b6 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- (cod b5 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
definition
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
let F be ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
func export F -> ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
CatStr ) ,
Functors (
B : ( ( ) ( )
set ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
means
for
f being ( ( ) ( )
Morphism of ( ( ) ( )
set ) ) holds
it : ( (
Function-like ) (
Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined B : ( ( ) ( )
set )
-valued Function-like )
Element of
bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
. f : ( ( ) ( )
Morphism of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier' of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) )
= [[(F : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ?- (dom f : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty Relation-like the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) ,(F : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ?- (cod f : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty Relation-like the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( ) set ) ,(F : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ?- f : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) natural_transformation of F : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ?- (dom b1 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty Relation-like the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) ,F : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ?- (cod b1 : ( ( ) ( ) Morphism of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty Relation-like the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) ) ] : ( ( ) ( )
set ) ;
end;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
a being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
(export F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) )
= F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
?- a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
a being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
(export F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) is ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
export F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
= export F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) holds
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
= F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
for
t being ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) holds
(
export F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
is_naturally_transformable_to export F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) & ex
G being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) st
for
s being ( (
Function-like quasi_total ) ( non
empty Relation-like [: the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Function of
[: the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set ) , the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) st
t : ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= s : ( (
Function-like quasi_total ) ( non
empty Relation-like [: the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Function of
[: the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set ) , the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) holds
for
a being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
G : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
. a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Morphism of
(export b4 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. b9 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ,
(export b5 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. b9 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) )
= [[((export F1 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of (Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) , Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of (Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) ) ,((export F2 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of (Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) , Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of (Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( ) Element of the carrier of [:(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ,(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) ) ,((curry s : ( ( Function-like quasi_total ) ( non empty Relation-like [: the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty Relation-like ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Function of [: the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty Relation-like ) set ) , the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined Funcs ( the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) -valued Function-like total quasi_total ) Element of bool [: the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ,(Funcs ( the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) )) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty ) set ) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Element of Funcs ( the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set ) ) ;
definition
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
let F1,
F2 be ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
assume
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
;
let t be ( ( ) ( non
empty Relation-like the
carrier of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
func export t -> ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export F1 : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
CatStr ) ,
Functors (
B : ( ( ) ( )
set ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export F2 : ( (
Function-like ) (
Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined B : ( ( ) ( )
set )
-valued Function-like )
Element of
bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
CatStr ) ,
Functors (
B : ( ( ) ( )
set ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
means
for
s being ( (
Function-like quasi_total ) ( non
empty Relation-like [: the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) , the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Function of
[: the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) , the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) , the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) st
t : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
CatStr ) ,
B : ( ( ) ( )
set ) )
= s : ( (
Function-like quasi_total ) ( non
empty Relation-like [: the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Function of
[: the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty Relation-like )
set ) , the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) ) holds
for
a being ( ( ) ( )
Object of ( ( ) ( )
set ) ) holds
it : ( ( ) ( non
empty Relation-like the
carrier of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ,
F2 : ( (
Function-like ) (
Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined B : ( ( ) ( )
set )
-valued Function-like )
Element of
bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) )
. a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Morphism of
(export F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
CatStr ) ,
Functors (
B : ( ( ) ( )
set ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. b2 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ,
(export F2 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
CatStr ) : ( ( ) ( )
set )
-defined the
carrier' of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
CatStr ) ,
Functors (
B : ( ( ) ( )
set ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. b2 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) )
= [[((export F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) -defined the carrier' of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) CatStr ) , Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) ) ,((export F2 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) -defined the carrier' of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) CatStr ) , Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( ) Element of the carrier of [:(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ,(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) ) ,((curry s : ( ( Function-like quasi_total ) ( non empty Relation-like [: the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty Relation-like ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Function of [: the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) , the carrier of B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty Relation-like ) set ) , the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like quasi_total ) ( non empty Relation-like the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) -defined Funcs ( the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) -valued Function-like total quasi_total ) Element of bool [: the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) ,(Funcs ( the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) )) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Element of Funcs ( the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) FUNCTION_DOMAIN of the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( )
set ) ;
end;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
id (export F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
= export (id F : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
F2,
F3 being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F3 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
for
t1 being ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
for
t2 being ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F3 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) holds
export (t2 : ( ( ) ( non empty Relation-like the carrier of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b5 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b6 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) `*` t1 : ( ( ) ( non empty Relation-like the carrier of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b4 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b6 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b6 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
= (export t2 : ( ( ) ( non empty Relation-like the carrier of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b5 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b6 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b6 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
`*` (export t1 : ( ( ) ( non empty Relation-like the carrier of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b4 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b6 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
for
t1,
t2 being ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) st
export t1 : ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
= export t2 : ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) holds
t1 : ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= t2 : ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
G being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ex
F being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
G : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
= export F : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
export F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
is_naturally_transformable_to export F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) holds
for
t being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) holds
(
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) & ex
u being ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) st
t : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
= export u : ( ( ) ( non
empty Relation-like the
carrier of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
export b4 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
export b5 : ( ( ) ( non
empty Relation-like the
carrier' of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
Functors (
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) ) ;
definition
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
func export (
A,
B,
C)
-> ( ( ) ( non
empty Relation-like the
carrier' of
(Functors ([:A : ( ( ) ( ) CatStr ) ,B : ( ( ) ( ) set ) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (A : ( ( ) ( ) CatStr ) ,(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
Functors (
[:A : ( ( ) ( ) CatStr ) ,B : ( ( ) ( ) set ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
Functors (
A : ( ( ) ( )
CatStr ) ,
(Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
means
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( ) ( ) CatStr ) ,B : ( ( ) ( ) set ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( ) ( ) CatStr ) ,B : ( ( ) ( ) set ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
for
t being ( ( ) ( non
empty Relation-like the
carrier of
[:A : ( ( ) ( ) CatStr ) ,B : ( ( ) ( ) set ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) holds
it : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
CatStr )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
. [[F1 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ] : ( ( ) ( ) set ) ,t : ( ( ) ( non empty Relation-like the carrier of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b1 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b2 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ] : ( ( ) ( )
set ) : ( ( ) ( )
set )
= [[(export F1 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) -defined the carrier' of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) CatStr ) , Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ) ,(export F2 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) -defined the carrier' of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) CatStr ) , Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ) ] : ( ( ) ( ) set ) ,(export t : ( ( ) ( non empty Relation-like the carrier of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b1 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b2 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ) : ( ( ) ( non empty Relation-like the carrier of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) -defined the carrier' of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of export b1 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) -defined the carrier' of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) CatStr ) , Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ) , export b2 : ( ( ) ( non empty Relation-like the carrier' of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of [:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) CatStr ) : ( ( ) ( ) set ) -defined the carrier' of (Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) CatStr ) , Functors (B : ( ( ) ( ) set ) ,C : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) CatStr ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) CatStr ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ) ) ] : ( ( ) ( )
set ) ;
end;
registration
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
cluster export (
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
(Functors ([:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
(Functors (A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,(Functors (B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
Functors (
[:A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
Functors (
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
(Functors (B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
-> isomorphic ;
end;
begin
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
G being ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
for
t being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) holds
G : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
* t : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b6 : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
* b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b6 : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
* b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= G : ( ( ) ( non
empty Relation-like the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
* t : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) : ( (
Relation-like ) (
Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued )
set ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
G being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
(
Pr1 <:F : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,G : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
= F : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
Pr2 <:F : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,G : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
= G : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F,
G being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) st
Pr1 F : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
= Pr1 G : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
Pr2 F : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
= Pr2 G : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
F : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
= G : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ;
definition
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
let F1,
F2 be ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ;
let t be ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) ;
func Pr1 t -> ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
natural_transformation of
Pr1 F1 : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
set )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
B : ( ( ) ( )
set ) ) ,
Pr1 F2 : ( (
Function-like ) (
Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined B : ( ( ) ( )
set )
-valued Function-like )
Element of
bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
B : ( ( ) ( )
set ) ) )
equals
(pr1 (B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( ) ( non
empty Relation-like the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
B : ( ( ) ( )
set ) )
* t : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
B : ( ( ) ( )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
natural_transformation of
(pr1 (B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( ) ( non
empty Relation-like the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
B : ( ( ) ( )
set ) )
* F1 : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
set )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like B : ( ( ) ( )
set )
-defined the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
B : ( ( ) ( )
set ) ) ,
(pr1 (B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( ) ( non
empty Relation-like the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
B : ( ( ) ( )
set ) )
* F2 : ( (
Function-like ) (
Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined B : ( ( ) ( )
set )
-valued Function-like )
Element of
bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
B : ( ( ) ( )
set ) ) ) ;
func Pr2 t -> ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
Pr2 F1 : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
set )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
Pr2 F2 : ( (
Function-like ) (
Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined B : ( ( ) ( )
set )
-valued Function-like )
Element of
bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
equals
(pr2 (B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( ) ( non
empty Relation-like the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
* t : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
B : ( ( ) ( )
set ) : ( ( ) ( )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
B : ( ( ) ( )
set ) ) : ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
(pr2 (B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( ) ( non
empty Relation-like the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
* F1 : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
set )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like B : ( ( ) ( )
set )
-defined the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
(pr2 (B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( ) ( non
empty Relation-like the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
* F2 : ( (
Function-like ) (
Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined B : ( ( ) ( )
set )
-valued Function-like )
Element of
bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set )
-defined the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) ;
end;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
F2,
G1,
G2 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) &
G1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
is_naturally_transformable_to G2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) holds
for
s being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
for
t being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
G1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
G2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) st
Pr1 s : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
Pr1 b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
Pr1 b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= Pr1 t : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b6 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
b7 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
Pr1 b6 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
Pr1 b7 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) &
Pr2 s : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
Pr2 b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
Pr2 b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= Pr2 t : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b6 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
b7 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
Pr2 b6 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
Pr2 b7 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) holds
s : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
= t : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b6 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
b7 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
G being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
a,
b being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) st
Hom (
a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
<> {} : ( ( ) (
empty Relation-like non-empty empty-yielding )
set ) holds
for
f being ( ( ) ( )
Morphism of
a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) holds
<:F : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,G : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. f : ( ( ) ( )
Morphism of
b6 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ,
b7 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) )
= [(F : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) . f : ( ( ) ( ) Morphism of b6 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b7 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ,(G : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) . f : ( ( ) ( ) Morphism of b6 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ,b7 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
G being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
a being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
<:F : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,G : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) )
= [(F : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ,(G : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( )
Element of the
carrier of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
G1 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
F2,
G2 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_transformable_to G1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_transformable_to G2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
<:F1 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
is_transformable_to <:G1 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,G2 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ;
definition
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
let F1,
G1 be ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
let F2,
G2 be ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
assume
(
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_transformable_to G1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_transformable_to G2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
;
let t1 be ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
G1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
let t2 be ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
transformation of
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
G2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
func <:t1,t2:> -> ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
transformation of
<:F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
<:G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G2 : ( ( ) ( non empty Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
equals
<:t1 : ( ( ) ( Relation-like the carrier of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued ) natural_transformation of F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) ,t2 : ( ( ) ( Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued ) natural_transformation of F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) ,G2 : ( ( ) ( non empty Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) ) :> : ( (
Function-like quasi_total ) (
Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined [: the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) :] : ( ( ) (
Relation-like )
set )
-valued Function-like total quasi_total )
Element of
bool [: the carrier of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) ,[: the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) , the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) ;
end;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
G1 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
F2,
G2 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_transformable_to G1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_transformable_to G2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
for
t1 being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
G1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
for
t2 being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
transformation of
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
G2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
for
a being ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) holds
<:t1 : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) transformation of b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ,t2 : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) transformation of b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) :> : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
transformation of
<:b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
<:b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
. a : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Morphism of
<:b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. b10 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ,
<:b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
. b10 : ( ( ) ( )
Object of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
Element of the
carrier of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) )
= [(t1 : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) transformation of b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Morphism of b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) . b10 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) . b10 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of the carrier of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) ,(t2 : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) transformation of b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) . a : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Morphism of b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) . b10 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of the carrier of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) . b10 : ( ( ) ( ) Object of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of the carrier of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
Element of the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
G1 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
F2,
G2 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to G1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to G2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
<:F1 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
is_naturally_transformable_to <:G1 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,G2 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ;
definition
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
let F1,
G1 be ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
let F2,
G2 be ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ;
assume
(
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to G1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to G2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
;
let t1 be ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
G1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
let t2 be ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
G2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ;
func <:t1,t2:> -> ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
<:F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
<:G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G2 : ( ( ) ( non empty Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) )
equals
<:t1 : ( ( ) ( Relation-like the carrier of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued ) natural_transformation of F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) ,t2 : ( ( ) ( Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued ) natural_transformation of F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) ,G2 : ( ( ) ( non empty Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) ) :> : ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
transformation of
<:F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
<:G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G2 : ( ( ) ( non empty Relation-like the carrier of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of F1 : ( ( Function-like quasi_total ) ( Relation-like B : ( ( ) ( ) set ) -defined A : ( ( ) ( ) set ) -valued Function-like quasi_total ) Element of bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ,G1 : ( ( Function-like ) ( Relation-like [:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) -defined B : ( ( ) ( ) set ) -valued Function-like ) Element of bool [:[:B : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) ,B : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) ;
end;
theorem
for
A,
B,
C being ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category)
for
F1,
G1 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
for
F2,
G2 being ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to G1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) &
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) )
is_naturally_transformable_to G2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) holds
for
t1 being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
G1 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
for
t2 being ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
G2 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) holds
(
Pr1 <:t1 : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ,t2 : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) :> : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
<:b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
<:b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
Pr1 <:b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
Pr1 <:b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= t1 : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b4 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b5 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b2 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) &
Pr2 <:t1 : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) ,t2 : ( ( ) ( non empty Relation-like the carrier of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ) :> : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
<:b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
<:b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
Pr2 <:b4 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b6 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
Pr2 <:b5 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) ,b7 : ( ( ) ( non empty Relation-like the carrier' of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of b1 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ) :> : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:b2 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,b3 : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) )
= t2 : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
b6 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ,
b7 : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
b1 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
b3 : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ) ) ) ;
definition
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
func distribute (
A,
B,
C)
-> ( ( ) ( non
empty Relation-like the
carrier' of
(Functors (A : ( ( ) ( ) set ) ,[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:(Functors (A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ,(Functors (A : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
Functors (
A : ( ( ) ( )
set ) ,
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
[:(Functors (A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ,(Functors (A : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
means
for
F1,
F2 being ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( ) ( )
set ) ,
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) st
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
is_naturally_transformable_to F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) holds
for
t being ( ( ) ( non
empty Relation-like the
carrier of
A : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
[:B : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
natural_transformation of
F1 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ,
F2 : ( ( ) ( non
empty Relation-like the
carrier' of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) ) holds
it : ( (
Function-like quasi_total ) (
Relation-like B : ( ( ) ( )
set )
-defined A : ( ( ) ( )
set )
-valued Function-like quasi_total )
Element of
bool [:B : ( ( ) ( ) set ) ,A : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
. [[F1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ,F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ] : ( ( ) ( ) set ) ,t : ( ( ) ( non empty Relation-like the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ,b2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ) ] : ( ( ) ( )
set ) : ( ( ) ( )
set )
= [[[(Pr1 F1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) ,(Pr1 F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) ] : ( ( ) ( ) set ) ,(Pr1 t : ( ( ) ( non empty Relation-like the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ,b2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ) ) : ( ( ) ( non empty Relation-like the carrier of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) natural_transformation of Pr1 b1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) , Pr1 b2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of B : ( ( ) ( ) set ) : ( ( ) ( ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,B : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) ,[[(Pr2 F1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ,(Pr2 F2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ] : ( ( ) ( ) set ) ,(Pr2 t : ( ( ) ( non empty Relation-like the carrier of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of b1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ,b2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ) ) : ( ( ) ( non empty Relation-like the carrier of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) natural_transformation of Pr2 b1 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) , Pr2 b2 : ( ( ) ( non empty Relation-like the carrier' of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) : ( ( ) ( non empty ) set ) -defined the carrier' of [:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) Category) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) : ( ( ) ( non empty Relation-like the carrier' of A : ( ( ) ( ) set ) : ( ( ) ( ) set ) -defined the carrier' of C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) : ( ( ) ( non empty ) set ) -valued Function-like total quasi_total ) Functor of A : ( ( ) ( ) set ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ) ) ] : ( ( ) ( ) set ) ] : ( ( ) ( )
set ) ;
end;
registration
let A,
B,
C be ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
Category) ;
cluster distribute (
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
B : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
C : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
(Functors (A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-defined the
carrier' of
[:(Functors (A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ,(Functors (A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) : ( ( ) ( non
empty )
set )
-valued Function-like total quasi_total )
Functor of
Functors (
A : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
[:B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) ) : ( ( non
empty non
void strict Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
strict Category-like V68()
V69()
V70()
with_identities )
CatStr ) ,
[:(Functors (A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,B : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) ,(Functors (A : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) ,C : ( ( non empty non void Category-like V68() V69() V70() with_identities ) ( non empty non void V55() Category-like V68() V69() V70() with_identities ) CatStr ) )) : ( ( non empty non void strict Category-like V68() V69() V70() with_identities ) ( non empty non void V55() strict Category-like V68() V69() V70() with_identities ) CatStr ) :] : ( ( non
empty non
void Category-like V68()
V69()
V70()
with_identities ) ( non
empty non
void V55()
Category-like V68()
V69()
V70()
with_identities )
CatStr ) )
-> isomorphic ;
end;