:: ISOCAT_1 semantic presentation

K120() is M2( bool K116())
K116() is set
bool K116() is set
{} is set
the empty set is empty set
1 is non empty set
{{},1} is set
K115() is set
bool K115() is set
bool K120() is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o is M2( the carrier of F)
s is M2( the carrier of F)
G . o is M2( the carrier of C)
the carrier of C is non empty set
Obj G is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
[: the carrier of F, the carrier of C:] is set
bool [: the carrier of F, the carrier of C:] is set
(Obj G) . o is M2( the carrier of C)
G . s is M2( the carrier of C)
(Obj G) . s is M2( the carrier of C)
b is Morphism of o,s
G /. b is Morphism of G . o,G . s
Hom (o,s) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o & cod b₁ = s ) } is set
Hom (s,o) is M2( bool the carrier' of F)
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = s & cod b₁ = o ) } is set
id s is Morphism of s,s
id o is Morphism of o,o
c₇ is Morphism of s,o
b * c₇ is Morphism of s,s
c₇ * b is Morphism of o,o
dom c₇ is M2( the carrier of F)
cod b is M2( the carrier of F)
cod c₇ is M2( the carrier of F)
dom b is M2( the carrier of F)
b (*) c₇ is M2( the carrier' of F)
id (cod b) is Morphism of cod b, cod b
c₇ (*) b is M2( the carrier' of F)
id (dom b) is Morphism of dom b, dom b
Hom ((G . o),(G . s)) is M2( bool the carrier' of C)
bool the carrier' of C is set
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = G . o & cod b₁ = G . s ) } is set
Hom ((G . s),(G . o)) is M2( bool the carrier' of C)
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = G . s & cod b₁ = G . o ) } is set
id (G . s) is Morphism of G . s,G . s
id (G . o) is Morphism of G . o,G . o
G /. c₇ is Morphism of G . s,G . o
(G /. b) * (G /. c₇) is Morphism of G . s,G . s
(G /. c₇) * (G /. b) is Morphism of G . o,G . o
G . b is M2( the carrier' of C)
G . c₇ is M2( the carrier' of C)
(G . b) (*) (G . c₇) is M2( the carrier' of C)
G . (b (*) c₇) is M2( the carrier' of C)
cod (G /. b) is M2( the carrier of C)
id (cod (G /. b)) is Morphism of cod (G /. b), cod (G /. b)
(G . c₇) (*) (G . b) is M2( the carrier' of C)
G . (c₇ (*) b) is M2( the carrier' of C)
dom (G /. b) is M2( the carrier of C)
id (dom (G /. b)) is Morphism of dom (G /. b), dom (G /. b)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) transformation of G,o
b is M2( the carrier of C)
s . b is Morphism of G . b,o . b
G . b is M2( the carrier of F)
the carrier of F is non empty set
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj G) . b is M2( the carrier of F)
o . b is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj o) . b is M2( the carrier of F)
Hom ((G . b),(o . b)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = G . b & cod b₁ = o . b ) } is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
the carrier of C is non empty set
f2 is M2( the carrier of C)
(b * o) . f2 is M2( the carrier of G)
the carrier of G is non empty set
Obj (b * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (b * o)) . f2 is M2( the carrier of G)
(c₇ * s) . f2 is M2( the carrier of G)
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * s)) . f2 is M2( the carrier of G)
Hom (((b * o) . f2),((c₇ * s) . f2)) is M2( bool the carrier' of G)
bool the carrier' of G is set
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (b * o) . f2 & cod b₁ = (c₇ * s) . f2 ) } is set
o . f2 is M2( the carrier of F)
the carrier of F is non empty set
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . f2 is M2( the carrier of F)
s . f2 is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj s) . f2 is M2( the carrier of F)
Hom ((o . f2),(s . f2)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . f2 & cod b₁ = s . f2 ) } is set
b . (o . f2) is M2( the carrier of G)
Obj b is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj b) . (o . f2) is M2( the carrier of G)
b . (s . f2) is M2( the carrier of G)
(Obj b) . (s . f2) is M2( the carrier of G)
Hom ((b . (o . f2)),(b . (s . f2))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (o . f2) & cod b₁ = b . (s . f2) ) } is set
c₇ . (s . f2) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj c₇) . (s . f2) is M2( the carrier of G)
Hom ((b . (s . f2)),(c₇ . (s . f2))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (s . f2) & cod b₁ = c₇ . (s . f2) ) } is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) transformation of G,o
b is M2( the carrier of C)
G . b is M2( the carrier of F)
the carrier of F is non empty set
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj G) . b is M2( the carrier of F)
o . b is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj o) . b is M2( the carrier of F)
s . b is Morphism of G . b,o . b
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
[: the carrier' of C, the carrier' of F:] is set
bool [: the carrier' of C, the carrier' of F:] is set
the carrier of C is non empty set
the carrier of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) M2( bool [: the carrier' of C, the carrier' of F:])
o is M2( the carrier of C)
id o is Morphism of o,o
G . (id o) is M2( the carrier' of F)
s is M2( the carrier' of C)
dom s is M2( the carrier of C)
id (dom s) is Morphism of dom s, dom s
G . (id (dom s)) is M2( the carrier' of F)
G . s is M2( the carrier' of F)
dom (G . s) is M2( the carrier of F)
id (dom (G . s)) is Morphism of dom (G . s), dom (G . s)
b is M2( the carrier' of C)
cod b is M2( the carrier of C)
id (cod b) is Morphism of cod b, cod b
G . (id (cod b)) is M2( the carrier' of F)
G . b is M2( the carrier' of F)
cod (G . b) is M2( the carrier of F)
id (cod (G . b)) is Morphism of cod (G . b), cod (G . b)
f2 is M2( the carrier' of C)
dom f2 is M2( the carrier of C)
c₇ is M2( the carrier' of C)
cod c₇ is M2( the carrier of C)
f2 (*) c₇ is M2( the carrier' of C)
G . (f2 (*) c₇) is M2( the carrier' of F)
G . c₇ is M2( the carrier' of F)
G . f2 is M2( the carrier' of F)
(G . f2) (*) (G . c₇) is M2( the carrier' of F)
f1 is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) M2( bool [: the carrier' of C, the carrier' of F:])
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o is M2( the carrier' of C)
rng G is M2( bool the carrier' of C)
bool the carrier' of C is set
dom G is M2( bool the carrier' of F)
bool the carrier' of F is set
s is set
G . s is set
b is M2( the carrier' of F)
G . b is M2( the carrier' of C)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o is M2( the carrier of C)
Obj G is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
[: the carrier of F, the carrier of C:] is set
bool [: the carrier of F, the carrier of C:] is set
rng (Obj G) is M2( bool the carrier of C)
bool the carrier of C is set
dom (Obj G) is M2( bool the carrier of F)
bool the carrier of F is set
s is set
(Obj G) . s is set
b is M2( the carrier of F)
G . b is M2( the carrier of C)
(Obj G) . b is M2( the carrier of C)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
the carrier of C is non empty set
the carrier of F is non empty set
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
o is set
dom (Obj G) is set
s is set
(Obj G) . o is set
(Obj G) . s is set
dom (Obj G) is M2( bool the carrier of C)
bool the carrier of C is set
b is M2( the carrier of C)
G . b is M2( the carrier of F)
(Obj G) . b is M2( the carrier of F)
c₇ is M2( the carrier of C)
G . c₇ is M2( the carrier of F)
(Obj G) . c₇ is M2( the carrier of F)
id b is Morphism of b,b
G . (id b) is M2( the carrier' of F)
id (G . c₇) is Morphism of G . c₇,G . c₇
id c₇ is Morphism of c₇,c₇
G . (id c₇) is M2( the carrier' of F)
dom G is M2( bool the carrier' of C)
bool the carrier' of C is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
G " is Relation-like Function-like set
rng G is M2( bool the carrier' of F)
bool the carrier' of F is set
[: the carrier' of F, the carrier' of C:] is set
bool [: the carrier' of F, the carrier' of C:] is set
dom G is M2( bool the carrier' of C)
bool the carrier' of C is set
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
the carrier of C is non empty set
the carrier of F is non empty set
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) M2( bool [: the carrier' of F, the carrier' of C:])
s is M2( the carrier of F)
id s is Morphism of s,s
o . (id s) is M2( the carrier' of C)
b is M2( the carrier of C)
G . b is M2( the carrier of F)
(Obj G) . b is M2( the carrier of F)
id b is Morphism of b,b
G . (id b) is M2( the carrier' of F)
o . (G . (id b)) is M2( the carrier' of C)
s is M2( the carrier' of F)
dom s is M2( the carrier of F)
id (dom s) is Morphism of dom s, dom s
o . (id (dom s)) is M2( the carrier' of C)
o . s is M2( the carrier' of C)
dom (o . s) is M2( the carrier of C)
id (dom (o . s)) is Morphism of dom (o . s), dom (o . s)
cod s is M2( the carrier of F)
id (cod s) is Morphism of cod s, cod s
o . (id (cod s)) is M2( the carrier' of C)
cod (o . s) is M2( the carrier of C)
id (cod (o . s)) is Morphism of cod (o . s), cod (o . s)
b is M2( the carrier' of C)
G . b is M2( the carrier' of F)
dom b is M2( the carrier of C)
G . (dom b) is M2( the carrier of F)
(Obj G) . (dom b) is M2( the carrier of F)
id (G . (dom b)) is Morphism of G . (dom b),G . (dom b)
o . (id (G . (dom b))) is M2( the carrier' of C)
id (dom b) is Morphism of dom b, dom b
G . (id (dom b)) is M2( the carrier' of F)
o . (G . (id (dom b))) is M2( the carrier' of C)
cod b is M2( the carrier of C)
G . (cod b) is M2( the carrier of F)
(Obj G) . (cod b) is M2( the carrier of F)
id (G . (cod b)) is Morphism of G . (cod b),G . (cod b)
o . (id (G . (cod b))) is M2( the carrier' of C)
id (cod b) is Morphism of cod b, cod b
G . (id (cod b)) is M2( the carrier' of F)
o . (G . (id (cod b))) is M2( the carrier' of C)
b is M2( the carrier' of F)
dom b is M2( the carrier of F)
s is M2( the carrier' of F)
cod s is M2( the carrier of F)
b (*) s is M2( the carrier' of F)
o . (b (*) s) is M2( the carrier' of C)
o . s is M2( the carrier' of C)
o . b is M2( the carrier' of C)
(o . b) (*) (o . s) is M2( the carrier' of C)
dom (Obj G) is M2( bool the carrier of C)
bool the carrier of C is set
c₇ is M2( the carrier' of C)
G . c₇ is M2( the carrier' of F)
f2 is M2( the carrier' of C)
G . f2 is M2( the carrier' of F)
dom f2 is M2( the carrier of C)
(Obj G) . (dom f2) is M2( the carrier of F)
G . (dom f2) is M2( the carrier of F)
cod c₇ is M2( the carrier of C)
G . (cod c₇) is M2( the carrier of F)
(Obj G) . (cod c₇) is M2( the carrier of F)
f2 (*) c₇ is M2( the carrier' of C)
G . (f2 (*) c₇) is M2( the carrier' of F)
o . (G . (f2 (*) c₇)) is M2( the carrier' of C)
f2 (*) (o . s) is M2( the carrier' of C)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
rng G is M2( bool the carrier' of F)
bool the carrier' of F is set
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
the carrier of C is non empty set
the carrier of F is non empty set
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
rng (Obj G) is set
rng (Obj G) is M2( bool the carrier of F)
bool the carrier of F is set
o is set
dom G is M2( bool the carrier' of C)
bool the carrier' of C is set
s is M2( the carrier of F)
id s is Morphism of s,s
b is set
G . b is set
c₇ is M2( the carrier' of C)
dom c₇ is M2( the carrier of C)
id (dom c₇) is Morphism of dom c₇, dom c₇
f2 is M2( the carrier' of C)
G . f2 is M2( the carrier' of F)
dom (id s) is M2( the carrier of F)
id (dom (id s)) is Morphism of dom (id s), dom (id s)
dom (Obj G) is M2( bool the carrier of C)
bool the carrier of C is set
(Obj G) . (dom c₇) is M2( the carrier of F)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
(C,F,G) is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
G " is Relation-like Function-like set
rng (C,F,G) is M2( bool the carrier' of C)
bool the carrier' of C is set
dom G is M2( bool the carrier' of C)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
the carrier of C is non empty set
the carrier of F is non empty set
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj G) " is Relation-like Function-like set
(C,F,G) is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
Obj (C,F,G) is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
[: the carrier of F, the carrier of C:] is set
bool [: the carrier of F, the carrier of C:] is set
rng (Obj G) is M2( bool the carrier of F)
bool the carrier of F is set
o is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
s is M2( the carrier of F)
o . s is M2( the carrier of C)
id (o . s) is Morphism of o . s,o . s
G . (id (o . s)) is M2( the carrier' of F)
(Obj G) . (o . s) is M2( the carrier of F)
id ((Obj G) . (o . s)) is Morphism of (Obj G) . (o . s),(Obj G) . (o . s)
id s is Morphism of s,s
G " is Relation-like Function-like set
(G ") . (id s) is set
(C,F,G) . (id s) is M2( the carrier' of C)
(Obj (C,F,G)) . s is M2( the carrier of C)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
(C,F,G) is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
(F,C,(C,F,G)) is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
[: the carrier' of C, the carrier' of F:] is set
bool [: the carrier' of C, the carrier' of F:] is set
[: the carrier' of F, the carrier' of C:] is set
bool [: the carrier' of F, the carrier' of C:] is set
s is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) M2( bool [: the carrier' of F, the carrier' of C:])
s " is Relation-like Function-like set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) M2( bool [: the carrier' of C, the carrier' of F:])
o " is Relation-like Function-like set
(o ") " is Relation-like Function-like set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
G is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
(F,C,G) is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
G * (F,C,G) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
(F,C,G) * G is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) V18( the carrier' of F, the carrier' of F) Functor of F,F
[: the carrier' of F, the carrier' of C:] is set
bool [: the carrier' of F, the carrier' of C:] is set
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) M2( bool [: the carrier' of F, the carrier' of C:])
dom o is M2( bool the carrier' of F)
bool the carrier' of F is set
rng o is M2( bool the carrier' of C)
bool the carrier' of C is set
o " is Relation-like Function-like set
(o ") (#) o is Relation-like set
o (#) (o ") is Relation-like set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
s * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
rng o is M2( bool the carrier' of F)
bool the carrier' of F is set
rng s is M2( bool the carrier' of G)
bool the carrier' of G is set
rng (s * o) is M2( bool the carrier' of G)
dom s is M2( bool the carrier' of F)
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
id G is Relation-like the carrier' of G -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) Functor of G,G
id the carrier' of G is Relation-like the carrier' of G -defined the carrier' of G -valued non empty total V18( the carrier' of G, the carrier' of G) M2( bool [: the carrier' of G, the carrier' of G:])
[: the carrier' of G, the carrier' of G:] is set
bool [: the carrier' of G, the carrier' of G:] is set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of o is non empty set
s is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
(G,o,s) is Relation-like the carrier' of o -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of o, the carrier' of G) Functor of o,G
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier' of F is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
the carrier' of G is non empty set
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
s * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
F is set
G is set
1Cat (F,G) is non empty trivial V49() non void V54(1) V55() trivial' strict Category-like V68() V69() V70() with_identities CatStr
{F} is set
{G} is set
K224(G,F) is Relation-like {G} -defined {F} -valued Function-like V18({G},{F}) M2( bool [:{G},{F}:])
[:{G},{F}:] is set
bool [:{G},{F}:] is set
K223(G,G,G) is Relation-like [:{G},{G}:] -defined {G} -valued Function-like V18([:{G},{G}:],{G}) M2( bool [:[:{G},{G}:],{G}:])
[:{G},{G}:] is set
[:[:{G},{G}:],{G}:] is set
bool [:[:{G},{G}:],{G}:] is set
CatStr(# {F},{G},K224(G,F),K224(G,F),K223(G,G,G) #) is strict CatStr
[:(1Cat (F,G)),C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of (1Cat (F,G)) is non empty trivial V31() set
the carrier of C is non empty set
[: the carrier of (1Cat (F,G)), the carrier of C:] is set
the carrier' of (1Cat (F,G)) is non empty trivial set
the carrier' of C is non empty set
[: the carrier' of (1Cat (F,G)), the carrier' of C:] is set
the Source of (1Cat (F,G)) is Relation-like the carrier' of (1Cat (F,G)) -defined the carrier of (1Cat (F,G)) -valued Function-like non empty total V18( the carrier' of (1Cat (F,G)), the carrier of (1Cat (F,G))) M2( bool [: the carrier' of (1Cat (F,G)), the carrier of (1Cat (F,G)):])
[: the carrier' of (1Cat (F,G)), the carrier of (1Cat (F,G)):] is set
bool [: the carrier' of (1Cat (F,G)), the carrier of (1Cat (F,G)):] is set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) M2( bool [: the carrier' of C, the carrier of C:])
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
[: the Source of (1Cat (F,G)), the Source of C:] is Relation-like [: the carrier' of (1Cat (F,G)), the carrier' of C:] -defined [: the carrier of (1Cat (F,G)), the carrier of C:] -valued Function-like V18([: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier of (1Cat (F,G)), the carrier of C:]) M2( bool [:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier of (1Cat (F,G)), the carrier of C:]:])
[:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier of (1Cat (F,G)), the carrier of C:]:] is set
bool [:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier of (1Cat (F,G)), the carrier of C:]:] is set
the Target of (1Cat (F,G)) is Relation-like the carrier' of (1Cat (F,G)) -defined the carrier of (1Cat (F,G)) -valued Function-like non empty total V18( the carrier' of (1Cat (F,G)), the carrier of (1Cat (F,G))) M2( bool [: the carrier' of (1Cat (F,G)), the carrier of (1Cat (F,G)):])
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) M2( bool [: the carrier' of C, the carrier of C:])
[: the Target of (1Cat (F,G)), the Target of C:] is Relation-like [: the carrier' of (1Cat (F,G)), the carrier' of C:] -defined [: the carrier of (1Cat (F,G)), the carrier of C:] -valued Function-like V18([: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier of (1Cat (F,G)), the carrier of C:]) M2( bool [:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier of (1Cat (F,G)), the carrier of C:]:])
the Comp of (1Cat (F,G)) is Relation-like [: the carrier' of (1Cat (F,G)), the carrier' of (1Cat (F,G)):] -defined the carrier' of (1Cat (F,G)) -valued Function-like M2( bool [:[: the carrier' of (1Cat (F,G)), the carrier' of (1Cat (F,G)):], the carrier' of (1Cat (F,G)):])
[: the carrier' of (1Cat (F,G)), the carrier' of (1Cat (F,G)):] is set
[:[: the carrier' of (1Cat (F,G)), the carrier' of (1Cat (F,G)):], the carrier' of (1Cat (F,G)):] is set
bool [:[: the carrier' of (1Cat (F,G)), the carrier' of (1Cat (F,G)):], the carrier' of (1Cat (F,G)):] is set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like M2( bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is set
K184( the carrier' of (1Cat (F,G)), the carrier' of C, the Comp of (1Cat (F,G)), the Comp of C) is Relation-like [:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier' of (1Cat (F,G)), the carrier' of C:]:] -defined [: the carrier' of (1Cat (F,G)), the carrier' of C:] -valued Function-like M2( bool [:[:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier' of (1Cat (F,G)), the carrier' of C:]:],[: the carrier' of (1Cat (F,G)), the carrier' of C:]:])
[:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier' of (1Cat (F,G)), the carrier' of C:]:] is set
[:[:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier' of (1Cat (F,G)), the carrier' of C:]:],[: the carrier' of (1Cat (F,G)), the carrier' of C:]:] is set
bool [:[:[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the carrier' of (1Cat (F,G)), the carrier' of C:]:],[: the carrier' of (1Cat (F,G)), the carrier' of C:]:] is set
CatStr(# [: the carrier of (1Cat (F,G)), the carrier of C:],[: the carrier' of (1Cat (F,G)), the carrier' of C:],[: the Source of (1Cat (F,G)), the Source of C:],[: the Target of (1Cat (F,G)), the Target of C:],K184( the carrier' of (1Cat (F,G)), the carrier' of C, the Comp of (1Cat (F,G)), the Comp of C) #) is strict CatStr
the carrier' of [:(1Cat (F,G)),C:] is non empty set
pr2 ((1Cat (F,G)),C) is Relation-like the carrier' of [:(1Cat (F,G)),C:] -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of [:(1Cat (F,G)),C:], the carrier' of C) Functor of [:(1Cat (F,G)),C:],C
pr2 ( the carrier' of (1Cat (F,G)), the carrier' of C) is Relation-like [: the carrier' of (1Cat (F,G)), the carrier' of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier' of (1Cat (F,G)), the carrier' of C:], the carrier' of C) M2( bool [:[: the carrier' of (1Cat (F,G)), the carrier' of C:], the carrier' of C:])
[:[: the carrier' of (1Cat (F,G)), the carrier' of C:], the carrier' of C:] is set
bool [:[: the carrier' of (1Cat (F,G)), the carrier' of C:], the carrier' of C:] is set
o is Relation-like the carrier' of [:(1Cat (F,G)),C:] -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of [:(1Cat (F,G)),C:], the carrier' of C) Functor of [:(1Cat (F,G)),C:],C
b is set
f2 is set
f1 is set
[f2,f1] is set
{f2,f1} is set
{f2} is set
{{f2,f1},{f2}} is set
c₇ is set
g is set
h is set
[g,h] is set
{g,h} is set
{g} is set
{{g,h},{g}} is set
o . b is set
o . c₇ is set
f is M2( the carrier' of (1Cat (F,G)))
t9 is M2( the carrier' of (1Cat (F,G)))
x21 is M2( the carrier' of C)
o . (f,x21) is M2( the carrier' of C)
[f,x21] is set
{f,x21} is set
{f} is set
{{f,x21},{f}} is set
o . [f,x21] is set
x11 is M2( the carrier' of C)
o . (t9,x11) is M2( the carrier' of C)
[t9,x11] is set
{t9,x11} is set
{t9} is set
{{t9,x11},{t9}} is set
o . [t9,x11] is set
rng o is M2( bool the carrier' of C)
bool the carrier' of C is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:C,F:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of C is non empty set
the carrier of F is non empty set
[: the carrier of C, the carrier of F:] is set
the carrier' of C is non empty set
the carrier' of F is non empty set
[: the carrier' of C, the carrier' of F:] is set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) M2( bool [: the carrier' of C, the carrier of C:])
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of F is Relation-like the carrier' of F -defined the carrier of F -valued Function-like non empty total V18( the carrier' of F, the carrier of F) M2( bool [: the carrier' of F, the carrier of F:])
[: the carrier' of F, the carrier of F:] is set
bool [: the carrier' of F, the carrier of F:] is set
[: the Source of C, the Source of F:] is Relation-like [: the carrier' of C, the carrier' of F:] -defined [: the carrier of C, the carrier of F:] -valued Function-like V18([: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]) M2( bool [:[: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]:])
[:[: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]:] is set
bool [:[: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]:] is set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) M2( bool [: the carrier' of C, the carrier of C:])
the Target of F is Relation-like the carrier' of F -defined the carrier of F -valued Function-like non empty total V18( the carrier' of F, the carrier of F) M2( bool [: the carrier' of F, the carrier of F:])
[: the Target of C, the Target of F:] is Relation-like [: the carrier' of C, the carrier' of F:] -defined [: the carrier of C, the carrier of F:] -valued Function-like V18([: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]) M2( bool [:[: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]:])
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like M2( bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is set
the Comp of F is Relation-like [: the carrier' of F, the carrier' of F:] -defined the carrier' of F -valued Function-like M2( bool [:[: the carrier' of F, the carrier' of F:], the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
[:[: the carrier' of F, the carrier' of F:], the carrier' of F:] is set
bool [:[: the carrier' of F, the carrier' of F:], the carrier' of F:] is set
K184( the carrier' of C, the carrier' of F, the Comp of C, the Comp of F) is Relation-like [:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:] -defined [: the carrier' of C, the carrier' of F:] -valued Function-like M2( bool [:[:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:],[: the carrier' of C, the carrier' of F:]:])
[:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:] is set
[:[:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:],[: the carrier' of C, the carrier' of F:]:] is set
bool [:[:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:],[: the carrier' of C, the carrier' of F:]:] is set
CatStr(# [: the carrier of C, the carrier of F:],[: the carrier' of C, the carrier' of F:],[: the Source of C, the Source of F:],[: the Target of C, the Target of F:],K184( the carrier' of C, the carrier' of F, the Comp of C, the Comp of F) #) is strict CatStr
[:F,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of F, the carrier of C:] is set
[: the carrier' of F, the carrier' of C:] is set
[: the Source of F, the Source of C:] is Relation-like [: the carrier' of F, the carrier' of C:] -defined [: the carrier of F, the carrier of C:] -valued Function-like V18([: the carrier' of F, the carrier' of C:],[: the carrier of F, the carrier of C:]) M2( bool [:[: the carrier' of F, the carrier' of C:],[: the carrier of F, the carrier of C:]:])
[:[: the carrier' of F, the carrier' of C:],[: the carrier of F, the carrier of C:]:] is set
bool [:[: the carrier' of F, the carrier' of C:],[: the carrier of F, the carrier of C:]:] is set
[: the Target of F, the Target of C:] is Relation-like [: the carrier' of F, the carrier' of C:] -defined [: the carrier of F, the carrier of C:] -valued Function-like V18([: the carrier' of F, the carrier' of C:],[: the carrier of F, the carrier of C:]) M2( bool [:[: the carrier' of F, the carrier' of C:],[: the carrier of F, the carrier of C:]:])
K184( the carrier' of F, the carrier' of C, the Comp of F, the Comp of C) is Relation-like [:[: the carrier' of F, the carrier' of C:],[: the carrier' of F, the carrier' of C:]:] -defined [: the carrier' of F, the carrier' of C:] -valued Function-like M2( bool [:[:[: the carrier' of F, the carrier' of C:],[: the carrier' of F, the carrier' of C:]:],[: the carrier' of F, the carrier' of C:]:])
[:[: the carrier' of F, the carrier' of C:],[: the carrier' of F, the carrier' of C:]:] is set
[:[:[: the carrier' of F, the carrier' of C:],[: the carrier' of F, the carrier' of C:]:],[: the carrier' of F, the carrier' of C:]:] is set
bool [:[:[: the carrier' of F, the carrier' of C:],[: the carrier' of F, the carrier' of C:]:],[: the carrier' of F, the carrier' of C:]:] is set
CatStr(# [: the carrier of F, the carrier of C:],[: the carrier' of F, the carrier' of C:],[: the Source of F, the Source of C:],[: the Target of F, the Target of C:],K184( the carrier' of F, the carrier' of C, the Comp of F, the Comp of C) #) is strict CatStr
the carrier' of [:C,F:] is non empty set
the carrier' of [:F,C:] is non empty set
pr2 (C,F) is Relation-like the carrier' of [:C,F:] -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of [:C,F:], the carrier' of F) Functor of [:C,F:],F
pr2 ( the carrier' of C, the carrier' of F) is Relation-like [: the carrier' of C, the carrier' of F:] -defined the carrier' of F -valued Function-like total V18([: the carrier' of C, the carrier' of F:], the carrier' of F) M2( bool [:[: the carrier' of C, the carrier' of F:], the carrier' of F:])
[:[: the carrier' of C, the carrier' of F:], the carrier' of F:] is set
bool [:[: the carrier' of C, the carrier' of F:], the carrier' of F:] is set
pr1 (C,F) is Relation-like the carrier' of [:C,F:] -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of [:C,F:], the carrier' of C) Functor of [:C,F:],C
pr1 ( the carrier' of C, the carrier' of F) is Relation-like [: the carrier' of C, the carrier' of F:] -defined the carrier' of C -valued Function-like total V18([: the carrier' of C, the carrier' of F:], the carrier' of C) M2( bool [:[: the carrier' of C, the carrier' of F:], the carrier' of C:])
[:[: the carrier' of C, the carrier' of F:], the carrier' of C:] is set
bool [:[: the carrier' of C, the carrier' of F:], the carrier' of C:] is set
<:(pr2 (C,F)),(pr1 (C,F)):> is Relation-like the carrier' of [:C,F:] -defined the carrier' of [:F,C:] -valued Function-like non empty total V18( the carrier' of [:C,F:], the carrier' of [:F,C:]) Functor of [:C,F:],[:F,C:]
G is Relation-like the carrier' of [:C,F:] -defined the carrier' of [:F,C:] -valued Function-like non empty total V18( the carrier' of [:C,F:], the carrier' of [:F,C:]) Functor of [:C,F:],[:F,C:]
dom (pr1 (C,F)) is M2( bool the carrier' of [:C,F:])
bool the carrier' of [:C,F:] is set
dom (pr2 (C,F)) is M2( bool the carrier' of [:C,F:])
o is set
b is set
c₇ is set
[b,c₇] is set
{b,c₇} is set
{b} is set
{{b,c₇},{b}} is set
s is set
f2 is set
f1 is set
[f2,f1] is set
{f2,f1} is set
{f2} is set
{{f2,f1},{f2}} is set
t9 is M2( the carrier' of C)
h is M2( the carrier' of F)
[t9,h] is M2( the carrier' of [:C,F:])
{t9,h} is set
{t9} is set
{{t9,h},{t9}} is set
G . o is set
G . s is set
f is M2( the carrier' of C)
g is M2( the carrier' of F)
[f,g] is M2( the carrier' of [:C,F:])
{f,g} is set
{f} is set
{{f,g},{f}} is set
[g,f] is M2( the carrier' of [:F,C:])
{g,f} is set
{g} is set
{{g,f},{g}} is set
(pr1 (C,F)) . (f,g) is M2( the carrier' of C)
[f,g] is set
(pr1 (C,F)) . [f,g] is set
[g,((pr1 (C,F)) . (f,g))] is M2( the carrier' of [:F,C:])
{g,((pr1 (C,F)) . (f,g))} is set
{{g,((pr1 (C,F)) . (f,g))},{g}} is set
(pr2 (C,F)) . (f,g) is M2( the carrier' of F)
(pr2 (C,F)) . [f,g] is set
[((pr2 (C,F)) . (f,g)),((pr1 (C,F)) . (f,g))] is M2( the carrier' of [:F,C:])
{((pr2 (C,F)) . (f,g)),((pr1 (C,F)) . (f,g))} is set
{((pr2 (C,F)) . (f,g))} is set
{{((pr2 (C,F)) . (f,g)),((pr1 (C,F)) . (f,g))},{((pr2 (C,F)) . (f,g))}} is set
G . (t9,h) is M2( the carrier' of [:F,C:])
[t9,h] is set
G . [t9,h] is set
(pr2 (C,F)) . (t9,h) is M2( the carrier' of F)
(pr2 (C,F)) . [t9,h] is set
(pr1 (C,F)) . (t9,h) is M2( the carrier' of C)
(pr1 (C,F)) . [t9,h] is set
[((pr2 (C,F)) . (t9,h)),((pr1 (C,F)) . (t9,h))] is M2( the carrier' of [:F,C:])
{((pr2 (C,F)) . (t9,h)),((pr1 (C,F)) . (t9,h))} is set
{((pr2 (C,F)) . (t9,h))} is set
{{((pr2 (C,F)) . (t9,h)),((pr1 (C,F)) . (t9,h))},{((pr2 (C,F)) . (t9,h))}} is set
[h,((pr1 (C,F)) . (t9,h))] is M2( the carrier' of [:F,C:])
{h,((pr1 (C,F)) . (t9,h))} is set
{h} is set
{{h,((pr1 (C,F)) . (t9,h))},{h}} is set
[h,t9] is M2( the carrier' of [:F,C:])
{h,t9} is set
{{h,t9},{h}} is set
rng G is M2( bool the carrier' of [:F,C:])
bool the carrier' of [:F,C:] is set
o is set
s is set
b is set
[s,b] is set
{s,b} is set
{s} is set
{{s,b},{s}} is set
c₇ is M2( the carrier' of C)
f2 is M2( the carrier' of F)
[c₇,f2] is M2( the carrier' of [:C,F:])
{c₇,f2} is set
{c₇} is set
{{c₇,f2},{c₇}} is set
G . [c₇,f2] is M2( the carrier' of [:F,C:])
(pr2 (C,F)) . (c₇,f2) is M2( the carrier' of F)
[c₇,f2] is set
(pr2 (C,F)) . [c₇,f2] is set
(pr1 (C,F)) . (c₇,f2) is M2( the carrier' of C)
(pr1 (C,F)) . [c₇,f2] is set
[((pr2 (C,F)) . (c₇,f2)),((pr1 (C,F)) . (c₇,f2))] is M2( the carrier' of [:F,C:])
{((pr2 (C,F)) . (c₇,f2)),((pr1 (C,F)) . (c₇,f2))} is set
{((pr2 (C,F)) . (c₇,f2))} is set
{{((pr2 (C,F)) . (c₇,f2)),((pr1 (C,F)) . (c₇,f2))},{((pr2 (C,F)) . (c₇,f2))}} is set
[f2,((pr1 (C,F)) . (c₇,f2))] is M2( the carrier' of [:F,C:])
{f2,((pr1 (C,F)) . (c₇,f2))} is set
{f2} is set
{{f2,((pr1 (C,F)) . (c₇,f2))},{f2}} is set
[f2,c₇] is M2( the carrier' of [:F,C:])
{f2,c₇} is set
{{f2,c₇},{f2}} is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:C,F:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of C is non empty set
the carrier of F is non empty set
[: the carrier of C, the carrier of F:] is set
the carrier' of C is non empty set
the carrier' of F is non empty set
[: the carrier' of C, the carrier' of F:] is set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) M2( bool [: the carrier' of C, the carrier of C:])
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of F is Relation-like the carrier' of F -defined the carrier of F -valued Function-like non empty total V18( the carrier' of F, the carrier of F) M2( bool [: the carrier' of F, the carrier of F:])
[: the carrier' of F, the carrier of F:] is set
bool [: the carrier' of F, the carrier of F:] is set
[: the Source of C, the Source of F:] is Relation-like [: the carrier' of C, the carrier' of F:] -defined [: the carrier of C, the carrier of F:] -valued Function-like V18([: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]) M2( bool [:[: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]:])
[:[: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]:] is set
bool [:[: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]:] is set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) M2( bool [: the carrier' of C, the carrier of C:])
the Target of F is Relation-like the carrier' of F -defined the carrier of F -valued Function-like non empty total V18( the carrier' of F, the carrier of F) M2( bool [: the carrier' of F, the carrier of F:])
[: the Target of C, the Target of F:] is Relation-like [: the carrier' of C, the carrier' of F:] -defined [: the carrier of C, the carrier of F:] -valued Function-like V18([: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]) M2( bool [:[: the carrier' of C, the carrier' of F:],[: the carrier of C, the carrier of F:]:])
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like M2( bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is set
the Comp of F is Relation-like [: the carrier' of F, the carrier' of F:] -defined the carrier' of F -valued Function-like M2( bool [:[: the carrier' of F, the carrier' of F:], the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
[:[: the carrier' of F, the carrier' of F:], the carrier' of F:] is set
bool [:[: the carrier' of F, the carrier' of F:], the carrier' of F:] is set
K184( the carrier' of C, the carrier' of F, the Comp of C, the Comp of F) is Relation-like [:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:] -defined [: the carrier' of C, the carrier' of F:] -valued Function-like M2( bool [:[:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:],[: the carrier' of C, the carrier' of F:]:])
[:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:] is set
[:[:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:],[: the carrier' of C, the carrier' of F:]:] is set
bool [:[:[: the carrier' of C, the carrier' of F:],[: the carrier' of C, the carrier' of F:]:],[: the carrier' of C, the carrier' of F:]:] is set
CatStr(# [: the carrier of C, the carrier of F:],[: the carrier' of C, the carrier' of F:],[: the Source of C, the Source of F:],[: the Target of C, the Target of F:],K184( the carrier' of C, the carrier' of F, the Comp of C, the Comp of F) #) is strict CatStr
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:[:C,F:],G:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of [:C,F:] is non empty set
the carrier of G is non empty set
[: the carrier of [:C,F:], the carrier of G:] is set
the carrier' of [:C,F:] is non empty set
the carrier' of G is non empty set
[: the carrier' of [:C,F:], the carrier' of G:] is set
the Source of [:C,F:] is Relation-like the carrier' of [:C,F:] -defined the carrier of [:C,F:] -valued Function-like non empty total V18( the carrier' of [:C,F:], the carrier of [:C,F:]) M2( bool [: the carrier' of [:C,F:], the carrier of [:C,F:]:])
[: the carrier' of [:C,F:], the carrier of [:C,F:]:] is set
bool [: the carrier' of [:C,F:], the carrier of [:C,F:]:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like non empty total V18( the carrier' of G, the carrier of G) M2( bool [: the carrier' of G, the carrier of G:])
[: the carrier' of G, the carrier of G:] is set
bool [: the carrier' of G, the carrier of G:] is set
[: the Source of [:C,F:], the Source of G:] is Relation-like [: the carrier' of [:C,F:], the carrier' of G:] -defined [: the carrier of [:C,F:], the carrier of G:] -valued Function-like V18([: the carrier' of [:C,F:], the carrier' of G:],[: the carrier of [:C,F:], the carrier of G:]) M2( bool [:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier of [:C,F:], the carrier of G:]:])
[:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier of [:C,F:], the carrier of G:]:] is set
bool [:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier of [:C,F:], the carrier of G:]:] is set
the Target of [:C,F:] is Relation-like the carrier' of [:C,F:] -defined the carrier of [:C,F:] -valued Function-like non empty total V18( the carrier' of [:C,F:], the carrier of [:C,F:]) M2( bool [: the carrier' of [:C,F:], the carrier of [:C,F:]:])
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like non empty total V18( the carrier' of G, the carrier of G) M2( bool [: the carrier' of G, the carrier of G:])
[: the Target of [:C,F:], the Target of G:] is Relation-like [: the carrier' of [:C,F:], the carrier' of G:] -defined [: the carrier of [:C,F:], the carrier of G:] -valued Function-like V18([: the carrier' of [:C,F:], the carrier' of G:],[: the carrier of [:C,F:], the carrier of G:]) M2( bool [:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier of [:C,F:], the carrier of G:]:])
the Comp of [:C,F:] is Relation-like [: the carrier' of [:C,F:], the carrier' of [:C,F:]:] -defined the carrier' of [:C,F:] -valued Function-like M2( bool [:[: the carrier' of [:C,F:], the carrier' of [:C,F:]:], the carrier' of [:C,F:]:])
[: the carrier' of [:C,F:], the carrier' of [:C,F:]:] is set
[:[: the carrier' of [:C,F:], the carrier' of [:C,F:]:], the carrier' of [:C,F:]:] is set
bool [:[: the carrier' of [:C,F:], the carrier' of [:C,F:]:], the carrier' of [:C,F:]:] is set
the Comp of G is Relation-like [: the carrier' of G, the carrier' of G:] -defined the carrier' of G -valued Function-like M2( bool [:[: the carrier' of G, the carrier' of G:], the carrier' of G:])
[: the carrier' of G, the carrier' of G:] is set
[:[: the carrier' of G, the carrier' of G:], the carrier' of G:] is set
bool [:[: the carrier' of G, the carrier' of G:], the carrier' of G:] is set
K184( the carrier' of [:C,F:], the carrier' of G, the Comp of [:C,F:], the Comp of G) is Relation-like [:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier' of [:C,F:], the carrier' of G:]:] -defined [: the carrier' of [:C,F:], the carrier' of G:] -valued Function-like M2( bool [:[:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier' of [:C,F:], the carrier' of G:]:],[: the carrier' of [:C,F:], the carrier' of G:]:])
[:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier' of [:C,F:], the carrier' of G:]:] is set
[:[:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier' of [:C,F:], the carrier' of G:]:],[: the carrier' of [:C,F:], the carrier' of G:]:] is set
bool [:[:[: the carrier' of [:C,F:], the carrier' of G:],[: the carrier' of [:C,F:], the carrier' of G:]:],[: the carrier' of [:C,F:], the carrier' of G:]:] is set
CatStr(# [: the carrier of [:C,F:], the carrier of G:],[: the carrier' of [:C,F:], the carrier' of G:],[: the Source of [:C,F:], the Source of G:],[: the Target of [:C,F:], the Target of G:],K184( the carrier' of [:C,F:], the carrier' of G, the Comp of [:C,F:], the Comp of G) #) is strict CatStr
[:F,G:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of F, the carrier of G:] is set
[: the carrier' of F, the carrier' of G:] is set
[: the Source of F, the Source of G:] is Relation-like [: the carrier' of F, the carrier' of G:] -defined [: the carrier of F, the carrier of G:] -valued Function-like V18([: the carrier' of F, the carrier' of G:],[: the carrier of F, the carrier of G:]) M2( bool [:[: the carrier' of F, the carrier' of G:],[: the carrier of F, the carrier of G:]:])
[:[: the carrier' of F, the carrier' of G:],[: the carrier of F, the carrier of G:]:] is set
bool [:[: the carrier' of F, the carrier' of G:],[: the carrier of F, the carrier of G:]:] is set
[: the Target of F, the Target of G:] is Relation-like [: the carrier' of F, the carrier' of G:] -defined [: the carrier of F, the carrier of G:] -valued Function-like V18([: the carrier' of F, the carrier' of G:],[: the carrier of F, the carrier of G:]) M2( bool [:[: the carrier' of F, the carrier' of G:],[: the carrier of F, the carrier of G:]:])
K184( the carrier' of F, the carrier' of G, the Comp of F, the Comp of G) is Relation-like [:[: the carrier' of F, the carrier' of G:],[: the carrier' of F, the carrier' of G:]:] -defined [: the carrier' of F, the carrier' of G:] -valued Function-like M2( bool [:[:[: the carrier' of F, the carrier' of G:],[: the carrier' of F, the carrier' of G:]:],[: the carrier' of F, the carrier' of G:]:])
[:[: the carrier' of F, the carrier' of G:],[: the carrier' of F, the carrier' of G:]:] is set
[:[:[: the carrier' of F, the carrier' of G:],[: the carrier' of F, the carrier' of G:]:],[: the carrier' of F, the carrier' of G:]:] is set
bool [:[:[: the carrier' of F, the carrier' of G:],[: the carrier' of F, the carrier' of G:]:],[: the carrier' of F, the carrier' of G:]:] is set
CatStr(# [: the carrier of F, the carrier of G:],[: the carrier' of F, the carrier' of G:],[: the Source of F, the Source of G:],[: the Target of F, the Target of G:],K184( the carrier' of F, the carrier' of G, the Comp of F, the Comp of G) #) is strict CatStr
[:C,[:F,G:]:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of [:F,G:] is non empty set
[: the carrier of C, the carrier of [:F,G:]:] is set
the carrier' of [:F,G:] is non empty set
[: the carrier' of C, the carrier' of [:F,G:]:] is set
the Source of [:F,G:] is Relation-like the carrier' of [:F,G:] -defined the carrier of [:F,G:] -valued Function-like non empty total V18( the carrier' of [:F,G:], the carrier of [:F,G:]) M2( bool [: the carrier' of [:F,G:], the carrier of [:F,G:]:])
[: the carrier' of [:F,G:], the carrier of [:F,G:]:] is set
bool [: the carrier' of [:F,G:], the carrier of [:F,G:]:] is set
[: the Source of C, the Source of [:F,G:]:] is Relation-like [: the carrier' of C, the carrier' of [:F,G:]:] -defined [: the carrier of C, the carrier of [:F,G:]:] -valued Function-like V18([: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier of C, the carrier of [:F,G:]:]) M2( bool [:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier of C, the carrier of [:F,G:]:]:])
[:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier of C, the carrier of [:F,G:]:]:] is set
bool [:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier of C, the carrier of [:F,G:]:]:] is set
the Target of [:F,G:] is Relation-like the carrier' of [:F,G:] -defined the carrier of [:F,G:] -valued Function-like non empty total V18( the carrier' of [:F,G:], the carrier of [:F,G:]) M2( bool [: the carrier' of [:F,G:], the carrier of [:F,G:]:])
[: the Target of C, the Target of [:F,G:]:] is Relation-like [: the carrier' of C, the carrier' of [:F,G:]:] -defined [: the carrier of C, the carrier of [:F,G:]:] -valued Function-like V18([: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier of C, the carrier of [:F,G:]:]) M2( bool [:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier of C, the carrier of [:F,G:]:]:])
the Comp of [:F,G:] is Relation-like [: the carrier' of [:F,G:], the carrier' of [:F,G:]:] -defined the carrier' of [:F,G:] -valued Function-like M2( bool [:[: the carrier' of [:F,G:], the carrier' of [:F,G:]:], the carrier' of [:F,G:]:])
[: the carrier' of [:F,G:], the carrier' of [:F,G:]:] is set
[:[: the carrier' of [:F,G:], the carrier' of [:F,G:]:], the carrier' of [:F,G:]:] is set
bool [:[: the carrier' of [:F,G:], the carrier' of [:F,G:]:], the carrier' of [:F,G:]:] is set
K184( the carrier' of C, the carrier' of [:F,G:], the Comp of C, the Comp of [:F,G:]) is Relation-like [:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier' of C, the carrier' of [:F,G:]:]:] -defined [: the carrier' of C, the carrier' of [:F,G:]:] -valued Function-like M2( bool [:[:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier' of C, the carrier' of [:F,G:]:]:],[: the carrier' of C, the carrier' of [:F,G:]:]:])
[:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier' of C, the carrier' of [:F,G:]:]:] is set
[:[:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier' of C, the carrier' of [:F,G:]:]:],[: the carrier' of C, the carrier' of [:F,G:]:]:] is set
bool [:[:[: the carrier' of C, the carrier' of [:F,G:]:],[: the carrier' of C, the carrier' of [:F,G:]:]:],[: the carrier' of C, the carrier' of [:F,G:]:]:] is set
CatStr(# [: the carrier of C, the carrier of [:F,G:]:],[: the carrier' of C, the carrier' of [:F,G:]:],[: the Source of C, the Source of [:F,G:]:],[: the Target of C, the Target of [:F,G:]:],K184( the carrier' of C, the carrier' of [:F,G:], the Comp of C, the Comp of [:F,G:]) #) is strict CatStr
pr1 ([:C,F:],G) is Relation-like the carrier' of [:[:C,F:],G:] -defined the carrier' of [:C,F:] -valued Function-like non empty total V18( the carrier' of [:[:C,F:],G:], the carrier' of [:C,F:]) Functor of [:[:C,F:],G:],[:C,F:]
the carrier' of [:[:C,F:],G:] is non empty set
pr1 ( the carrier' of [:C,F:], the carrier' of G) is Relation-like [: the carrier' of [:C,F:], the carrier' of G:] -defined the carrier' of [:C,F:] -valued Function-like total V18([: the carrier' of [:C,F:], the carrier' of G:], the carrier' of [:C,F:]) M2( bool [:[: the carrier' of [:C,F:], the carrier' of G:], the carrier' of [:C,F:]:])
[:[: the carrier' of [:C,F:], the carrier' of G:], the carrier' of [:C,F:]:] is set
bool [:[: the carrier' of [:C,F:], the carrier' of G:], the carrier' of [:C,F:]:] is set
pr1 (C,F) is Relation-like the carrier' of [:C,F:] -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of [:C,F:], the carrier' of C) Functor of [:C,F:],C
pr1 ( the carrier' of C, the carrier' of F) is Relation-like [: the carrier' of C, the carrier' of F:] -defined the carrier' of C -valued Function-like total V18([: the carrier' of C, the carrier' of F:], the carrier' of C) M2( bool [:[: the carrier' of C, the carrier' of F:], the carrier' of C:])
[:[: the carrier' of C, the carrier' of F:], the carrier' of C:] is set
bool [:[: the carrier' of C, the carrier' of F:], the carrier' of C:] is set
(pr1 (C,F)) * (pr1 ([:C,F:],G)) is Relation-like the carrier' of [:[:C,F:],G:] -defined the carrier' of [:[:C,F:],G:] -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of [:[:C,F:],G:], the carrier' of C) V18( the carrier' of [:[:C,F:],G:], the carrier' of C) Functor of [:[:C,F:],G:],C
pr2 (C,F) is Relation-like the carrier' of [:C,F:] -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of [:C,F:], the carrier' of F) Functor of [:C,F:],F
pr2 ( the carrier' of C, the carrier' of F) is Relation-like [: the carrier' of C, the carrier' of F:] -defined the carrier' of F -valued Function-like total V18([: the carrier' of C, the carrier' of F:], the carrier' of F) M2( bool [:[: the carrier' of C, the carrier' of F:], the carrier' of F:])
[:[: the carrier' of C, the carrier' of F:], the carrier' of F:] is set
bool [:[: the carrier' of C, the carrier' of F:], the carrier' of F:] is set
(pr2 (C,F)) * (pr1 ([:C,F:],G)) is Relation-like the carrier' of [:[:C,F:],G:] -defined the carrier' of [:[:C,F:],G:] -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of [:[:C,F:],G:], the carrier' of F) V18( the carrier' of [:[:C,F:],G:], the carrier' of F) Functor of [:[:C,F:],G:],F
pr2 ([:C,F:],G) is Relation-like the carrier' of [:[:C,F:],G:] -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of [:[:C,F:],G:], the carrier' of G) Functor of [:[:C,F:],G:],G
pr2 ( the carrier' of [:C,F:], the carrier' of G) is Relation-like [: the carrier' of [:C,F:], the carrier' of G:] -defined the carrier' of G -valued Function-like total V18([: the carrier' of [:C,F:], the carrier' of G:], the carrier' of G) M2( bool [:[: the carrier' of [:C,F:], the carrier' of G:], the carrier' of G:])
[:[: the carrier' of [:C,F:], the carrier' of G:], the carrier' of G:] is set
bool [:[: the carrier' of [:C,F:], the carrier' of G:], the carrier' of G:] is set
<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> is Relation-like the carrier' of [:[:C,F:],G:] -defined the carrier' of [:F,G:] -valued Function-like non empty total V18( the carrier' of [:[:C,F:],G:], the carrier' of [:F,G:]) Functor of [:[:C,F:],G:],[:F,G:]
the carrier' of [:C,[:F,G:]:] is non empty set
<:((pr1 (C,F)) * (pr1 ([:C,F:],G))),<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):>:> is Relation-like the carrier' of [:[:C,F:],G:] -defined the carrier' of [:C,[:F,G:]:] -valued Function-like non empty total V18( the carrier' of [:[:C,F:],G:], the carrier' of [:C,[:F,G:]:]) Functor of [:[:C,F:],G:],[:C,[:F,G:]:]
b is Relation-like the carrier' of [:[:C,F:],G:] -defined the carrier' of [:C,[:F,G:]:] -valued Function-like non empty total V18( the carrier' of [:[:C,F:],G:], the carrier' of [:C,[:F,G:]:]) Functor of [:[:C,F:],G:],[:C,[:F,G:]:]
dom (pr2 ([:C,F:],G)) is M2( bool the carrier' of [:[:C,F:],G:])
bool the carrier' of [:[:C,F:],G:] is set
dom ((pr2 (C,F)) * (pr1 ([:C,F:],G))) is M2( bool the carrier' of [:[:C,F:],G:])
dom ((pr1 (C,F)) * (pr1 ([:C,F:],G))) is M2( bool the carrier' of [:[:C,F:],G:])
dom <:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> is M2( bool the carrier' of [:[:C,F:],G:])
c₇ is set
[:[: the carrier' of C, the carrier' of F:], the carrier' of G:] is set
f1 is set
g is set
[f1,g] is set
{f1,g} is set
{f1} is set
{{f1,g},{f1}} is set
f2 is set
h is set
f is set
[h,f] is set
{h,f} is set
{h} is set
{{h,f},{h}} is set
b . c₇ is set
b . f2 is set
x11 is set
x12 is set
[x11,x12] is set
{x11,x12} is set
{x11} is set
{{x11,x12},{x11}} is set
y11 is set
y12 is set
[y11,y12] is set
{y11,y12} is set
{y11} is set
{{y11,y12},{y11}} is set
f11 is M2( the carrier' of C)
f12 is M2( the carrier' of F)
t9 is M2( the carrier' of G)
[f12,t9] is M2( the carrier' of [:F,G:])
{f12,t9} is set
{f12} is set
{{f12,t9},{f12}} is set
[f11,[f12,t9]] is M2( the carrier' of [:C,[:F,G:]:])
{f11,[f12,t9]} is set
{f11} is set
{{f11,[f12,t9]},{f11}} is set
(pr1 (C,F)) . (f11,f12) is M2( the carrier' of C)
[f11,f12] is set
{f11,f12} is set
{{f11,f12},{f11}} is set
(pr1 (C,F)) . [f11,f12] is set
[((pr1 (C,F)) . (f11,f12)),[f12,t9]] is M2( the carrier' of [:C,[:F,G:]:])
{((pr1 (C,F)) . (f11,f12)),[f12,t9]} is set
{((pr1 (C,F)) . (f11,f12))} is set
{{((pr1 (C,F)) . (f11,f12)),[f12,t9]},{((pr1 (C,F)) . (f11,f12))}} is set
[f11,f12] is M2( the carrier' of [:C,F:])
(pr1 ([:C,F:],G)) . ([f11,f12],t9) is M2( the carrier' of [:C,F:])
[[f11,f12],t9] is set
{[f11,f12],t9} is set
{[f11,f12]} is set
{{[f11,f12],t9},{[f11,f12]}} is set
(pr1 ([:C,F:],G)) . [[f11,f12],t9] is set
(pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9)) is M2( the carrier' of C)
[((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),[f12,t9]] is M2( the carrier' of [:C,[:F,G:]:])
{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),[f12,t9]} is set
{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9)))} is set
{{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),[f12,t9]},{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9)))}} is set
[[f11,f12],t9] is M2( the carrier' of [:[:C,F:],G:])
(pr1 ([:C,F:],G)) . [[f11,f12],t9] is M2( the carrier' of [:C,F:])
(pr1 (C,F)) . ((pr1 ([:C,F:],G)) . [[f11,f12],t9]) is M2( the carrier' of C)
[((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . [[f11,f12],t9])),[f12,t9]] is M2( the carrier' of [:C,[:F,G:]:])
{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . [[f11,f12],t9])),[f12,t9]} is set
{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . [[f11,f12],t9]))} is set
{{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . [[f11,f12],t9])),[f12,t9]},{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . [[f11,f12],t9]))}} is set
((pr1 (C,F)) * (pr1 ([:C,F:],G))) . ([f11,f12],t9) is M2( the carrier' of C)
((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9] is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . ([f11,f12],t9)),[f12,t9]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . ([f11,f12],t9)),[f12,t9]} is set
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . ([f11,f12],t9))} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . ([f11,f12],t9)),[f12,t9]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . ([f11,f12],t9))}} is set
((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9] is M2( the carrier' of C)
(pr2 (C,F)) . (f11,f12) is M2( the carrier' of F)
(pr2 (C,F)) . [f11,f12] is set
[((pr2 (C,F)) . (f11,f12)),t9] is M2( the carrier' of [:F,G:])
{((pr2 (C,F)) . (f11,f12)),t9} is set
{((pr2 (C,F)) . (f11,f12))} is set
{{((pr2 (C,F)) . (f11,f12)),t9},{((pr2 (C,F)) . (f11,f12))}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[((pr2 (C,F)) . (f11,f12)),t9]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[((pr2 (C,F)) . (f11,f12)),t9]} is set
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[((pr2 (C,F)) . (f11,f12)),t9]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])}} is set
(pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9)) is M2( the carrier' of F)
[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),t9] is M2( the carrier' of [:F,G:])
{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),t9} is set
{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9)))} is set
{{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),t9},{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9)))}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),t9]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),t9]} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([f11,f12],t9))),t9]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])}} is set
((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9] is M2( the carrier' of F)
[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),t9] is M2( the carrier' of [:F,G:])
{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),t9} is set
{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])} is set
{{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),t9},{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),t9]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),t9]} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),t9]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])}} is set
(pr2 ([:C,F:],G)) . ([f11,f12],t9) is M2( the carrier' of G)
(pr2 ([:C,F:],G)) . [[f11,f12],t9] is set
[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),((pr2 ([:C,F:],G)) . ([f11,f12],t9))] is M2( the carrier' of [:F,G:])
{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),((pr2 ([:C,F:],G)) . ([f11,f12],t9))} is set
{{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),((pr2 ([:C,F:],G)) . ([f11,f12],t9))},{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),((pr2 ([:C,F:],G)) . ([f11,f12],t9))]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),((pr2 ([:C,F:],G)) . ([f11,f12],t9))]} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),((pr2 ([:C,F:],G)) . ([f11,f12],t9))]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])}} is set
<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[f11,f12],t9] is M2( the carrier' of [:F,G:])
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[f11,f12],t9])] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[f11,f12],t9])} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[f11,f12],t9])},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[f11,f12],t9])}} is set
g11 is M2( the carrier' of C)
g12 is M2( the carrier' of F)
[g11,g12] is M2( the carrier' of [:C,F:])
{g11,g12} is set
{g11} is set
{{g11,g12},{g11}} is set
x21 is M2( the carrier' of G)
[[g11,g12],x21] is M2( the carrier' of [:[:C,F:],G:])
{[g11,g12],x21} is set
{[g11,g12]} is set
{{[g11,g12],x21},{[g11,g12]}} is set
b . [[g11,g12],x21] is M2( the carrier' of [:C,[:F,G:]:])
((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21] is M2( the carrier' of C)
<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g11,g12],x21] is M2( the carrier' of [:F,G:])
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g11,g12],x21])] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g11,g12],x21])} is set
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g11,g12],x21])},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])}} is set
((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21] is M2( the carrier' of F)
(pr2 ([:C,F:],G)) . ([g11,g12],x21) is M2( the carrier' of G)
[[g11,g12],x21] is set
(pr2 ([:C,F:],G)) . [[g11,g12],x21] is set
[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),((pr2 ([:C,F:],G)) . ([g11,g12],x21))] is M2( the carrier' of [:F,G:])
{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),((pr2 ([:C,F:],G)) . ([g11,g12],x21))} is set
{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])} is set
{{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),((pr2 ([:C,F:],G)) . ([g11,g12],x21))},{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),((pr2 ([:C,F:],G)) . ([g11,g12],x21))]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),((pr2 ([:C,F:],G)) . ([g11,g12],x21))]} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),((pr2 ([:C,F:],G)) . ([g11,g12],x21))]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])}} is set
[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),x21] is M2( the carrier' of [:F,G:])
{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),x21} is set
{{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),x21},{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),x21]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),x21]} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),x21]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])}} is set
(pr1 ([:C,F:],G)) . ([g11,g12],x21) is M2( the carrier' of [:C,F:])
(pr1 ([:C,F:],G)) . [[g11,g12],x21] is set
(pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21)) is M2( the carrier' of F)
[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),x21] is M2( the carrier' of [:F,G:])
{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),x21} is set
{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21)))} is set
{{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),x21},{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21)))}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),x21]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),x21]} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),x21]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])}} is set
(pr2 (C,F)) . (g11,g12) is M2( the carrier' of F)
[g11,g12] is set
(pr2 (C,F)) . [g11,g12] is set
[((pr2 (C,F)) . (g11,g12)),x21] is M2( the carrier' of [:F,G:])
{((pr2 (C,F)) . (g11,g12)),x21} is set
{((pr2 (C,F)) . (g11,g12))} is set
{{((pr2 (C,F)) . (g11,g12)),x21},{((pr2 (C,F)) . (g11,g12))}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[((pr2 (C,F)) . (g11,g12)),x21]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[((pr2 (C,F)) . (g11,g12)),x21]} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[((pr2 (C,F)) . (g11,g12)),x21]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])}} is set
[g12,x21] is M2( the carrier' of [:F,G:])
{g12,x21} is set
{g12} is set
{{g12,x21},{g12}} is set
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[g12,x21]] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[g12,x21]} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21]),[g12,x21]},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g11,g12],x21])}} is set
(pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21)) is M2( the carrier' of C)
[((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),[g12,x21]] is M2( the carrier' of [:C,[:F,G:]:])
{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),[g12,x21]} is set
{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21)))} is set
{{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21))),[g12,x21]},{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g11,g12],x21)))}} is set
(pr1 (C,F)) . (g11,g12) is M2( the carrier' of C)
(pr1 (C,F)) . [g11,g12] is set
[((pr1 (C,F)) . (g11,g12)),[g12,x21]] is M2( the carrier' of [:C,[:F,G:]:])
{((pr1 (C,F)) . (g11,g12)),[g12,x21]} is set
{((pr1 (C,F)) . (g11,g12))} is set
{{((pr1 (C,F)) . (g11,g12)),[g12,x21]},{((pr1 (C,F)) . (g11,g12))}} is set
[g11,[g12,x21]] is M2( the carrier' of [:C,[:F,G:]:])
{g11,[g12,x21]} is set
{{g11,[g12,x21]},{g11}} is set
[x12,g] is set
{x12,g} is set
{x12} is set
{{x12,g},{x12}} is set
[y12,f] is set
{y12,f} is set
{y12} is set
{{y12,f},{y12}} is set
rng b is M2( bool the carrier' of [:C,[:F,G:]:])
bool the carrier' of [:C,[:F,G:]:] is set
c₇ is set
f2 is set
f1 is set
[f2,f1] is set
{f2,f1} is set
{f2} is set
{{f2,f1},{f2}} is set
h is set
f is set
[h,f] is set
{h,f} is set
{h} is set
{{h,f},{h}} is set
g is M2( the carrier' of C)
x21 is M2( the carrier' of F)
[g,x21] is M2( the carrier' of [:C,F:])
{g,x21} is set
{g} is set
{{g,x21},{g}} is set
t9 is M2( the carrier' of G)
[[g,x21],t9] is M2( the carrier' of [:[:C,F:],G:])
{[g,x21],t9} is set
{[g,x21]} is set
{{[g,x21],t9},{[g,x21]}} is set
b . [[g,x21],t9] is M2( the carrier' of [:C,[:F,G:]:])
((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9] is M2( the carrier' of C)
<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9] is M2( the carrier' of [:F,G:])
[(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])] is M2( the carrier' of [:C,[:F,G:]:])
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])} is set
{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9])} is set
{{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])},{(((pr1 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9])}} is set
(pr1 ([:C,F:],G)) . ([g,x21],t9) is M2( the carrier' of [:C,F:])
[[g,x21],t9] is set
(pr1 ([:C,F:],G)) . [[g,x21],t9] is set
(pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9)) is M2( the carrier' of C)
[((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])] is M2( the carrier' of [:C,[:F,G:]:])
{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])} is set
{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9)))} is set
{{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])},{((pr1 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9)))}} is set
(pr1 (C,F)) . (g,x21) is M2( the carrier' of C)
[g,x21] is set
(pr1 (C,F)) . [g,x21] is set
[((pr1 (C,F)) . (g,x21)),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])] is M2( the carrier' of [:C,[:F,G:]:])
{((pr1 (C,F)) . (g,x21)),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])} is set
{((pr1 (C,F)) . (g,x21))} is set
{{((pr1 (C,F)) . (g,x21)),(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])},{((pr1 (C,F)) . (g,x21))}} is set
[g,(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])] is M2( the carrier' of [:C,[:F,G:]:])
{g,(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])} is set
{{g,(<:((pr2 (C,F)) * (pr1 ([:C,F:],G))),(pr2 ([:C,F:],G)):> . [[g,x21],t9])},{g}} is set
((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9] is M2( the carrier' of F)
(pr2 ([:C,F:],G)) . [[g,x21],t9] is M2( the carrier' of G)
[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),((pr2 ([:C,F:],G)) . [[g,x21],t9])] is M2( the carrier' of [:F,G:])
{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),((pr2 ([:C,F:],G)) . [[g,x21],t9])} is set
{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9])} is set
{{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),((pr2 ([:C,F:],G)) . [[g,x21],t9])},{(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9])}} is set
[g,[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),((pr2 ([:C,F:],G)) . [[g,x21],t9])]] is M2( the carrier' of [:C,[:F,G:]:])
{g,[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),((pr2 ([:C,F:],G)) . [[g,x21],t9])]} is set
{{g,[(((pr2 (C,F)) * (pr1 ([:C,F:],G))) . [[g,x21],t9]),((pr2 ([:C,F:],G)) . [[g,x21],t9])]},{g}} is set
(pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9)) is M2( the carrier' of F)
[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),((pr2 ([:C,F:],G)) . [[g,x21],t9])] is M2( the carrier' of [:F,G:])
{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),((pr2 ([:C,F:],G)) . [[g,x21],t9])} is set
{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9)))} is set
{{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),((pr2 ([:C,F:],G)) . [[g,x21],t9])},{((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9)))}} is set
[g,[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),((pr2 ([:C,F:],G)) . [[g,x21],t9])]] is M2( the carrier' of [:C,[:F,G:]:])
{g,[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),((pr2 ([:C,F:],G)) . [[g,x21],t9])]} is set
{{g,[((pr2 (C,F)) . ((pr1 ([:C,F:],G)) . ([g,x21],t9))),((pr2 ([:C,F:],G)) . [[g,x21],t9])]},{g}} is set
(pr2 (C,F)) . (g,x21) is M2( the carrier' of F)
(pr2 (C,F)) . [g,x21] is set
(pr2 ([:C,F:],G)) . ([g,x21],t9) is M2( the carrier' of G)
(pr2 ([:C,F:],G)) . [[g,x21],t9] is set
[((pr2 (C,F)) . (g,x21)),((pr2 ([:C,F:],G)) . ([g,x21],t9))] is M2( the carrier' of [:F,G:])
{((pr2 (C,F)) . (g,x21)),((pr2 ([:C,F:],G)) . ([g,x21],t9))} is set
{((pr2 (C,F)) . (g,x21))} is set
{{((pr2 (C,F)) . (g,x21)),((pr2 ([:C,F:],G)) . ([g,x21],t9))},{((pr2 (C,F)) . (g,x21))}} is set
[g,[((pr2 (C,F)) . (g,x21)),((pr2 ([:C,F:],G)) . ([g,x21],t9))]] is M2( the carrier' of [:C,[:F,G:]:])
{g,[((pr2 (C,F)) . (g,x21)),((pr2 ([:C,F:],G)) . ([g,x21],t9))]} is set
{{g,[((pr2 (C,F)) . (g,x21)),((pr2 ([:C,F:],G)) . ([g,x21],t9))]},{g}} is set
[x21,((pr2 ([:C,F:],G)) . ([g,x21],t9))] is M2( the carrier' of [:F,G:])
{x21,((pr2 ([:C,F:],G)) . ([g,x21],t9))} is set
{x21} is set
{{x21,((pr2 ([:C,F:],G)) . ([g,x21],t9))},{x21}} is set
[g,[x21,((pr2 ([:C,F:],G)) . ([g,x21],t9))]] is M2( the carrier' of [:C,[:F,G:]:])
{g,[x21,((pr2 ([:C,F:],G)) . ([g,x21],t9))]} is set
{{g,[x21,((pr2 ([:C,F:],G)) . ([g,x21],t9))]},{g}} is set
[x21,t9] is M2( the carrier' of [:F,G:])
{x21,t9} is set
{{x21,t9},{x21}} is set
[g,[x21,t9]] is M2( the carrier' of [:C,[:F,G:]:])
{g,[x21,t9]} is set
{{g,[x21,t9]},{g}} is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:C,G:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of C is non empty set
the carrier of G is non empty set
[: the carrier of C, the carrier of G:] is set
the carrier' of C is non empty set
the carrier' of G is non empty set
[: the carrier' of C, the carrier' of G:] is set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) M2( bool [: the carrier' of C, the carrier of C:])
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like non empty total V18( the carrier' of G, the carrier of G) M2( bool [: the carrier' of G, the carrier of G:])
[: the carrier' of G, the carrier of G:] is set
bool [: the carrier' of G, the carrier of G:] is set
[: the Source of C, the Source of G:] is Relation-like [: the carrier' of C, the carrier' of G:] -defined [: the carrier of C, the carrier of G:] -valued Function-like V18([: the carrier' of C, the carrier' of G:],[: the carrier of C, the carrier of G:]) M2( bool [:[: the carrier' of C, the carrier' of G:],[: the carrier of C, the carrier of G:]:])
[:[: the carrier' of C, the carrier' of G:],[: the carrier of C, the carrier of G:]:] is set
bool [:[: the carrier' of C, the carrier' of G:],[: the carrier of C, the carrier of G:]:] is set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) M2( bool [: the carrier' of C, the carrier of C:])
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like non empty total V18( the carrier' of G, the carrier of G) M2( bool [: the carrier' of G, the carrier of G:])
[: the Target of C, the Target of G:] is Relation-like [: the carrier' of C, the carrier' of G:] -defined [: the carrier of C, the carrier of G:] -valued Function-like V18([: the carrier' of C, the carrier' of G:],[: the carrier of C, the carrier of G:]) M2( bool [:[: the carrier' of C, the carrier' of G:],[: the carrier of C, the carrier of G:]:])
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like M2( bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is set
the Comp of G is Relation-like [: the carrier' of G, the carrier' of G:] -defined the carrier' of G -valued Function-like M2( bool [:[: the carrier' of G, the carrier' of G:], the carrier' of G:])
[: the carrier' of G, the carrier' of G:] is set
[:[: the carrier' of G, the carrier' of G:], the carrier' of G:] is set
bool [:[: the carrier' of G, the carrier' of G:], the carrier' of G:] is set
K184( the carrier' of C, the carrier' of G, the Comp of C, the Comp of G) is Relation-like [:[: the carrier' of C, the carrier' of G:],[: the carrier' of C, the carrier' of G:]:] -defined [: the carrier' of C, the carrier' of G:] -valued Function-like M2( bool [:[:[: the carrier' of C, the carrier' of G:],[: the carrier' of C, the carrier' of G:]:],[: the carrier' of C, the carrier' of G:]:])
[:[: the carrier' of C, the carrier' of G:],[: the carrier' of C, the carrier' of G:]:] is set
[:[:[: the carrier' of C, the carrier' of G:],[: the carrier' of C, the carrier' of G:]:],[: the carrier' of C, the carrier' of G:]:] is set
bool [:[:[: the carrier' of C, the carrier' of G:],[: the carrier' of C, the carrier' of G:]:],[: the carrier' of C, the carrier' of G:]:] is set
CatStr(# [: the carrier of C, the carrier of G:],[: the carrier' of C, the carrier' of G:],[: the Source of C, the Source of G:],[: the Target of C, the Target of G:],K184( the carrier' of C, the carrier' of G, the Comp of C, the Comp of G) #) is strict CatStr
o is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:F,o:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of F is non empty set
the carrier of o is non empty set
[: the carrier of F, the carrier of o:] is set
the carrier' of F is non empty set
the carrier' of o is non empty set
[: the carrier' of F, the carrier' of o:] is set
the Source of F is Relation-like the carrier' of F -defined the carrier of F -valued Function-like non empty total V18( the carrier' of F, the carrier of F) M2( bool [: the carrier' of F, the carrier of F:])
[: the carrier' of F, the carrier of F:] is set
bool [: the carrier' of F, the carrier of F:] is set
the Source of o is Relation-like the carrier' of o -defined the carrier of o -valued Function-like non empty total V18( the carrier' of o, the carrier of o) M2( bool [: the carrier' of o, the carrier of o:])
[: the carrier' of o, the carrier of o:] is set
bool [: the carrier' of o, the carrier of o:] is set
[: the Source of F, the Source of o:] is Relation-like [: the carrier' of F, the carrier' of o:] -defined [: the carrier of F, the carrier of o:] -valued Function-like V18([: the carrier' of F, the carrier' of o:],[: the carrier of F, the carrier of o:]) M2( bool [:[: the carrier' of F, the carrier' of o:],[: the carrier of F, the carrier of o:]:])
[:[: the carrier' of F, the carrier' of o:],[: the carrier of F, the carrier of o:]:] is set
bool [:[: the carrier' of F, the carrier' of o:],[: the carrier of F, the carrier of o:]:] is set
the Target of F is Relation-like the carrier' of F -defined the carrier of F -valued Function-like non empty total V18( the carrier' of F, the carrier of F) M2( bool [: the carrier' of F, the carrier of F:])
the Target of o is Relation-like the carrier' of o -defined the carrier of o -valued Function-like non empty total V18( the carrier' of o, the carrier of o) M2( bool [: the carrier' of o, the carrier of o:])
[: the Target of F, the Target of o:] is Relation-like [: the carrier' of F, the carrier' of o:] -defined [: the carrier of F, the carrier of o:] -valued Function-like V18([: the carrier' of F, the carrier' of o:],[: the carrier of F, the carrier of o:]) M2( bool [:[: the carrier' of F, the carrier' of o:],[: the carrier of F, the carrier of o:]:])
the Comp of F is Relation-like [: the carrier' of F, the carrier' of F:] -defined the carrier' of F -valued Function-like M2( bool [:[: the carrier' of F, the carrier' of F:], the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
[:[: the carrier' of F, the carrier' of F:], the carrier' of F:] is set
bool [:[: the carrier' of F, the carrier' of F:], the carrier' of F:] is set
the Comp of o is Relation-like [: the carrier' of o, the carrier' of o:] -defined the carrier' of o -valued Function-like M2( bool [:[: the carrier' of o, the carrier' of o:], the carrier' of o:])
[: the carrier' of o, the carrier' of o:] is set
[:[: the carrier' of o, the carrier' of o:], the carrier' of o:] is set
bool [:[: the carrier' of o, the carrier' of o:], the carrier' of o:] is set
K184( the carrier' of F, the carrier' of o, the Comp of F, the Comp of o) is Relation-like [:[: the carrier' of F, the carrier' of o:],[: the carrier' of F, the carrier' of o:]:] -defined [: the carrier' of F, the carrier' of o:] -valued Function-like M2( bool [:[:[: the carrier' of F, the carrier' of o:],[: the carrier' of F, the carrier' of o:]:],[: the carrier' of F, the carrier' of o:]:])
[:[: the carrier' of F, the carrier' of o:],[: the carrier' of F, the carrier' of o:]:] is set
[:[:[: the carrier' of F, the carrier' of o:],[: the carrier' of F, the carrier' of o:]:],[: the carrier' of F, the carrier' of o:]:] is set
bool [:[:[: the carrier' of F, the carrier' of o:],[: the carrier' of F, the carrier' of o:]:],[: the carrier' of F, the carrier' of o:]:] is set
CatStr(# [: the carrier of F, the carrier of o:],[: the carrier' of F, the carrier' of o:],[: the Source of F, the Source of o:],[: the Target of F, the Target of o:],K184( the carrier' of F, the carrier' of o, the Comp of F, the Comp of o) #) is strict CatStr
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
[:s,b:] is Relation-like the carrier' of [:C,G:] -defined the carrier' of [:F,o:] -valued Function-like non empty total V18( the carrier' of [:C,G:], the carrier' of [:F,o:]) Functor of [:C,G:],[:F,o:]
the carrier' of [:C,G:] is non empty set
the carrier' of [:F,o:] is non empty set
rng [:s,b:] is M2( bool the carrier' of [:F,o:])
bool the carrier' of [:F,o:] is set
rng s is M2( bool the carrier' of F)
bool the carrier' of F is set
rng b is M2( bool the carrier' of o)
bool the carrier' of o is set
[:(rng s),(rng b):] is set
[: the carrier' of F,(rng b):] is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
the carrier of C is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
b is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) transformation of o,s
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ * b is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) M2( bool [: the carrier of C, the carrier' of G:])
[: the carrier of C, the carrier' of G:] is set
bool [: the carrier of C, the carrier' of G:] is set
c₇ * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) M2( bool [: the carrier of C, the carrier' of G:])
f1 is M2( the carrier of C)
f2 . f1 is M2( the carrier' of G)
(c₇ * o) . f1 is M2( the carrier of G)
the carrier of G is non empty set
Obj (c₇ * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (c₇ * o)) . f1 is M2( the carrier of G)
(c₇ * s) . f1 is M2( the carrier of G)
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * s)) . f1 is M2( the carrier of G)
o . f1 is M2( the carrier of F)
the carrier of F is non empty set
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . f1 is M2( the carrier of F)
c₇ . (o . f1) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj c₇) . (o . f1) is M2( the carrier of G)
s . f1 is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj s) . f1 is M2( the carrier of F)
c₇ . (s . f1) is M2( the carrier of G)
(Obj c₇) . (s . f1) is M2( the carrier of G)
b . f1 is Morphism of o . f1,s . f1
Hom ((o . f1),(s . f1)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . f1 & cod b₁ = s . f1 ) } is set
c₇ . (b . f1) is M2( the carrier' of G)
Hom (((c₇ * o) . f1),((c₇ * s) . f1)) is M2( bool the carrier' of G)
bool the carrier' of G is set
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (c₇ * o) . f1 & cod b₁ = (c₇ * s) . f1 ) } is set
b . f1 is M2( the carrier' of F)
c₇ . (b . f1) is M2( the carrier' of G)
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of F is non empty set
the carrier of C is non empty set
b is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
Obj b is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
c₇ is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) transformation of o,s
c₇ * (Obj b) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) M2( bool [: the carrier of C, the carrier' of G:])
[: the carrier of C, the carrier' of G:] is set
bool [: the carrier of C, the carrier' of G:] is set
o * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
s * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) M2( bool [: the carrier of C, the carrier' of G:])
f1 is M2( the carrier of C)
f2 . f1 is M2( the carrier' of G)
(o * b) . f1 is M2( the carrier of G)
the carrier of G is non empty set
Obj (o * b) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (o * b)) . f1 is M2( the carrier of G)
(s * b) . f1 is M2( the carrier of G)
Obj (s * b) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (s * b)) . f1 is M2( the carrier of G)
b . f1 is M2( the carrier of F)
(Obj b) . f1 is M2( the carrier of F)
o . (b . f1) is M2( the carrier of G)
Obj o is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj o) . (b . f1) is M2( the carrier of G)
c₇ . ((Obj b) . f1) is set
c₇ . (b . f1) is Morphism of o . (b . f1),s . (b . f1)
s . (b . f1) is M2( the carrier of G)
Obj s is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj s) . (b . f1) is M2( the carrier of G)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
the carrier of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of G -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of G, the carrier' of C) Functor of G,C
o * b is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
s * b is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
c₇ is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) transformation of o,s
(G,C,F,o,s,b,c₇) is Relation-like the carrier of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier of G, the carrier' of F) transformation of o * b,s * b
f2 is M2( the carrier of G)
(G,C,F,o,s,b,c₇) . f2 is Morphism of (o * b) . f2,(s * b) . f2
(o * b) . f2 is M2( the carrier of F)
the carrier of F is non empty set
Obj (o * b) is Relation-like the carrier of G -defined the carrier of F -valued Function-like non empty total V18( the carrier of G, the carrier of F) M2( bool [: the carrier of G, the carrier of F:])
[: the carrier of G, the carrier of F:] is set
bool [: the carrier of G, the carrier of F:] is set
(Obj (o * b)) . f2 is M2( the carrier of F)
(s * b) . f2 is M2( the carrier of F)
Obj (s * b) is Relation-like the carrier of G -defined the carrier of F -valued Function-like non empty total V18( the carrier of G, the carrier of F) M2( bool [: the carrier of G, the carrier of F:])
(Obj (s * b)) . f2 is M2( the carrier of F)
b . f2 is M2( the carrier of C)
Obj b is Relation-like the carrier of G -defined the carrier of C -valued Function-like non empty total V18( the carrier of G, the carrier of C) M2( bool [: the carrier of G, the carrier of C:])
[: the carrier of G, the carrier of C:] is set
bool [: the carrier of G, the carrier of C:] is set
(Obj b) . f2 is M2( the carrier of C)
c₇ . (b . f2) is Morphism of o . (b . f2),s . (b . f2)
o . (b . f2) is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . (b . f2) is M2( the carrier of F)
s . (b . f2) is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj s) . (b . f2) is M2( the carrier of F)
(G,C,F,o,s,b,c₇) . f2 is set
c₇ * (Obj b) is Relation-like the carrier of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier of G, the carrier' of F) M2( bool [: the carrier of G, the carrier' of F:])
[: the carrier of G, the carrier' of F:] is set
bool [: the carrier of G, the carrier' of F:] is set
(c₇ * (Obj b)) . f2 is M2( the carrier' of F)
c₇ . ((Obj b) . f2) is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) transformation of o,s
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,o,s,b,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) transformation of c₇ * o,c₇ * s
f2 is M2( the carrier of C)
(C,F,G,o,s,b,c₇) . f2 is Morphism of (c₇ * o) . f2,(c₇ * s) . f2
(c₇ * o) . f2 is M2( the carrier of G)
the carrier of G is non empty set
Obj (c₇ * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (c₇ * o)) . f2 is M2( the carrier of G)
(c₇ * s) . f2 is M2( the carrier of G)
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * s)) . f2 is M2( the carrier of G)
o . f2 is M2( the carrier of F)
the carrier of F is non empty set
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . f2 is M2( the carrier of F)
s . f2 is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj s) . f2 is M2( the carrier of F)
b . f2 is Morphism of o . f2,s . f2
c₇ /. (b . f2) is Morphism of c₇ . (o . f2),c₇ . (s . f2)
c₇ . (o . f2) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj c₇) . (o . f2) is M2( the carrier of G)
c₇ . (s . f2) is M2( the carrier of G)
(Obj c₇) . (s . f2) is M2( the carrier of G)
Hom ((o . f2),(s . f2)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . f2 & cod b₁ = s . f2 ) } is set
(C,F,G,o,s,b,c₇) . f2 is set
c₇ * b is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) M2( bool [: the carrier of C, the carrier' of G:])
[: the carrier of C, the carrier' of G:] is set
bool [: the carrier of C, the carrier' of G:] is set
(c₇ * b) . f2 is M2( the carrier' of G)
b . f2 is set
c₇ . (b . f2) is set
c₇ . (b . f2) is M2( the carrier' of G)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
the carrier of C is non empty set
the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s
the carrier of F is non empty set
the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇
b * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) transformation of b * o,b * s
(C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) transformation of b * s,c₇ * s
(C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) `*` (C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) transformation of b * o,c₇ * s
g is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) transformation of b * o,c₇ * s
h is M2( the carrier of C)
f is M2( the carrier of C)
Hom (h,f) is M2( bool the carrier' of C)
bool the carrier' of C is set
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = h & cod b₁ = f ) } is set
(b * o) . h is M2( the carrier of G)
the carrier of G is non empty set
Obj (b * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (b * o)) . h is M2( the carrier of G)
(b * o) . f is M2( the carrier of G)
(Obj (b * o)) . f is M2( the carrier of G)
(c₇ * s) . f is M2( the carrier of G)
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * s)) . f is M2( the carrier of G)
g . f is Morphism of (b * o) . f,(c₇ * s) . f
(c₇ * s) . h is M2( the carrier of G)
(Obj (c₇ * s)) . h is M2( the carrier of G)
g . h is Morphism of (b * o) . h,(c₇ * s) . h
s . f is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj s) . f is M2( the carrier of F)
b . (s . f) is M2( the carrier of G)
Obj b is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj b) . (s . f) is M2( the carrier of G)
c₇ . (s . f) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj c₇) . (s . f) is M2( the carrier of G)
Hom ((b . (s . f)),(c₇ . (s . f))) is M2( bool the carrier' of G)
bool the carrier' of G is set
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (s . f) & cod b₁ = c₇ . (s . f) ) } is set
Hom (((b * o) . h),((c₇ * s) . h)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (b * o) . h & cod b₁ = (c₇ * s) . h ) } is set
(b * s) . f is M2( the carrier of G)
Obj (b * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (b * s)) . f is M2( the carrier of G)
Hom (((b * o) . f),((b * s) . f)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (b * o) . f & cod b₁ = (b * s) . f ) } is set
Hom (((b * o) . f),((c₇ * s) . f)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (b * o) . f & cod b₁ = (c₇ * s) . f ) } is set
Hom (((c₇ * s) . h),((c₇ * s) . f)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (c₇ * s) . h & cod b₁ = (c₇ * s) . f ) } is set
o . f is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj o) . f is M2( the carrier of F)
Hom ((o . f),(s . f)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . f & cod b₁ = s . f ) } is set
b . (o . f) is M2( the carrier of G)
(Obj b) . (o . f) is M2( the carrier of G)
Hom ((b . (o . f)),(b . (s . f))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (o . f) & cod b₁ = b . (s . f) ) } is set
Hom ((b . (o . f)),(c₇ . (s . f))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (o . f) & cod b₁ = c₇ . (s . f) ) } is set
Hom (((b * s) . f),((c₇ * s) . f)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (b * s) . f & cod b₁ = (c₇ * s) . f ) } is set
(b * s) . h is M2( the carrier of G)
(Obj (b * s)) . h is M2( the carrier of G)
Hom (((b * o) . h),((b * s) . h)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (b * o) . h & cod b₁ = (b * s) . h ) } is set
Hom (((b * s) . h),((c₇ * s) . h)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (b * s) . h & cod b₁ = (c₇ * s) . h ) } is set
o . h is M2( the carrier of F)
(Obj o) . h is M2( the carrier of F)
s . h is M2( the carrier of F)
(Obj s) . h is M2( the carrier of F)
Hom ((o . h),(s . h)) is M2( bool the carrier' of F)
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . h & cod b₁ = s . h ) } is set
b . (o . h) is M2( the carrier of G)
(Obj b) . (o . h) is M2( the carrier of G)
b . (s . h) is M2( the carrier of G)
(Obj b) . (s . h) is M2( the carrier of G)
Hom ((b . (o . h)),(b . (s . h))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (o . h) & cod b₁ = b . (s . h) ) } is set
t9 is Morphism of h,f
(b * o) /. t9 is Morphism of (b * o) . h,(b * o) . f
(g . f) * ((b * o) /. t9) is Morphism of (b * o) . h,(c₇ * s) . f
(c₇ * s) /. t9 is Morphism of (c₇ * s) . h,(c₇ * s) . f
((c₇ * s) /. t9) * (g . h) is Morphism of (b * o) . h,(c₇ * s) . f
Hom ((s . h),(s . f)) is M2( bool the carrier' of F)
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = s . h & cod b₁ = s . f ) } is set
Hom ((b . (s . h)),(b . (s . f))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (s . h) & cod b₁ = b . (s . f) ) } is set
Hom ((o . h),(o . f)) is M2( bool the carrier' of F)
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . h & cod b₁ = o . f ) } is set
Hom ((b . (o . h)),(b . (o . f))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (o . h) & cod b₁ = b . (o . f) ) } is set
c₇ . (s . h) is M2( the carrier of G)
(Obj c₇) . (s . h) is M2( the carrier of G)
Hom ((b . (s . h)),(c₇ . (s . h))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (s . h) & cod b₁ = c₇ . (s . h) ) } is set
Hom ((b . (o . h)),(c₇ . (s . h))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = b . (o . h) & cod b₁ = c₇ . (s . h) ) } is set
Hom ((c₇ . (s . h)),(c₇ . (s . f))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = c₇ . (s . h) & cod b₁ = c₇ . (s . f) ) } is set
Hom (((b * o) . h),((b * o) . f)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (b * o) . h & cod b₁ = (b * o) . f ) } is set
(g . f) (*) ((b * o) /. t9) is M2( the carrier' of G)
o /. t9 is Morphism of o . h,o . f
b /. (o /. t9) is Morphism of b . (o . h),b . (o . f)
(g . f) (*) (b /. (o /. t9)) is M2( the carrier' of G)
(C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . f is Morphism of (b * o) . f,(b * s) . f
(C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . f is Morphism of (b * s) . f,(c₇ * s) . f
((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . f) * ((C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . f) is Morphism of (b * o) . f,(c₇ * s) . f
(((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . f) * ((C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . f)) (*) (b /. (o /. t9)) is M2( the carrier' of G)
((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . f) (*) ((C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . f) is M2( the carrier' of G)
(((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . f) (*) ((C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . f)) (*) (b /. (o /. t9)) is M2( the carrier' of G)
the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f is Morphism of o . f,s . f
b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f) is Morphism of b . (o . f),b . (s . f)
((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . f) (*) (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f)) is M2( the carrier' of G)
(((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . f) (*) (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f))) (*) (b /. (o /. t9)) is M2( the carrier' of G)
the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f) is Morphism of b . (s . f),c₇ . (s . f)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) (*) (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f)) is M2( the carrier' of G)
(( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) (*) (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f))) (*) (b /. (o /. t9)) is M2( the carrier' of G)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f)) is Morphism of b . (o . f),c₇ . (s . f)
(( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f))) (*) (b /. (o /. t9)) is M2( the carrier' of G)
(( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f))) * (b /. (o /. t9)) is Morphism of b . (o . h),c₇ . (s . f)
(b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f)) * (b /. (o /. t9)) is Morphism of b . (o . h),b . (s . f)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * ((b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f)) * (b /. (o /. t9))) is Morphism of b . (o . h),c₇ . (s . f)
( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f) * (o /. t9) is Morphism of o . h,s . f
b /. (( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f) * (o /. t9)) is Morphism of b . (o . h),b . (s . f)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * (b /. (( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . f) * (o /. t9))) is Morphism of b . (o . h),c₇ . (s . f)
the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h is Morphism of o . h,s . h
s /. t9 is Morphism of s . h,s . f
(s /. t9) * ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h) is Morphism of o . h,s . f
b /. ((s /. t9) * ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h)) is Morphism of b . (o . h),b . (s . f)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * (b /. ((s /. t9) * ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h))) is Morphism of b . (o . h),c₇ . (s . f)
b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h) is Morphism of b . (o . h),b . (s . h)
b /. (s /. t9) is Morphism of b . (s . h),b . (s . f)
(b /. (s /. t9)) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h)) is Morphism of b . (o . h),b . (s . f)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * ((b /. (s /. t9)) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h))) is Morphism of b . (o . h),c₇ . (s . f)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * (b /. (s /. t9)) is Morphism of b . (s . h),c₇ . (s . f)
(( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . f)) * (b /. (s /. t9))) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h)) is Morphism of b . (o . h),c₇ . (s . f)
the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . h) is Morphism of b . (s . h),c₇ . (s . h)
c₇ /. (s /. t9) is Morphism of c₇ . (s . h),c₇ . (s . f)
(c₇ /. (s /. t9)) * ( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . h)) is Morphism of b . (s . h),c₇ . (s . f)
((c₇ /. (s /. t9)) * ( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . h))) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h)) is Morphism of b . (o . h),c₇ . (s . f)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . h)) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h)) is Morphism of b . (o . h),c₇ . (s . h)
(c₇ /. (s /. t9)) * (( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . h)) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h))) is Morphism of b . (o . h),c₇ . (s . f)
(c₇ /. (s /. t9)) (*) (( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . h)) * (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h))) is M2( the carrier' of G)
( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . h)) (*) (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h)) is M2( the carrier' of G)
(c₇ /. (s /. t9)) (*) (( the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇ . (s . h)) (*) (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h))) is M2( the carrier' of G)
(C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . h is Morphism of (b * s) . h,(c₇ * s) . h
((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . h) (*) (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h)) is M2( the carrier' of G)
(c₇ /. (s /. t9)) (*) (((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . h) (*) (b /. ( the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s . h))) is M2( the carrier' of G)
(C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . h is Morphism of (b * o) . h,(b * s) . h
((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . h) (*) ((C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . h) is M2( the carrier' of G)
(c₇ /. (s /. t9)) (*) (((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . h) (*) ((C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . h)) is M2( the carrier' of G)
((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . h) * ((C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . h) is Morphism of (b * o) . h,(c₇ * s) . h
(c₇ /. (s /. t9)) (*) (((C,F,G,b,c₇,s, the Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇) . h) * ((C,F,G,o,s, the Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s,b) . h)) is M2( the carrier' of G)
(c₇ /. (s /. t9)) (*) (g . h) is M2( the carrier' of G)
((c₇ * s) /. t9) (*) (g . h) is M2( the carrier' of G)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
the carrier of C is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
b is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
(C,F,G,o,s,b,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) transformation of c₇ * o,c₇ * s
c₇ * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is M2( the carrier of C)
f1 is M2( the carrier of C)
Hom (f2,f1) is M2( bool the carrier' of C)
bool the carrier' of C is set
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = f2 & cod b₁ = f1 ) } is set
(c₇ * o) . f2 is M2( the carrier of G)
the carrier of G is non empty set
Obj (c₇ * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (c₇ * o)) . f2 is M2( the carrier of G)
(c₇ * o) . f1 is M2( the carrier of G)
(Obj (c₇ * o)) . f1 is M2( the carrier of G)
(c₇ * s) . f1 is M2( the carrier of G)
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * s)) . f1 is M2( the carrier of G)
(C,F,G,o,s,b,c₇) . f1 is Morphism of (c₇ * o) . f1,(c₇ * s) . f1
(c₇ * s) . f2 is M2( the carrier of G)
(Obj (c₇ * s)) . f2 is M2( the carrier of G)
(C,F,G,o,s,b,c₇) . f2 is Morphism of (c₇ * o) . f2,(c₇ * s) . f2
Hom (((c₇ * o) . f2),((c₇ * o) . f1)) is M2( bool the carrier' of G)
bool the carrier' of G is set
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (c₇ * o) . f2 & cod b₁ = (c₇ * o) . f1 ) } is set
Hom (((c₇ * s) . f2),((c₇ * s) . f1)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (c₇ * s) . f2 & cod b₁ = (c₇ * s) . f1 ) } is set
Hom (((c₇ * o) . f2),((c₇ * s) . f2)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (c₇ * o) . f2 & cod b₁ = (c₇ * s) . f2 ) } is set
g is Morphism of f2,f1
(c₇ * o) /. g is Morphism of (c₇ * o) . f2,(c₇ * o) . f1
((C,F,G,o,s,b,c₇) . f1) * ((c₇ * o) /. g) is Morphism of (c₇ * o) . f2,(c₇ * s) . f1
(c₇ * s) /. g is Morphism of (c₇ * s) . f2,(c₇ * s) . f1
((c₇ * s) /. g) * ((C,F,G,o,s,b,c₇) . f2) is Morphism of (c₇ * o) . f2,(c₇ * s) . f1
o . f1 is M2( the carrier of F)
the carrier of F is non empty set
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . f1 is M2( the carrier of F)
s . f1 is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj s) . f1 is M2( the carrier of F)
Hom ((o . f1),(s . f1)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . f1 & cod b₁ = s . f1 ) } is set
c₇ . (o . f1) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj c₇) . (o . f1) is M2( the carrier of G)
c₇ . (s . f1) is M2( the carrier of G)
(Obj c₇) . (s . f1) is M2( the carrier of G)
Hom ((c₇ . (o . f1)),(c₇ . (s . f1))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = c₇ . (o . f1) & cod b₁ = c₇ . (s . f1) ) } is set
o . f2 is M2( the carrier of F)
(Obj o) . f2 is M2( the carrier of F)
s . f2 is M2( the carrier of F)
(Obj s) . f2 is M2( the carrier of F)
Hom ((o . f2),(s . f2)) is M2( bool the carrier' of F)
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . f2 & cod b₁ = s . f2 ) } is set
c₇ . (o . f2) is M2( the carrier of G)
(Obj c₇) . (o . f2) is M2( the carrier of G)
c₇ . (s . f2) is M2( the carrier of G)
(Obj c₇) . (s . f2) is M2( the carrier of G)
Hom ((c₇ . (o . f2)),(c₇ . (s . f2))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = c₇ . (o . f2) & cod b₁ = c₇ . (s . f2) ) } is set
Hom ((s . f2),(s . f1)) is M2( bool the carrier' of F)
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = s . f2 & cod b₁ = s . f1 ) } is set
Hom ((c₇ . (s . f2)),(c₇ . (s . f1))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = c₇ . (s . f2) & cod b₁ = c₇ . (s . f1) ) } is set
Hom ((o . f2),(o . f1)) is M2( bool the carrier' of F)
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . f2 & cod b₁ = o . f1 ) } is set
Hom ((c₇ . (o . f2)),(c₇ . (o . f1))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = c₇ . (o . f2) & cod b₁ = c₇ . (o . f1) ) } is set
Hom (((c₇ * o) . f1),((c₇ * s) . f1)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (c₇ * o) . f1 & cod b₁ = (c₇ * s) . f1 ) } is set
((C,F,G,o,s,b,c₇) . f1) (*) ((c₇ * o) /. g) is M2( the carrier' of G)
o /. g is Morphism of o . f2,o . f1
c₇ /. (o /. g) is Morphism of c₇ . (o . f2),c₇ . (o . f1)
((C,F,G,o,s,b,c₇) . f1) (*) (c₇ /. (o /. g)) is M2( the carrier' of G)
b . f1 is Morphism of o . f1,s . f1
c₇ /. (b . f1) is Morphism of c₇ . (o . f1),c₇ . (s . f1)
(c₇ /. (b . f1)) (*) (c₇ /. (o /. g)) is M2( the carrier' of G)
(c₇ /. (b . f1)) * (c₇ /. (o /. g)) is Morphism of c₇ . (o . f2),c₇ . (s . f1)
(b . f1) * (o /. g) is Morphism of o . f2,s . f1
c₇ /. ((b . f1) * (o /. g)) is Morphism of c₇ . (o . f2),c₇ . (s . f1)
b . f2 is Morphism of o . f2,s . f2
s /. g is Morphism of s . f2,s . f1
(s /. g) * (b . f2) is Morphism of o . f2,s . f1
c₇ /. ((s /. g) * (b . f2)) is Morphism of c₇ . (o . f2),c₇ . (s . f1)
c₇ /. (b . f2) is Morphism of c₇ . (o . f2),c₇ . (s . f2)
c₇ /. (s /. g) is Morphism of c₇ . (s . f2),c₇ . (s . f1)
(c₇ /. (s /. g)) * (c₇ /. (b . f2)) is Morphism of c₇ . (o . f2),c₇ . (s . f1)
(c₇ /. (s /. g)) (*) (c₇ /. (b . f2)) is M2( the carrier' of G)
(c₇ /. (s /. g)) (*) ((C,F,G,o,s,b,c₇) . f2) is M2( the carrier' of G)
((c₇ * s) /. g) (*) ((C,F,G,o,s,b,c₇) . f2) is M2( the carrier' of G)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,o,s,b,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,c₇ * s
f2 is M2( the carrier of C)
(C,F,G,o,s,b,c₇) . f2 is Morphism of (c₇ * o) . f2,(c₇ * s) . f2
(c₇ * o) . f2 is M2( the carrier of G)
the carrier of G is non empty set
Obj (c₇ * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (c₇ * o)) . f2 is M2( the carrier of G)
(c₇ * s) . f2 is M2( the carrier of G)
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * s)) . f2 is M2( the carrier of G)
o . f2 is M2( the carrier of F)
the carrier of F is non empty set
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . f2 is M2( the carrier of F)
s . f2 is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj s) . f2 is M2( the carrier of F)
b . f2 is Morphism of o . f2,s . f2
c₇ /. (b . f2) is Morphism of c₇ . (o . f2),c₇ . (s . f2)
c₇ . (o . f2) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj c₇) . (o . f2) is M2( the carrier of G)
c₇ . (s . f2) is M2( the carrier of G)
(Obj c₇) . (s . f2) is M2( the carrier of G)
(C,F,G,o,s,b,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) transformation of c₇ * o,c₇ * s
(C,F,G,o,s,b,c₇) . f2 is Morphism of (c₇ * o) . f2,(c₇ * s) . f2
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of F is non empty set
b is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
c₇ is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of o,s
(C,F,G,o,s,b,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) transformation of o * b,s * b
the carrier of C is non empty set
o * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
s * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is M2( the carrier of C)
f1 is M2( the carrier of C)
Hom (f2,f1) is M2( bool the carrier' of C)
bool the carrier' of C is set
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = f2 & cod b₁ = f1 ) } is set
(o * b) . f2 is M2( the carrier of G)
the carrier of G is non empty set
Obj (o * b) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (o * b)) . f2 is M2( the carrier of G)
(o * b) . f1 is M2( the carrier of G)
(Obj (o * b)) . f1 is M2( the carrier of G)
(s * b) . f1 is M2( the carrier of G)
Obj (s * b) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (s * b)) . f1 is M2( the carrier of G)
(C,F,G,o,s,b,c₇) . f1 is Morphism of (o * b) . f1,(s * b) . f1
(s * b) . f2 is M2( the carrier of G)
(Obj (s * b)) . f2 is M2( the carrier of G)
(C,F,G,o,s,b,c₇) . f2 is Morphism of (o * b) . f2,(s * b) . f2
Hom (((o * b) . f1),((s * b) . f1)) is M2( bool the carrier' of G)
bool the carrier' of G is set
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (o * b) . f1 & cod b₁ = (s * b) . f1 ) } is set
Hom (((o * b) . f2),((s * b) . f2)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (o * b) . f2 & cod b₁ = (s * b) . f2 ) } is set
Hom (((s * b) . f2),((s * b) . f1)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (s * b) . f2 & cod b₁ = (s * b) . f1 ) } is set
g is Morphism of f2,f1
(o * b) /. g is Morphism of (o * b) . f2,(o * b) . f1
((C,F,G,o,s,b,c₇) . f1) * ((o * b) /. g) is Morphism of (o * b) . f2,(s * b) . f1
(s * b) /. g is Morphism of (s * b) . f2,(s * b) . f1
((s * b) /. g) * ((C,F,G,o,s,b,c₇) . f2) is Morphism of (o * b) . f2,(s * b) . f1
b . f2 is M2( the carrier of F)
Obj b is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj b) . f2 is M2( the carrier of F)
b . f1 is M2( the carrier of F)
(Obj b) . f1 is M2( the carrier of F)
Hom ((b . f2),(b . f1)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = b . f2 & cod b₁ = b . f1 ) } is set
o . (b . f2) is M2( the carrier of G)
Obj o is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj o) . (b . f2) is M2( the carrier of G)
o . (b . f1) is M2( the carrier of G)
(Obj o) . (b . f1) is M2( the carrier of G)
Hom ((o . (b . f2)),(o . (b . f1))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = o . (b . f2) & cod b₁ = o . (b . f1) ) } is set
s . (b . f2) is M2( the carrier of G)
Obj s is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj s) . (b . f2) is M2( the carrier of G)
Hom ((o . (b . f2)),(s . (b . f2))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = o . (b . f2) & cod b₁ = s . (b . f2) ) } is set
s . (b . f1) is M2( the carrier of G)
(Obj s) . (b . f1) is M2( the carrier of G)
Hom ((o . (b . f1)),(s . (b . f1))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = o . (b . f1) & cod b₁ = s . (b . f1) ) } is set
Hom ((s . (b . f2)),(s . (b . f1))) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = s . (b . f2) & cod b₁ = s . (b . f1) ) } is set
Hom (((o * b) . f2),((o * b) . f1)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = (o * b) . f2 & cod b₁ = (o * b) . f1 ) } is set
((C,F,G,o,s,b,c₇) . f1) (*) ((o * b) /. g) is M2( the carrier' of G)
b /. g is Morphism of b . f2,b . f1
o /. (b /. g) is Morphism of o . (b . f2),o . (b . f1)
((C,F,G,o,s,b,c₇) . f1) (*) (o /. (b /. g)) is M2( the carrier' of G)
c₇ . (b . f1) is Morphism of o . (b . f1),s . (b . f1)
(c₇ . (b . f1)) (*) (o /. (b /. g)) is M2( the carrier' of G)
(c₇ . (b . f1)) * (o /. (b /. g)) is Morphism of o . (b . f2),s . (b . f1)
c₇ . (b . f2) is Morphism of o . (b . f2),s . (b . f2)
s /. (b /. g) is Morphism of s . (b . f2),s . (b . f1)
(s /. (b /. g)) * (c₇ . (b . f2)) is Morphism of o . (b . f2),s . (b . f1)
(s /. (b /. g)) (*) (c₇ . (b . f2)) is M2( the carrier' of G)
(s /. (b /. g)) (*) ((C,F,G,o,s,b,c₇) . f2) is M2( the carrier' of G)
((s * b) /. g) (*) ((C,F,G,o,s,b,c₇) . f2) is M2( the carrier' of G)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
the carrier of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of G -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of G, the carrier' of C) Functor of G,C
o * b is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
s * b is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
c₇ is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s
(G,C,F,o,s,b,c₇) is Relation-like the carrier of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier of G, the carrier' of F) natural_transformation of o * b,s * b
f2 is M2( the carrier of G)
(G,C,F,o,s,b,c₇) . f2 is Morphism of (o * b) . f2,(s * b) . f2
(o * b) . f2 is M2( the carrier of F)
the carrier of F is non empty set
Obj (o * b) is Relation-like the carrier of G -defined the carrier of F -valued Function-like non empty total V18( the carrier of G, the carrier of F) M2( bool [: the carrier of G, the carrier of F:])
[: the carrier of G, the carrier of F:] is set
bool [: the carrier of G, the carrier of F:] is set
(Obj (o * b)) . f2 is M2( the carrier of F)
(s * b) . f2 is M2( the carrier of F)
Obj (s * b) is Relation-like the carrier of G -defined the carrier of F -valued Function-like non empty total V18( the carrier of G, the carrier of F) M2( bool [: the carrier of G, the carrier of F:])
(Obj (s * b)) . f2 is M2( the carrier of F)
b . f2 is M2( the carrier of C)
Obj b is Relation-like the carrier of G -defined the carrier of C -valued Function-like non empty total V18( the carrier of G, the carrier of C) M2( bool [: the carrier of G, the carrier of C:])
[: the carrier of G, the carrier of C:] is set
bool [: the carrier of G, the carrier of C:] is set
(Obj b) . f2 is M2( the carrier of C)
c₇ . (b . f2) is Morphism of o . (b . f2),s . (b . f2)
o . (b . f2) is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . (b . f2) is M2( the carrier of F)
s . (b . f2) is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj s) . (b . f2) is M2( the carrier of F)
(G,C,F,o,s,b,c₇) is Relation-like the carrier of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier of G, the carrier' of F) transformation of o * b,s * b
(G,C,F,o,s,b,c₇) . f2 is Morphism of (o * b) . f2,(s * b) . f2
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
s is M2( the carrier of F)
G . s is M2( the carrier of C)
the carrier of C is non empty set
Obj G is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
[: the carrier of F, the carrier of C:] is set
bool [: the carrier of F, the carrier of C:] is set
(Obj G) . s is M2( the carrier of C)
o . s is M2( the carrier of C)
Obj o is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
(Obj o) . s is M2( the carrier of C)
Hom ((G . s),(o . s)) is M2( bool the carrier' of C)
bool the carrier' of C is set
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = G . s & cod b₁ = o . s ) } is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
s is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G,o
b is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G,o
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ is Relation-like the carrier' of G -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of G, the carrier' of C) Functor of G,C
c₇ * o is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
c₇ * s is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
c₇ * b is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
f2 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of o,s
(F,G,C,o,s,f2,c₇) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of c₇ * o,c₇ * s
f1 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of s,b
f1 `*` f2 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of o,b
(F,G,C,o,b,(f1 `*` f2),c₇) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of c₇ * o,c₇ * b
(F,G,C,s,b,f1,c₇) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of c₇ * s,c₇ * b
(F,G,C,s,b,f1,c₇) `*` (F,G,C,o,s,f2,c₇) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of c₇ * o,c₇ * b
g is M2( the carrier of F)
o . g is M2( the carrier of G)
the carrier of G is non empty set
Obj o is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj o) . g is M2( the carrier of G)
c₇ . (o . g) is M2( the carrier of C)
the carrier of C is non empty set
Obj c₇ is Relation-like the carrier of G -defined the carrier of C -valued Function-like non empty total V18( the carrier of G, the carrier of C) M2( bool [: the carrier of G, the carrier of C:])
[: the carrier of G, the carrier of C:] is set
bool [: the carrier of G, the carrier of C:] is set
(Obj c₇) . (o . g) is M2( the carrier of C)
(c₇ * o) . g is M2( the carrier of C)
Obj (c₇ * o) is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
[: the carrier of F, the carrier of C:] is set
bool [: the carrier of F, the carrier of C:] is set
(Obj (c₇ * o)) . g is M2( the carrier of C)
s . g is M2( the carrier of G)
Obj s is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj s) . g is M2( the carrier of G)
c₇ . (s . g) is M2( the carrier of C)
(Obj c₇) . (s . g) is M2( the carrier of C)
(c₇ * s) . g is M2( the carrier of C)
Obj (c₇ * s) is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
(Obj (c₇ * s)) . g is M2( the carrier of C)
b . g is M2( the carrier of G)
Obj b is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj b) . g is M2( the carrier of G)
c₇ . (b . g) is M2( the carrier of C)
(Obj c₇) . (b . g) is M2( the carrier of C)
(c₇ * b) . g is M2( the carrier of C)
Obj (c₇ * b) is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
(Obj (c₇ * b)) . g is M2( the carrier of C)
Hom ((o . g),(s . g)) is M2( bool the carrier' of G)
bool the carrier' of G is set
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = o . g & cod b₁ = s . g ) } is set
Hom ((s . g),(b . g)) is M2( bool the carrier' of G)
{ b₁ where b₁ is M2( the carrier' of G) : ( dom b₁ = s . g & cod b₁ = b . g ) } is set
f1 . g is Morphism of s . g,b . g
c₇ /. (f1 . g) is Morphism of c₇ . (s . g),c₇ . (b . g)
(F,G,C,s,b,f1,c₇) . g is Morphism of (c₇ * s) . g,(c₇ * b) . g
f2 . g is Morphism of o . g,s . g
c₇ /. (f2 . g) is Morphism of c₇ . (o . g),c₇ . (s . g)
(F,G,C,o,s,f2,c₇) . g is Morphism of (c₇ * o) . g,(c₇ * s) . g
(F,G,C,o,b,(f1 `*` f2),c₇) . g is Morphism of (c₇ * o) . g,(c₇ * b) . g
(f1 `*` f2) . g is Morphism of o . g,b . g
c₇ /. ((f1 `*` f2) . g) is Morphism of c₇ . (o . g),c₇ . (b . g)
(f1 . g) * (f2 . g) is Morphism of o . g,b . g
c₇ /. ((f1 . g) * (f2 . g)) is Morphism of c₇ . (o . g),c₇ . (b . g)
(c₇ /. (f1 . g)) * (c₇ /. (f2 . g)) is Morphism of c₇ . (o . g),c₇ . (b . g)
((F,G,C,s,b,f1,c₇) `*` (F,G,C,o,s,f2,c₇)) . g is Morphism of (c₇ * o) . g,(c₇ * b) . g
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
s * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of s,b
(C,F,G,s,b,o,f2) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,b * o
f1 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇
f1 `*` f2 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of s,c₇
(C,F,G,s,c₇,o,(f1 `*` f2)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,c₇ * o
(C,F,G,b,c₇,o,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * o,c₇ * o
(C,F,G,b,c₇,o,f1) `*` (C,F,G,s,b,o,f2) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,c₇ * o
g is M2( the carrier of C)
o . g is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . g is M2( the carrier of F)
s . (o . g) is M2( the carrier of G)
the carrier of G is non empty set
Obj s is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj s) . (o . g) is M2( the carrier of G)
(s * o) . g is M2( the carrier of G)
Obj (s * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (s * o)) . g is M2( the carrier of G)
b . (o . g) is M2( the carrier of G)
Obj b is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj b) . (o . g) is M2( the carrier of G)
(b * o) . g is M2( the carrier of G)
Obj (b * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (b * o)) . g is M2( the carrier of G)
c₇ . (o . g) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj c₇) . (o . g) is M2( the carrier of G)
(c₇ * o) . g is M2( the carrier of G)
Obj (c₇ * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * o)) . g is M2( the carrier of G)
f1 . (o . g) is Morphism of b . (o . g),c₇ . (o . g)
(C,F,G,b,c₇,o,f1) . g is Morphism of (b * o) . g,(c₇ * o) . g
f2 . (o . g) is Morphism of s . (o . g),b . (o . g)
(C,F,G,s,b,o,f2) . g is Morphism of (s * o) . g,(b * o) . g
(C,F,G,s,c₇,o,(f1 `*` f2)) . g is Morphism of (s * o) . g,(c₇ * o) . g
(f1 `*` f2) . (o . g) is Morphism of s . (o . g),c₇ . (o . g)
(f1 . (o . g)) * (f2 . (o . g)) is Morphism of s . (o . g),c₇ . (o . g)
((C,F,G,b,c₇,o,f1) `*` (C,F,G,s,b,o,f2)) . g is Morphism of (s * o) . g,(c₇ * o) . g
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
the carrier of G is non empty set
o is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of o is non empty set
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
c₇ * b is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of F, the carrier' of o) V18( the carrier' of F, the carrier' of o) Functor of F,o
f2 is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
f2 * b is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of F, the carrier' of o) V18( the carrier' of F, the carrier' of o) Functor of F,o
f1 is Relation-like the carrier of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier of G, the carrier' of o) natural_transformation of c₇,f2
(F,G,o,c₇,f2,b,f1) is Relation-like the carrier of F -defined the carrier' of o -valued Function-like non empty total V18( the carrier of F, the carrier' of o) natural_transformation of c₇ * b,f2 * b
the carrier of F is non empty set
(C,F,o,(c₇ * b),(f2 * b),s,(F,G,o,c₇,f2,b,f1)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (c₇ * b) * s,(f2 * b) * s
(c₇ * b) * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
(f2 * b) * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
(C,G,o,c₇,f2,(b * s),f1) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of c₇ * (b * s),f2 * (b * s)
c₇ * (b * s) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
f2 * (b * s) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
h is M2( the carrier of C)
(C,F,o,(c₇ * b),(f2 * b),s,(F,G,o,c₇,f2,b,f1)) . h is Morphism of ((c₇ * b) * s) . h,((f2 * b) * s) . h
((c₇ * b) * s) . h is M2( the carrier of o)
the carrier of o is non empty set
Obj ((c₇ * b) * s) is Relation-like the carrier of C -defined the carrier of o -valued Function-like non empty total V18( the carrier of C, the carrier of o) M2( bool [: the carrier of C, the carrier of o:])
[: the carrier of C, the carrier of o:] is set
bool [: the carrier of C, the carrier of o:] is set
(Obj ((c₇ * b) * s)) . h is M2( the carrier of o)
((f2 * b) * s) . h is M2( the carrier of o)
Obj ((f2 * b) * s) is Relation-like the carrier of C -defined the carrier of o -valued Function-like non empty total V18( the carrier of C, the carrier of o) M2( bool [: the carrier of C, the carrier of o:])
(Obj ((f2 * b) * s)) . h is M2( the carrier of o)
s . h is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj s) . h is M2( the carrier of F)
(F,G,o,c₇,f2,b,f1) . (s . h) is Morphism of (c₇ * b) . (s . h),(f2 * b) . (s . h)
(c₇ * b) . (s . h) is M2( the carrier of o)
Obj (c₇ * b) is Relation-like the carrier of F -defined the carrier of o -valued Function-like non empty total V18( the carrier of F, the carrier of o) M2( bool [: the carrier of F, the carrier of o:])
[: the carrier of F, the carrier of o:] is set
bool [: the carrier of F, the carrier of o:] is set
(Obj (c₇ * b)) . (s . h) is M2( the carrier of o)
(f2 * b) . (s . h) is M2( the carrier of o)
Obj (f2 * b) is Relation-like the carrier of F -defined the carrier of o -valued Function-like non empty total V18( the carrier of F, the carrier of o) M2( bool [: the carrier of F, the carrier of o:])
(Obj (f2 * b)) . (s . h) is M2( the carrier of o)
b . (s . h) is M2( the carrier of G)
Obj b is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj b) . (s . h) is M2( the carrier of G)
f1 . (b . (s . h)) is Morphism of c₇ . (b . (s . h)),f2 . (b . (s . h))
c₇ . (b . (s . h)) is M2( the carrier of o)
Obj c₇ is Relation-like the carrier of G -defined the carrier of o -valued Function-like non empty total V18( the carrier of G, the carrier of o) M2( bool [: the carrier of G, the carrier of o:])
[: the carrier of G, the carrier of o:] is set
bool [: the carrier of G, the carrier of o:] is set
(Obj c₇) . (b . (s . h)) is M2( the carrier of o)
f2 . (b . (s . h)) is M2( the carrier of o)
Obj f2 is Relation-like the carrier of G -defined the carrier of o -valued Function-like non empty total V18( the carrier of G, the carrier of o) M2( bool [: the carrier of G, the carrier of o:])
(Obj f2) . (b . (s . h)) is M2( the carrier of o)
(b * s) . h is M2( the carrier of G)
Obj (b * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (b * s)) . h is M2( the carrier of G)
f1 . ((b * s) . h) is Morphism of c₇ . ((b * s) . h),f2 . ((b * s) . h)
c₇ . ((b * s) . h) is M2( the carrier of o)
(Obj c₇) . ((b * s) . h) is M2( the carrier of o)
f2 . ((b * s) . h) is M2( the carrier of o)
(Obj f2) . ((b * s) . h) is M2( the carrier of o)
g is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (c₇ * b) * s,(f2 * b) * s
g . h is Morphism of ((c₇ * b) * s) . h,((f2 * b) * s) . h
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
the carrier of G is non empty set
o is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of o is non empty set
s is Relation-like the carrier' of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) Functor of C,G
b is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
b * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
c₇ is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
f2 is Relation-like the carrier' of o -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of o, the carrier' of F) Functor of o,F
f2 * b is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
f2 * c₇ is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
f1 is Relation-like the carrier of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier of G, the carrier' of o) natural_transformation of b,c₇
(G,o,F,b,c₇,f1,f2) is Relation-like the carrier of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier of G, the carrier' of F) natural_transformation of f2 * b,f2 * c₇
(C,G,F,(f2 * b),(f2 * c₇),s,(G,o,F,b,c₇,f1,f2)) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (f2 * b) * s,(f2 * c₇) * s
(f2 * b) * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
(f2 * c₇) * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
(C,G,o,b,c₇,s,f1) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of b * s,c₇ * s
(C,o,F,(b * s),(c₇ * s),(C,G,o,b,c₇,s,f1),f2) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of f2 * (b * s),f2 * (c₇ * s)
f2 * (b * s) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
f2 * (c₇ * s) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
h is M2( the carrier of C)
s . h is M2( the carrier of G)
Obj s is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj s) . h is M2( the carrier of G)
b . (s . h) is M2( the carrier of o)
the carrier of o is non empty set
Obj b is Relation-like the carrier of G -defined the carrier of o -valued Function-like non empty total V18( the carrier of G, the carrier of o) M2( bool [: the carrier of G, the carrier of o:])
[: the carrier of G, the carrier of o:] is set
bool [: the carrier of G, the carrier of o:] is set
(Obj b) . (s . h) is M2( the carrier of o)
(b * s) . h is M2( the carrier of o)
Obj (b * s) is Relation-like the carrier of C -defined the carrier of o -valued Function-like non empty total V18( the carrier of C, the carrier of o) M2( bool [: the carrier of C, the carrier of o:])
[: the carrier of C, the carrier of o:] is set
bool [: the carrier of C, the carrier of o:] is set
(Obj (b * s)) . h is M2( the carrier of o)
c₇ . (s . h) is M2( the carrier of o)
Obj c₇ is Relation-like the carrier of G -defined the carrier of o -valued Function-like non empty total V18( the carrier of G, the carrier of o) M2( bool [: the carrier of G, the carrier of o:])
(Obj c₇) . (s . h) is M2( the carrier of o)
(c₇ * s) . h is M2( the carrier of o)
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of o -valued Function-like non empty total V18( the carrier of C, the carrier of o) M2( bool [: the carrier of C, the carrier of o:])
(Obj (c₇ * s)) . h is M2( the carrier of o)
(C,G,F,(f2 * b),(f2 * c₇),s,(G,o,F,b,c₇,f1,f2)) . h is Morphism of ((f2 * b) * s) . h,((f2 * c₇) * s) . h
((f2 * b) * s) . h is M2( the carrier of F)
the carrier of F is non empty set
Obj ((f2 * b) * s) is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj ((f2 * b) * s)) . h is M2( the carrier of F)
((f2 * c₇) * s) . h is M2( the carrier of F)
Obj ((f2 * c₇) * s) is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj ((f2 * c₇) * s)) . h is M2( the carrier of F)
(G,o,F,b,c₇,f1,f2) . (s . h) is Morphism of (f2 * b) . (s . h),(f2 * c₇) . (s . h)
(f2 * b) . (s . h) is M2( the carrier of F)
Obj (f2 * b) is Relation-like the carrier of G -defined the carrier of F -valued Function-like non empty total V18( the carrier of G, the carrier of F) M2( bool [: the carrier of G, the carrier of F:])
[: the carrier of G, the carrier of F:] is set
bool [: the carrier of G, the carrier of F:] is set
(Obj (f2 * b)) . (s . h) is M2( the carrier of F)
(f2 * c₇) . (s . h) is M2( the carrier of F)
Obj (f2 * c₇) is Relation-like the carrier of G -defined the carrier of F -valued Function-like non empty total V18( the carrier of G, the carrier of F) M2( bool [: the carrier of G, the carrier of F:])
(Obj (f2 * c₇)) . (s . h) is M2( the carrier of F)
f1 . (s . h) is Morphism of b . (s . h),c₇ . (s . h)
f2 /. (f1 . (s . h)) is Morphism of f2 . (b . (s . h)),f2 . (c₇ . (s . h))
f2 . (b . (s . h)) is M2( the carrier of F)
Obj f2 is Relation-like the carrier of o -defined the carrier of F -valued Function-like non empty total V18( the carrier of o, the carrier of F) M2( bool [: the carrier of o, the carrier of F:])
[: the carrier of o, the carrier of F:] is set
bool [: the carrier of o, the carrier of F:] is set
(Obj f2) . (b . (s . h)) is M2( the carrier of F)
f2 . (c₇ . (s . h)) is M2( the carrier of F)
(Obj f2) . (c₇ . (s . h)) is M2( the carrier of F)
(C,G,o,b,c₇,s,f1) . h is Morphism of (b * s) . h,(c₇ * s) . h
f2 /. ((C,G,o,b,c₇,s,f1) . h) is Morphism of f2 . ((b * s) . h),f2 . ((c₇ * s) . h)
f2 . ((b * s) . h) is M2( the carrier of F)
(Obj f2) . ((b * s) . h) is M2( the carrier of F)
f2 . ((c₇ * s) . h) is M2( the carrier of F)
(Obj f2) . ((c₇ * s) . h) is M2( the carrier of F)
g is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (f2 * b) * s,(f2 * c₇) * s
g . h is Morphism of ((f2 * b) * s) . h,((f2 * c₇) * s) . h
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
the carrier of G is non empty set
o is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of o is non empty set
s is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
b is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
c₇ is Relation-like the carrier' of o -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of o, the carrier' of C) Functor of o,C
c₇ * s is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of G, the carrier' of C) V18( the carrier' of G, the carrier' of C) Functor of G,C
c₇ * b is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of G, the carrier' of C) V18( the carrier' of G, the carrier' of C) Functor of G,C
f2 is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
f2 * c₇ is Relation-like the carrier' of o -defined the carrier' of o -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of o, the carrier' of F) V18( the carrier' of o, the carrier' of F) Functor of o,F
f1 is Relation-like the carrier of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier of G, the carrier' of o) natural_transformation of s,b
(G,o,F,s,b,f1,(f2 * c₇)) is Relation-like the carrier of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier of G, the carrier' of F) natural_transformation of (f2 * c₇) * s,(f2 * c₇) * b
(f2 * c₇) * s is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
(f2 * c₇) * b is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
(G,o,C,s,b,f1,c₇) is Relation-like the carrier of G -defined the carrier' of C -valued Function-like non empty total V18( the carrier of G, the carrier' of C) natural_transformation of c₇ * s,c₇ * b
(G,C,F,(c₇ * s),(c₇ * b),(G,o,C,s,b,f1,c₇),f2) is Relation-like the carrier of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier of G, the carrier' of F) natural_transformation of f2 * (c₇ * s),f2 * (c₇ * b)
f2 * (c₇ * s) is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
f2 * (c₇ * b) is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) V18( the carrier' of G, the carrier' of F) Functor of G,F
h is M2( the carrier of G)
s . h is M2( the carrier of o)
the carrier of o is non empty set
Obj s is Relation-like the carrier of G -defined the carrier of o -valued Function-like non empty total V18( the carrier of G, the carrier of o) M2( bool [: the carrier of G, the carrier of o:])
[: the carrier of G, the carrier of o:] is set
bool [: the carrier of G, the carrier of o:] is set
(Obj s) . h is M2( the carrier of o)
c₇ . (s . h) is M2( the carrier of C)
the carrier of C is non empty set
Obj c₇ is Relation-like the carrier of o -defined the carrier of C -valued Function-like non empty total V18( the carrier of o, the carrier of C) M2( bool [: the carrier of o, the carrier of C:])
[: the carrier of o, the carrier of C:] is set
bool [: the carrier of o, the carrier of C:] is set
(Obj c₇) . (s . h) is M2( the carrier of C)
(c₇ * s) . h is M2( the carrier of C)
Obj (c₇ * s) is Relation-like the carrier of G -defined the carrier of C -valued Function-like non empty total V18( the carrier of G, the carrier of C) M2( bool [: the carrier of G, the carrier of C:])
[: the carrier of G, the carrier of C:] is set
bool [: the carrier of G, the carrier of C:] is set
(Obj (c₇ * s)) . h is M2( the carrier of C)
b . h is M2( the carrier of o)
Obj b is Relation-like the carrier of G -defined the carrier of o -valued Function-like non empty total V18( the carrier of G, the carrier of o) M2( bool [: the carrier of G, the carrier of o:])
(Obj b) . h is M2( the carrier of o)
c₇ . (b . h) is M2( the carrier of C)
(Obj c₇) . (b . h) is M2( the carrier of C)
(c₇ * b) . h is M2( the carrier of C)
Obj (c₇ * b) is Relation-like the carrier of G -defined the carrier of C -valued Function-like non empty total V18( the carrier of G, the carrier of C) M2( bool [: the carrier of G, the carrier of C:])
(Obj (c₇ * b)) . h is M2( the carrier of C)
Hom ((s . h),(b . h)) is M2( bool the carrier' of o)
bool the carrier' of o is set
{ b₁ where b₁ is M2( the carrier' of o) : ( dom b₁ = s . h & cod b₁ = b . h ) } is set
(G,o,F,s,b,f1,(f2 * c₇)) . h is Morphism of ((f2 * c₇) * s) . h,((f2 * c₇) * b) . h
((f2 * c₇) * s) . h is M2( the carrier of F)
the carrier of F is non empty set
Obj ((f2 * c₇) * s) is Relation-like the carrier of G -defined the carrier of F -valued Function-like non empty total V18( the carrier of G, the carrier of F) M2( bool [: the carrier of G, the carrier of F:])
[: the carrier of G, the carrier of F:] is set
bool [: the carrier of G, the carrier of F:] is set
(Obj ((f2 * c₇) * s)) . h is M2( the carrier of F)
((f2 * c₇) * b) . h is M2( the carrier of F)
Obj ((f2 * c₇) * b) is Relation-like the carrier of G -defined the carrier of F -valued Function-like non empty total V18( the carrier of G, the carrier of F) M2( bool [: the carrier of G, the carrier of F:])
(Obj ((f2 * c₇) * b)) . h is M2( the carrier of F)
f1 . h is Morphism of s . h,b . h
(f2 * c₇) /. (f1 . h) is Morphism of (f2 * c₇) . (s . h),(f2 * c₇) . (b . h)
(f2 * c₇) . (s . h) is M2( the carrier of F)
Obj (f2 * c₇) is Relation-like the carrier of o -defined the carrier of F -valued Function-like non empty total V18( the carrier of o, the carrier of F) M2( bool [: the carrier of o, the carrier of F:])
[: the carrier of o, the carrier of F:] is set
bool [: the carrier of o, the carrier of F:] is set
(Obj (f2 * c₇)) . (s . h) is M2( the carrier of F)
(f2 * c₇) . (b . h) is M2( the carrier of F)
(Obj (f2 * c₇)) . (b . h) is M2( the carrier of F)
c₇ /. (f1 . h) is Morphism of c₇ . (s . h),c₇ . (b . h)
f2 /. (c₇ /. (f1 . h)) is Morphism of f2 . (c₇ . (s . h)),f2 . (c₇ . (b . h))
f2 . (c₇ . (s . h)) is M2( the carrier of F)
Obj f2 is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj f2) . (c₇ . (s . h)) is M2( the carrier of F)
f2 . (c₇ . (b . h)) is M2( the carrier of F)
(Obj f2) . (c₇ . (b . h)) is M2( the carrier of F)
(G,o,C,s,b,f1,c₇) . h is Morphism of (c₇ * s) . h,(c₇ * b) . h
f2 /. ((G,o,C,s,b,f1,c₇) . h) is Morphism of f2 . ((c₇ * s) . h),f2 . ((c₇ * b) . h)
f2 . ((c₇ * s) . h) is M2( the carrier of F)
(Obj f2) . ((c₇ * s) . h) is M2( the carrier of F)
f2 . ((c₇ * b) . h) is M2( the carrier of F)
(Obj f2) . ((c₇ * b) . h) is M2( the carrier of F)
g is Relation-like the carrier of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier of G, the carrier' of F) natural_transformation of (f2 * c₇) * s,(f2 * c₇) * b
g . h is Morphism of ((f2 * c₇) * s) . h,((f2 * c₇) * b) . h
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
id s is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of s,s
the carrier of F is non empty set
(C,F,G,s,s,o,(id s)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,s * o
s * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
id (s * o) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,s * o
b is M2( the carrier of C)
(C,F,G,s,s,o,(id s)) . b is Morphism of (s * o) . b,(s * o) . b
(s * o) . b is M2( the carrier of G)
the carrier of G is non empty set
Obj (s * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (s * o)) . b is M2( the carrier of G)
o . b is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . b is M2( the carrier of F)
(id s) . (o . b) is Morphism of s . (o . b),s . (o . b)
s . (o . b) is M2( the carrier of G)
Obj s is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj s) . (o . b) is M2( the carrier of G)
id (s . (o . b)) is Morphism of s . (o . b),s . (o . b)
id ((s * o) . b) is Morphism of (s * o) . b,(s * o) . b
(id (s * o)) . b is Morphism of (s * o) . b,(s * o) . b
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
id o is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,o
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
(C,F,G,o,o,(id o),s) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,s * o
s * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
id (s * o) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,s * o
b is M2( the carrier of C)
(C,F,G,o,o,(id o),s) . b is Morphism of (s * o) . b,(s * o) . b
(s * o) . b is M2( the carrier of G)
the carrier of G is non empty set
Obj (s * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (s * o)) . b is M2( the carrier of G)
o . b is M2( the carrier of F)
the carrier of F is non empty set
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . b is M2( the carrier of F)
(id o) . b is Morphism of o . b,o . b
s /. ((id o) . b) is Morphism of s . (o . b),s . (o . b)
s . (o . b) is M2( the carrier of G)
Obj s is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj s) . (o . b) is M2( the carrier of G)
id (o . b) is Morphism of o . b,o . b
s /. (id (o . b)) is Morphism of s . (o . b),s . (o . b)
id (s . (o . b)) is Morphism of s . (o . b),s . (o . b)
id ((s * o) . b) is Morphism of (s * o) . b,(s * o) . b
(id (s * o)) . b is Morphism of (s * o) . b,(s * o) . b
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
G is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
s is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G,o
(F,F,C,G,o,(id F),s) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G * (id F),o * (id F)
G * (id F) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
o * (id F) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
b is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G,o
c₇ is M2( the carrier of F)
b . c₇ is Morphism of G . c₇,o . c₇
G . c₇ is M2( the carrier of C)
the carrier of C is non empty set
Obj G is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
[: the carrier of F, the carrier of C:] is set
bool [: the carrier of F, the carrier of C:] is set
(Obj G) . c₇ is M2( the carrier of C)
o . c₇ is M2( the carrier of C)
Obj o is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
(Obj o) . c₇ is M2( the carrier of C)
(id F) . c₇ is M2( the carrier of F)
Obj (id F) is Relation-like the carrier of F -defined the carrier of F -valued Function-like non empty total V18( the carrier of F, the carrier of F) M2( bool [: the carrier of F, the carrier of F:])
[: the carrier of F, the carrier of F:] is set
bool [: the carrier of F, the carrier of F:] is set
(Obj (id F)) . c₇ is M2( the carrier of F)
s . ((id F) . c₇) is Morphism of G . ((id F) . c₇),o . ((id F) . c₇)
G . ((id F) . c₇) is M2( the carrier of C)
(Obj G) . ((id F) . c₇) is M2( the carrier of C)
o . ((id F) . c₇) is M2( the carrier of C)
(Obj o) . ((id F) . c₇) is M2( the carrier of C)
s . c₇ is Morphism of G . c₇,o . c₇
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of G,o
(C,F,F,G,o,s,(id F)) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (id F) * G,(id F) * o
(id F) * G is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
(id F) * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
c₇ is M2( the carrier of C)
G . c₇ is M2( the carrier of F)
the carrier of F is non empty set
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj G) . c₇ is M2( the carrier of F)
o . c₇ is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj o) . c₇ is M2( the carrier of F)
Hom ((G . c₇),(o . c₇)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = G . c₇ & cod b₁ = o . c₇ ) } is set
b is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of G,o
b . c₇ is Morphism of G . c₇,o . c₇
s . c₇ is Morphism of G . c₇,o . c₇
(id F) /. (s . c₇) is Morphism of (id F) . (G . c₇),(id F) . (o . c₇)
(id F) . (G . c₇) is M2( the carrier of F)
Obj (id F) is Relation-like the carrier of F -defined the carrier of F -valued Function-like non empty total V18( the carrier of F, the carrier of F) M2( bool [: the carrier of F, the carrier of F:])
[: the carrier of F, the carrier of F:] is set
bool [: the carrier of F, the carrier of F:] is set
(Obj (id F)) . (G . c₇) is M2( the carrier of F)
(id F) . (o . c₇) is M2( the carrier of F)
(Obj (id F)) . (o . c₇) is M2( the carrier of F)
(id F) . (s . c₇) is M2( the carrier' of F)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
the carrier of C is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
the carrier of F is non empty set
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
b * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s
(C,F,G,o,s,f2,b) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * o,b * s
f1 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇
(C,F,G,b,c₇,s,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * s,c₇ * s
(C,F,G,b,c₇,s,f1) `*` (C,F,G,o,s,f2,b) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * o,c₇ * s
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s
(C,F,G,o,s,f2,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,c₇ * s
f1 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of b,c₇
(C,F,G,o,s,b,c₇,f2,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * o,c₇ * s
b * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,o,s,f2,b) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * o,b * s
(C,F,G,b,c₇,s,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * s,c₇ * s
(C,F,G,b,c₇,s,f1) `*` (C,F,G,o,s,f2,b) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * o,c₇ * s
(C,F,G,b,c₇,o,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * o,c₇ * o
(C,F,G,o,s,f2,c₇) `*` (C,F,G,b,c₇,o,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of b * o,c₇ * s
g is M2( the carrier of C)
(b * o) . g is M2( the carrier of G)
the carrier of G is non empty set
Obj (b * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (b * o)) . g is M2( the carrier of G)
o . g is M2( the carrier of F)
Obj o is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj o) . g is M2( the carrier of F)
b . (o . g) is M2( the carrier of G)
Obj b is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj b) . (o . g) is M2( the carrier of G)
(b * s) . g is M2( the carrier of G)
Obj (b * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (b * s)) . g is M2( the carrier of G)
s . g is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
(Obj s) . g is M2( the carrier of F)
b . (s . g) is M2( the carrier of G)
(Obj b) . (s . g) is M2( the carrier of G)
(c₇ * s) . g is M2( the carrier of G)
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * s)) . g is M2( the carrier of G)
c₇ . (s . g) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj c₇) . (s . g) is M2( the carrier of G)
(C,F,G,o,s,f2,c₇) . g is Morphism of (c₇ * o) . g,(c₇ * s) . g
(c₇ * o) . g is M2( the carrier of G)
Obj (c₇ * o) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (c₇ * o)) . g is M2( the carrier of G)
f2 . g is Morphism of o . g,s . g
c₇ /. (f2 . g) is Morphism of c₇ . (o . g),c₇ . (s . g)
c₇ . (o . g) is M2( the carrier of G)
(Obj c₇) . (o . g) is M2( the carrier of G)
Hom ((o . g),(s . g)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = o . g & cod b₁ = s . g ) } is set
(C,F,G,b,c₇,o,f1) . g is Morphism of (b * o) . g,(c₇ * o) . g
f1 . (o . g) is Morphism of b . (o . g),c₇ . (o . g)
(C,F,G,b,c₇,s,f1) . g is Morphism of (b * s) . g,(c₇ * s) . g
f1 . (s . g) is Morphism of b . (s . g),c₇ . (s . g)
(C,F,G,o,s,f2,b) . g is Morphism of (b * o) . g,(b * s) . g
b /. (f2 . g) is Morphism of b . (o . g),b . (s . g)
((C,F,G,b,c₇,s,f1) `*` (C,F,G,o,s,f2,b)) . g is Morphism of (b * o) . g,(c₇ * s) . g
(f1 . (s . g)) * (b /. (f2 . g)) is Morphism of b . (o . g),c₇ . (s . g)
((C,F,G,o,s,f2,c₇) . g) * ((C,F,G,b,c₇,o,f1) . g) is Morphism of (b * o) . g,(c₇ * s) . g
((C,F,G,o,s,f2,c₇) `*` (C,F,G,b,c₇,o,f1)) . g is Morphism of (b * o) . g,(c₇ * s) . g
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
id (id F) is Relation-like the carrier of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier of F, the carrier' of F) natural_transformation of id F, id F
the carrier of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of G,o
(C,F,F,G,o,(id F),(id F),s,(id (id F))) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (id F) * G,(id F) * o
(id F) * G is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
(id F) * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
(C,F,F,G,o,s,(id F)) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (id F) * G,(id F) * o
(C,F,F,(id F),(id F),o,(id (id F))) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (id F) * o,(id F) * o
(C,F,F,(id F),(id F),o,(id (id F))) `*` (C,F,F,G,o,s,(id F)) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (id F) * G,(id F) * o
id ((id F) * o) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (id F) * o,(id F) * o
(id ((id F) * o)) `*` (C,F,F,G,o,s,(id F)) is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of (id F) * G,(id F) * o
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
id (id F) is Relation-like the carrier of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier of F, the carrier' of F) natural_transformation of id F, id F
G is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
s is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G,o
(F,F,C,(id F),(id F),G,o,(id (id F)),s) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G * (id F),o * (id F)
G * (id F) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
o * (id F) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
(F,F,C,(id F),(id F),(id (id F)),G) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G * (id F),G * (id F)
(F,F,C,G,o,(id F),s) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G * (id F),o * (id F)
(F,F,C,G,o,(id F),s) `*` (F,F,C,(id F),(id F),(id (id F)),G) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G * (id F),o * (id F)
id (G * (id F)) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G * (id F),G * (id F)
(F,F,C,G,o,(id F),s) `*` (id (G * (id F))) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of G * (id F),o * (id F)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
the carrier of G is non empty set
o is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of o is non empty set
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
f2 * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f1 is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
f1 * c₇ is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of F, the carrier' of o) V18( the carrier' of F, the carrier' of o) Functor of F,o
g is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
g * f2 is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of F, the carrier' of o) V18( the carrier' of F, the carrier' of o) Functor of F,o
h is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of s,b
f is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of c₇,f2
(C,F,G,s,b,c₇,f2,h,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * s,f2 * b
c₇ * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,s,b,h,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * s,c₇ * b
(C,F,G,c₇,f2,b,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * b,f2 * b
(C,F,G,c₇,f2,b,f) `*` (C,F,G,s,b,h,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * s,f2 * b
t9 is Relation-like the carrier of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier of G, the carrier' of o) natural_transformation of f1,g
(C,G,o,(c₇ * s),(f2 * b),f1,g,(C,F,G,s,b,c₇,f2,h,f),t9) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of f1 * (c₇ * s),g * (f2 * b)
f1 * (c₇ * s) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
g * (f2 * b) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
f1 * (f2 * b) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
(C,G,o,(c₇ * s),(f2 * b),(C,F,G,s,b,c₇,f2,h,f),f1) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of f1 * (c₇ * s),f1 * (f2 * b)
(C,G,o,f1,g,(f2 * b),t9) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of f1 * (f2 * b),g * (f2 * b)
(C,G,o,f1,g,(f2 * b),t9) `*` (C,G,o,(c₇ * s),(f2 * b),(C,F,G,s,b,c₇,f2,h,f),f1) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of f1 * (c₇ * s),g * (f2 * b)
(F,G,o,c₇,f2,f1,g,f,t9) is Relation-like the carrier of F -defined the carrier' of o -valued Function-like non empty total V18( the carrier of F, the carrier' of o) natural_transformation of f1 * c₇,g * f2
f1 * f2 is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of F, the carrier' of o) V18( the carrier' of F, the carrier' of o) Functor of F,o
(F,G,o,c₇,f2,f,f1) is Relation-like the carrier of F -defined the carrier' of o -valued Function-like non empty total V18( the carrier of F, the carrier' of o) natural_transformation of f1 * c₇,f1 * f2
(F,G,o,f1,g,f2,t9) is Relation-like the carrier of F -defined the carrier' of o -valued Function-like non empty total V18( the carrier of F, the carrier' of o) natural_transformation of f1 * f2,g * f2
(F,G,o,f1,g,f2,t9) `*` (F,G,o,c₇,f2,f,f1) is Relation-like the carrier of F -defined the carrier' of o -valued Function-like non empty total V18( the carrier of F, the carrier' of o) natural_transformation of f1 * c₇,g * f2
(C,F,o,s,b,(f1 * c₇),(g * f2),h,(F,G,o,c₇,f2,f1,g,f,t9)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (f1 * c₇) * s,(g * f2) * b
(f1 * c₇) * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
(g * f2) * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
(f1 * c₇) * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
(C,F,o,s,b,h,(f1 * c₇)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (f1 * c₇) * s,(f1 * c₇) * b
(C,F,o,(f1 * c₇),(g * f2),b,(F,G,o,c₇,f2,f1,g,f,t9)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (f1 * c₇) * b,(g * f2) * b
(C,F,o,(f1 * c₇),(g * f2),b,(F,G,o,c₇,f2,f1,g,f,t9)) `*` (C,F,o,s,b,h,(f1 * c₇)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (f1 * c₇) * s,(g * f2) * b
(C,F,o,(f1 * f2),(g * f2),b,(F,G,o,f1,g,f2,t9)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (f1 * f2) * b,(g * f2) * b
(f1 * f2) * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
(C,G,o,(c₇ * b),(f2 * b),(C,F,G,c₇,f2,b,f),f1) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of f1 * (c₇ * b),f1 * (f2 * b)
f1 * (c₇ * b) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of C, the carrier' of o) V18( the carrier' of C, the carrier' of o) Functor of C,o
(C,F,o,(f1 * c₇),(f1 * f2),b,(F,G,o,c₇,f2,f,f1)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (f1 * c₇) * b,(f1 * f2) * b
(C,G,o,(c₇ * s),(c₇ * b),(C,F,G,s,b,h,c₇),f1) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of f1 * (c₇ * s),f1 * (c₇ * b)
(C,G,o,(c₇ * b),(f2 * b),(C,F,G,c₇,f2,b,f),f1) `*` (C,G,o,(c₇ * s),(c₇ * b),(C,F,G,s,b,h,c₇),f1) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of f1 * (c₇ * s),f1 * (f2 * b)
(C,G,o,f1,g,(f2 * b),t9) `*` ((C,G,o,(c₇ * b),(f2 * b),(C,F,G,c₇,f2,b,f),f1) `*` (C,G,o,(c₇ * s),(c₇ * b),(C,F,G,s,b,h,c₇),f1)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of f1 * (c₇ * s),g * (f2 * b)
(C,F,o,(f1 * f2),(g * f2),b,(F,G,o,f1,g,f2,t9)) `*` (C,F,o,(f1 * c₇),(f1 * f2),b,(F,G,o,c₇,f2,f,f1)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (f1 * c₇) * b,(g * f2) * b
((C,F,o,(f1 * f2),(g * f2),b,(F,G,o,f1,g,f2,t9)) `*` (C,F,o,(f1 * c₇),(f1 * f2),b,(F,G,o,c₇,f2,f,f1))) `*` (C,F,o,s,b,h,(f1 * c₇)) is Relation-like the carrier of C -defined the carrier' of o -valued Function-like non empty total V18( the carrier of C, the carrier' of o) natural_transformation of (f1 * c₇) * s,(g * f2) * b
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
id o is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,o
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of s,b
(C,F,G,s,b,o,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,b * o
s * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
b * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,o,o,s,b,(id o),c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,b * o
(C,F,G,o,o,(id o),s) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,s * o
(C,F,G,s,b,o,c₇) `*` (C,F,G,o,o,(id o),s) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,b * o
id (s * o) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,s * o
(C,F,G,s,b,o,c₇) `*` (id (s * o)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of s * o,b * o
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b is Relation-like the carrier' of G -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of G, the carrier' of C) Functor of G,C
id b is Relation-like the carrier of G -defined the carrier' of C -valued Function-like non empty total V18( the carrier of G, the carrier' of C) natural_transformation of b,b
the carrier of G is non empty set
c₇ is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of o,s
(F,G,C,o,s,c₇,b) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of b * o,b * s
b * o is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
b * s is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
(F,G,C,o,s,b,b,c₇,(id b)) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of b * o,b * s
(F,G,C,b,b,s,(id b)) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of b * s,b * s
(F,G,C,b,b,s,(id b)) `*` (F,G,C,o,s,c₇,b) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of b * o,b * s
id (b * s) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of b * s,b * s
(id (b * s)) `*` (F,G,C,o,s,c₇,b) is Relation-like the carrier of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier of F, the carrier' of C) natural_transformation of b * o,b * s
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
f2 * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f1 is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
f1 * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
g is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,s
h is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of s,b
h `*` g is Relation-like the carrier of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier of C, the carrier' of F) natural_transformation of o,b
f is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of c₇,f2
(C,F,G,o,s,c₇,f2,g,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f2 * s
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,o,s,g,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,c₇ * s
(C,F,G,c₇,f2,s,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * s,f2 * s
(C,F,G,c₇,f2,s,f) `*` (C,F,G,o,s,g,c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f2 * s
t9 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of f2,f1
t9 `*` f is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of c₇,f1
(C,F,G,o,b,c₇,f1,(h `*` g),(t9 `*` f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
c₇ * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,o,b,(h `*` g),c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,c₇ * b
(C,F,G,c₇,f1,b,(t9 `*` f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * b,f1 * b
(C,F,G,c₇,f1,b,(t9 `*` f)) `*` (C,F,G,o,b,(h `*` g),c₇) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
(C,F,G,s,b,f2,f1,h,t9) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * s,f1 * b
f2 * b is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,s,b,h,f2) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * s,f2 * b
(C,F,G,f2,f1,b,t9) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * b,f1 * b
(C,F,G,f2,f1,b,t9) `*` (C,F,G,s,b,h,f2) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * s,f1 * b
(C,F,G,s,b,f2,f1,h,t9) `*` (C,F,G,o,s,c₇,f2,g,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
f1 * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,f2,f1,s,t9) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * s,f1 * s
(C,F,G,s,b,h,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f1 * s,f1 * b
(C,F,G,s,b,h,f1) `*` (C,F,G,f2,f1,s,t9) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * s,f1 * b
f2 * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,c₇,f2,o,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f2 * o
(C,F,G,o,s,g,f2) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * o,f2 * s
(C,F,G,o,s,g,f2) `*` (C,F,G,c₇,f2,o,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f2 * s
f1 * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
(C,F,G,c₇,f1,o,(t9 `*` f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * o
(C,F,G,o,b,(h `*` g),f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f1 * o,f1 * b
(C,F,G,o,b,(h `*` g),f1) `*` (C,F,G,c₇,f1,o,(t9 `*` f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
(C,F,G,o,s,g,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f1 * o,f1 * s
(C,F,G,s,b,h,f1) `*` (C,F,G,o,s,g,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f1 * o,f1 * b
((C,F,G,s,b,h,f1) `*` (C,F,G,o,s,g,f1)) `*` (C,F,G,c₇,f1,o,(t9 `*` f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
(C,F,G,f2,f1,o,t9) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * o,f1 * o
(C,F,G,f2,f1,o,t9) `*` (C,F,G,c₇,f2,o,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * o
((C,F,G,s,b,h,f1) `*` (C,F,G,o,s,g,f1)) `*` ((C,F,G,f2,f1,o,t9) `*` (C,F,G,c₇,f2,o,f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
(C,F,G,o,s,g,f1) `*` ((C,F,G,f2,f1,o,t9) `*` (C,F,G,c₇,f2,o,f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * s
(C,F,G,s,b,h,f1) `*` ((C,F,G,o,s,g,f1) `*` ((C,F,G,f2,f1,o,t9) `*` (C,F,G,c₇,f2,o,f))) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
(C,F,G,o,s,g,f1) `*` (C,F,G,f2,f1,o,t9) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * o,f1 * s
((C,F,G,o,s,g,f1) `*` (C,F,G,f2,f1,o,t9)) `*` (C,F,G,c₇,f2,o,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * s
(C,F,G,s,b,h,f1) `*` (((C,F,G,o,s,g,f1) `*` (C,F,G,f2,f1,o,t9)) `*` (C,F,G,c₇,f2,o,f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
(C,F,G,o,s,f2,f1,g,t9) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * o,f1 * s
(C,F,G,f2,f1,s,t9) `*` (C,F,G,o,s,g,f2) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of f2 * o,f1 * s
(C,F,G,o,s,f2,f1,g,t9) `*` (C,F,G,c₇,f2,o,f) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * s
(C,F,G,s,b,h,f1) `*` ((C,F,G,o,s,f2,f1,g,t9) `*` (C,F,G,c₇,f2,o,f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
(C,F,G,f2,f1,s,t9) `*` ((C,F,G,o,s,g,f2) `*` (C,F,G,c₇,f2,o,f)) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * s
(C,F,G,s,b,h,f1) `*` ((C,F,G,f2,f1,s,t9) `*` ((C,F,G,o,s,g,f2) `*` (C,F,G,c₇,f2,o,f))) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * o,f1 * b
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of o is non empty set
s is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
b is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
c₇ is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
f2 is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
b * c₇ is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of F, the carrier' of o) V18( the carrier' of F, the carrier' of o) Functor of F,o
b * f2 is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of F, the carrier' of o) V18( the carrier' of F, the carrier' of o) Functor of F,o
c₇ * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
f2 * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
the carrier of F is non empty set
f1 is Relation-like the carrier of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier of F, the carrier' of G) natural_transformation of c₇,f2
(F,G,o,c₇,f2,f1,b) is Relation-like the carrier of F -defined the carrier' of o -valued Function-like non empty total V18( the carrier of F, the carrier' of o) natural_transformation of b * c₇,b * f2
g is M2( the carrier of F)
(b * c₇) . g is M2( the carrier of o)
the carrier of o is non empty set
Obj (b * c₇) is Relation-like the carrier of F -defined the carrier of o -valued Function-like non empty total V18( the carrier of F, the carrier of o) M2( bool [: the carrier of F, the carrier of o:])
[: the carrier of F, the carrier of o:] is set
bool [: the carrier of F, the carrier of o:] is set
(Obj (b * c₇)) . g is M2( the carrier of o)
(b * f2) . g is M2( the carrier of o)
Obj (b * f2) is Relation-like the carrier of F -defined the carrier of o -valued Function-like non empty total V18( the carrier of F, the carrier of o) M2( bool [: the carrier of F, the carrier of o:])
(Obj (b * f2)) . g is M2( the carrier of o)
(F,G,o,c₇,f2,f1,b) . g is Morphism of (b * c₇) . g,(b * f2) . g
c₇ . g is M2( the carrier of G)
the carrier of G is non empty set
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj c₇) . g is M2( the carrier of G)
f2 . g is M2( the carrier of G)
Obj f2 is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj f2) . g is M2( the carrier of G)
f1 . g is Morphism of c₇ . g,f2 . g
b . (c₇ . g) is M2( the carrier of o)
Obj b is Relation-like the carrier of G -defined the carrier of o -valued Function-like non empty total V18( the carrier of G, the carrier of o) M2( bool [: the carrier of G, the carrier of o:])
[: the carrier of G, the carrier of o:] is set
bool [: the carrier of G, the carrier of o:] is set
(Obj b) . (c₇ . g) is M2( the carrier of o)
b . (f2 . g) is M2( the carrier of o)
(Obj b) . (f2 . g) is M2( the carrier of o)
b /. (f1 . g) is Morphism of b . (c₇ . g),b . (f2 . g)
the carrier of C is non empty set
(C,F,G,c₇,f2,s,f1) is Relation-like the carrier of C -defined the carrier' of G -valued Function-like non empty total V18( the carrier of C, the carrier' of G) natural_transformation of c₇ * s,f2 * s
g is M2( the carrier of C)
(c₇ * s) . g is M2( the carrier of G)
the carrier of G is non empty set
Obj (c₇ * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
[: the carrier of C, the carrier of G:] is set
bool [: the carrier of C, the carrier of G:] is set
(Obj (c₇ * s)) . g is M2( the carrier of G)
(f2 * s) . g is M2( the carrier of G)
Obj (f2 * s) is Relation-like the carrier of C -defined the carrier of G -valued Function-like non empty total V18( the carrier of C, the carrier of G) M2( bool [: the carrier of C, the carrier of G:])
(Obj (f2 * s)) . g is M2( the carrier of G)
(C,F,G,c₇,f2,s,f1) . g is Morphism of (c₇ * s) . g,(f2 * s) . g
s . g is M2( the carrier of F)
Obj s is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj s) . g is M2( the carrier of F)
c₇ . (s . g) is M2( the carrier of G)
Obj c₇ is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
[: the carrier of F, the carrier of G:] is set
bool [: the carrier of F, the carrier of G:] is set
(Obj c₇) . (s . g) is M2( the carrier of G)
f2 . (s . g) is M2( the carrier of G)
Obj f2 is Relation-like the carrier of F -defined the carrier of G -valued Function-like non empty total V18( the carrier of F, the carrier of G) M2( bool [: the carrier of F, the carrier of G:])
(Obj f2) . (s . g) is M2( the carrier of G)
f1 . (s . g) is Morphism of c₇ . (s . g),f2 . (s . g)
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
s is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
G * s is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
s * o is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
G * (id C) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) V18( the carrier' of C, the carrier' of F) Functor of C,F
(id C) * o is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
id G is Relation-like the carrier' of G -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) Functor of G,G
id the carrier' of G is Relation-like the carrier' of G -defined the carrier' of G -valued non empty total V18( the carrier' of G, the carrier' of G) M2( bool [: the carrier' of G, the carrier' of G:])
[: the carrier' of G, the carrier' of G:] is set
bool [: the carrier' of G, the carrier' of G:] is set
(id G) * (id G) is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) V18( the carrier' of G, the carrier' of G) Functor of G,G
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of o is non empty set
s is Relation-like the carrier' of G -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of G, the carrier' of o) Functor of G,o
b is Relation-like the carrier' of o -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of o, the carrier' of G) Functor of o,G
b * s is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) V18( the carrier' of G, the carrier' of G) Functor of G,G
id G is Relation-like the carrier' of G -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) Functor of G,G
id the carrier' of G is Relation-like the carrier' of G -defined the carrier' of G -valued non empty total V18( the carrier' of G, the carrier' of G) M2( bool [: the carrier' of G, the carrier' of G:])
[: the carrier' of G, the carrier' of G:] is set
bool [: the carrier' of G, the carrier' of G:] is set
s * b is Relation-like the carrier' of o -defined the carrier' of o -defined the carrier' of o -valued the carrier' of o -valued Function-like non empty total V18( the carrier' of o, the carrier' of o) V18( the carrier' of o, the carrier' of o) Functor of o,o
id o is Relation-like the carrier' of o -defined the carrier' of o -valued Function-like non empty total V18( the carrier' of o, the carrier' of o) Functor of o,o
id the carrier' of o is Relation-like the carrier' of o -defined the carrier' of o -valued non empty total V18( the carrier' of o, the carrier' of o) M2( bool [: the carrier' of o, the carrier' of o:])
[: the carrier' of o, the carrier' of o:] is set
bool [: the carrier' of o, the carrier' of o:] is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
(C,F,G) is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
(C,F,G) * G is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
G * (C,F,G) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) V18( the carrier' of F, the carrier' of F) Functor of F,F
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier' of F is non empty set
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
s is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
s * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
o * s is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) V18( the carrier' of F, the carrier' of F) Functor of F,F
the carrier' of G is non empty set
id G is Relation-like the carrier' of G -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) Functor of G,G
id the carrier' of G is Relation-like the carrier' of G -defined the carrier' of G -valued non empty total V18( the carrier' of G, the carrier' of G) M2( bool [: the carrier' of G, the carrier' of G:])
[: the carrier' of G, the carrier' of G:] is set
bool [: the carrier' of G, the carrier' of G:] is set
b is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ is Relation-like the carrier' of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) Functor of G,F
c₇ * b is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) V18( the carrier' of F, the carrier' of F) Functor of F,F
b * c₇ is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) V18( the carrier' of G, the carrier' of G) Functor of G,G
b * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
s * c₇ is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of G, the carrier' of C) V18( the carrier' of G, the carrier' of C) Functor of G,C
(s * c₇) * (b * o) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
(b * o) * (s * c₇) is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) V18( the carrier' of G, the carrier' of G) Functor of G,G
(s * c₇) * b is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
s * (c₇ * b) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
((s * c₇) * b) * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
(b * o) * s is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) V18( the carrier' of F, the carrier' of G) Functor of F,G
b * (o * s) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) V18( the carrier' of F, the carrier' of G) Functor of F,G
((b * o) * s) * c₇ is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) V18( the carrier' of G, the carrier' of G) Functor of G,G
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier' of F is non empty set
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
the carrier' of C is non empty set
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
(id C) * (id C) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of G is non empty set
o is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) (C,F)
s is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) (F,G)
s * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of C, the carrier' of G) V18( the carrier' of C, the carrier' of G) Functor of C,G
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
id G is Relation-like the carrier' of G -defined the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) Functor of G,G
id the carrier' of G is Relation-like the carrier' of G -defined the carrier' of G -valued non empty total V18( the carrier' of G, the carrier' of G) M2( bool [: the carrier' of G, the carrier' of G:])
[: the carrier' of G, the carrier' of G:] is set
bool [: the carrier' of G, the carrier' of G:] is set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
b is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
b * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
o * b is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) V18( the carrier' of F, the carrier' of F) Functor of F,F
(s * o) * b is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) V18( the carrier' of F, the carrier' of G) Functor of F,G
s * (o * b) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of F, the carrier' of G) V18( the carrier' of F, the carrier' of G) Functor of F,G
c₇ is Relation-like the carrier' of G -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of G, the carrier' of F) Functor of G,F
c₇ * s is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) V18( the carrier' of F, the carrier' of F) Functor of F,F
s * c₇ is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) V18( the carrier' of G, the carrier' of G) Functor of G,G
b * c₇ is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of G, the carrier' of C) V18( the carrier' of G, the carrier' of C) Functor of G,C
(b * c₇) * (s * o) is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
(s * o) * (b * c₇) is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) V18( the carrier' of G, the carrier' of G) Functor of G,G
(b * c₇) * s is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
b * (c₇ * s) is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) V18( the carrier' of F, the carrier' of C) Functor of F,C
((b * c₇) * s) * o is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
((s * o) * b) * c₇ is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of G -valued the carrier' of G -valued Function-like non empty total V18( the carrier' of G, the carrier' of G) V18( the carrier' of G, the carrier' of G) Functor of G,G
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) (C,F)
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o * G is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
G * o is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) V18( the carrier' of F, the carrier' of F) Functor of F,F
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) Functor of C,F
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) Functor of F,C
o * G is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
the carrier of C is non empty set
s is Relation-like the carrier of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier of C, the carrier' of C) natural_transformation of id C,o * G
b is M2( the carrier of C)
c₇ is M2( the carrier of C)
Hom (b,c₇) is M2( bool the carrier' of C)
bool the carrier' of C is set
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = b & cod b₁ = c₇ ) } is set
(id C) . b is M2( the carrier of C)
Obj (id C) is Relation-like the carrier of C -defined the carrier of C -valued Function-like non empty total V18( the carrier of C, the carrier of C) M2( bool [: the carrier of C, the carrier of C:])
[: the carrier of C, the carrier of C:] is set
bool [: the carrier of C, the carrier of C:] is set
(Obj (id C)) . b is M2( the carrier of C)
(id C) . c₇ is M2( the carrier of C)
(Obj (id C)) . c₇ is M2( the carrier of C)
Hom (((id C) . b),((id C) . c₇)) is M2( bool the carrier' of C)
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = (id C) . b & cod b₁ = (id C) . c₇ ) } is set
f2 is Morphism of b,c₇
G . f2 is M2( the carrier' of F)
f1 is Morphism of b,c₇
G . f1 is M2( the carrier' of F)
(o * G) /. f2 is Morphism of (o * G) . b,(o * G) . c₇
(o * G) . b is M2( the carrier of C)
Obj (o * G) is Relation-like the carrier of C -defined the carrier of C -valued Function-like non empty total V18( the carrier of C, the carrier of C) M2( bool [: the carrier of C, the carrier of C:])
(Obj (o * G)) . b is M2( the carrier of C)
(o * G) . c₇ is M2( the carrier of C)
(Obj (o * G)) . c₇ is M2( the carrier of C)
(o * G) . f2 is M2( the carrier' of C)
o . (G . f1) is M2( the carrier' of C)
(o * G) . f1 is M2( the carrier' of C)
(o * G) /. f1 is Morphism of (o * G) . b,(o * G) . c₇
(id C) /. f2 is Morphism of (id C) . b,(id C) . c₇
s . c₇ is Morphism of (id C) . c₇,(o * G) . c₇
(s . c₇) * ((id C) /. f2) is Morphism of (id C) . b,(o * G) . c₇
s . b is Morphism of (id C) . b,(o * G) . b
((o * G) /. f2) * (s . b) is Morphism of (id C) . b,(o * G) . c₇
(id C) /. f1 is Morphism of (id C) . b,(id C) . c₇
(s . c₇) * ((id C) /. f1) is Morphism of (id C) . b,(o * G) . c₇
Hom (((id C) . c₇),((o * G) . c₇)) is M2( bool the carrier' of C)
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = (id C) . c₇ & cod b₁ = (o * G) . c₇ ) } is set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
F is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of F is non empty set
the carrier of F is non empty set
G is Relation-like the carrier' of C -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of C, the carrier' of F) (C,F)
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) Functor of C,C
id the carrier' of C is Relation-like the carrier' of C -defined the carrier' of C -valued non empty total V18( the carrier' of C, the carrier' of C) M2( bool [: the carrier' of C, the carrier' of C:])
[: the carrier' of C, the carrier' of C:] is set
bool [: the carrier' of C, the carrier' of C:] is set
id F is Relation-like the carrier' of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) Functor of F,F
id the carrier' of F is Relation-like the carrier' of F -defined the carrier' of F -valued non empty total V18( the carrier' of F, the carrier' of F) M2( bool [: the carrier' of F, the carrier' of F:])
[: the carrier' of F, the carrier' of F:] is set
bool [: the carrier' of F, the carrier' of F:] is set
o is Relation-like the carrier' of F -defined the carrier' of C -valued Function-like non empty total V18( the carrier' of F, the carrier' of C) (F,C)
o * G is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of C -valued the carrier' of C -valued Function-like non empty total V18( the carrier' of C, the carrier' of C) V18( the carrier' of C, the carrier' of C) Functor of C,C
G * o is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of F -valued the carrier' of F -valued Function-like non empty total V18( the carrier' of F, the carrier' of F) V18( the carrier' of F, the carrier' of F) Functor of F,F
s is Relation-like the carrier of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier of C, the carrier' of C) natural_transformation of id C,o * G
b is M2( the carrier of C)
G . b is M2( the carrier of F)
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj G) . b is M2( the carrier of F)
c₇ is M2( the carrier of C)
G . c₇ is M2( the carrier of F)
(Obj G) . c₇ is M2( the carrier of F)
Hom ((G . b),(G . c₇)) is M2( bool the carrier' of F)
bool the carrier' of F is set
{ b₁ where b₁ is M2( the carrier' of F) : ( dom b₁ = G . b & cod b₁ = G . c₇ ) } is set
Hom (b,c₇) is M2( bool the carrier' of C)
bool the carrier' of C is set
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = b & cod b₁ = c₇ ) } is set
(o * G) . c₇ is M2( the carrier of C)
Obj (o * G) is Relation-like the carrier of C -defined the carrier of C -valued Function-like non empty total V18( the carrier of C, the carrier of C) M2( bool [: the carrier of C, the carrier of C:])
[: the carrier of C, the carrier of C:] is set
bool [: the carrier of C, the carrier of C:] is set
(Obj (o * G)) . c₇ is M2( the carrier of C)
s . c₇ is Morphism of (id C) . c₇,(o * G) . c₇
(id C) . c₇ is M2( the carrier of C)
Obj (id C) is Relation-like the carrier of C -defined the carrier of C -valued Function-like non empty total V18( the carrier of C, the carrier of C) M2( bool [: the carrier of C, the carrier of C:])
(Obj (id C)) . c₇ is M2( the carrier of C)
(o * G) . b is M2( the carrier of C)
(Obj (o * G)) . b is M2( the carrier of C)
s . b is Morphism of (id C) . b,(o * G) . b
(id C) . b is M2( the carrier of C)
(Obj (id C)) . b is M2( the carrier of C)
Hom (((id C) . c₇),((o * G) . c₇)) is M2( bool the carrier' of C)
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = (id C) . c₇ & cod b₁ = (o * G) . c₇ ) } is set
g is Morphism of G . b,G . c₇
o . (G . b) is M2( the carrier of C)
Obj o is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
[: the carrier of F, the carrier of C:] is set
bool [: the carrier of F, the carrier of C:] is set
(Obj o) . (G . b) is M2( the carrier of C)
o /. g is Morphism of o . (G . b),o . (G . c₇)
o . (G . c₇) is M2( the carrier of C)
(Obj o) . (G . c₇) is M2( the carrier of C)
Hom (((id C) . b),((o * G) . b)) is M2( bool the carrier' of C)
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = (id C) . b & cod b₁ = (o * G) . b ) } is set
Hom (((o * G) . b),((o * G) . c₇)) is M2( bool the carrier' of C)
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = (o * G) . b & cod b₁ = (o * G) . c₇ ) } is set
Hom (((id C) . b),((o * G) . c₇)) is M2( bool the carrier' of C)
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = (id C) . b & cod b₁ = (o * G) . c₇ ) } is set
Hom (((o * G) . c₇),((id C) . c₇)) is M2( bool the carrier' of C)
{ b₁ where b₁ is M2( the carrier' of C) : ( dom b₁ = (o * G) . c₇ & cod b₁ = (id C) . c₇ ) } is set
f1 is Morphism of b,(o * G) . b
h is Morphism of (o * G) . b,(o * G) . c₇
h * f1 is Morphism of b,(o * G) . c₇
f2 is Morphism of c₇,(o * G) . c₇
f2 " is Morphism of (o * G) . c₇,c₇
(f2 ") * (h * f1) is Morphism of b,c₇
f is Morphism of b,c₇
G . f is M2( the carrier' of F)
(id C) /. f is Morphism of (id C) . b,(id C) . c₇
h * (s . b) is Morphism of (id C) . b,(o * G) . c₇
(s . c₇) " is Morphism of (o * G) . c₇,(id C) . c₇
((s . c₇) ") * (h * (s . b)) is Morphism of (id C) . b,(id C) . c₇
id ((o * G) . c₇) is Morphism of (o * G) . c₇,(o * G) . c₇
(id ((o * G) . c₇)) * (h * (s . b)) is Morphism of (id C) . b,(o * G) . c₇
(s . c₇) * ((s . c₇) ") is Morphism of (o * G) . c₇,(o * G) . c₇
((s . c₇) * ((s . c₇) ")) * (h * (s . b)) is Morphism of (id C) . b,(o * G) . c₇
(s . c₇) * ((id C) /. f) is Morphism of (id C) . b,(o * G) . c₇
(o * G) /. f is Morphism of (o * G) . b,(o * G) . c₇
((o * G) /. f) * (s . b) is Morphism of (id C) . b,(o * G) . c₇
o . g is M2( the carrier' of C)
(o * G) . f is M2( the carrier' of C)
o . (G . f) is M2( the carrier' of C)
G /. f is Morphism of G . b,G . c₇
o . (G /. f) is M2( the carrier' of C)
b is M2( the carrier of F)
o . b is M2( the carrier of C)
Obj o is Relation-like the carrier of F -defined the carrier of C -valued Function-like non empty total V18( the carrier of F, the carrier of C) M2( bool [: the carrier of F, the carrier of C:])
[: the carrier of F, the carrier of C:] is set
bool [: the carrier of F, the carrier of C:] is set
(Obj o) . b is M2( the carrier of C)
G . (o . b) is M2( the carrier of F)
Obj G is Relation-like the carrier of C -defined the carrier of F -valued Function-like non empty total V18( the carrier of C, the carrier of F) M2( bool [: the carrier of C, the carrier of F:])
[: the carrier of C, the carrier of F:] is set
bool [: the carrier of C, the carrier of F:] is set
(Obj G) . (o . b) is M2( the carrier of F)
(G * o) . b is M2( the carrier of F)
Obj (G * o) is Relation-like the carrier of F -defined the carrier of F -valued Function-like non empty total V18( the carrier of F, the carrier of F) M2( bool [: the carrier of F, the carrier of F:])
[: the carrier of F, the carrier of F:] is set
bool [: the carrier of F, the carrier of F:] is set
(Obj (G * o)) . b is M2( the carrier of F)
(id F) . b is M2( the carrier of F)
Obj (id F) is Relation-like the carrier of F -defined the carrier of F -valued Function-like non empty total V18( the carrier of F, the carrier of F) M2( bool [: the carrier of F, the carrier of F:])
(Obj (id F)) . b is M2( the carrier of F)
c₇ is Relation-like the carrier of F -defined the carrier' of F -valued Function-like non empty total V18( the carrier of F, the carrier' of F) natural_transformation of id F,G * o
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
[: the carrier of C, the carrier' of C:] is set
bool [: the carrier of C, the carrier' of C:] is set
F is Relation-like the carrier of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier of C, the carrier' of C) M2( bool [: the carrier of C, the carrier' of C:])
G is M2( the carrier of C)
F . G is M2( the carrier' of C)
id G is Morphism of G,G
F is Relation-like the carrier of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier of C, the carrier' of C) M2( bool [: the carrier of C, the carrier' of C:])
G is Relation-like the carrier of C -defined the carrier' of C -valued Function-like non empty total V18( the carrier of C, the carrier' of C) M2( bool [: the carrier of C, the carrier' of C:])
o is M2( the carrier of C)
F . o is set
G . o is set
F . o is M2( the carrier' of C)
id o is Morphism of o,o
G . o is M2( the carrier' of C)