:: ISOCAT_2 semantic presentation

K145() is Element of bool K141()
K141() is set
bool K141() is non empty set
{} is empty Relation-like non-empty empty-yielding set
the empty Relation-like non-empty empty-yielding set is empty Relation-like non-empty empty-yielding set
1 is non empty set
{{},1} is non empty set
K140() is set
bool K140() is non empty set
bool K145() is non empty set
[:1,1:] is non empty Relation-like set
bool [:1,1:] is non empty set
[:[:1,1:],1:] is non empty Relation-like set
bool [:[:1,1:],1:] is non empty set
A is non empty set
B is non empty set
C is non empty set
Funcs (B,C) is non empty functional FUNCTION_DOMAIN of B,C
[:A,(Funcs (B,C)):] is non empty Relation-like set
bool [:A,(Funcs (B,C)):] is non empty set
c₄ is non empty Relation-like A -defined Funcs (B,C) -valued Function-like total quasi_total Element of bool [:A,(Funcs (B,C)):]
uncurry c₄ is Relation-like Function-like set
[:A,B:] is non empty Relation-like set
[:[:A,B:],C:] is non empty Relation-like set
bool [:[:A,B:],C:] is non empty set
rng c₄ is non empty Element of bool (Funcs (B,C))
bool (Funcs (B,C)) is non empty set
uncurry c₄ is non empty Relation-like [:A,B:] -defined C -valued Function-like total quasi_total Element of bool [:[:A,B:],C:]
dom (uncurry c₄) is non empty Relation-like A -defined B -valued Element of bool [:A,B:]
bool [:A,B:] is non empty set
dom c₄ is non empty Element of bool A
bool A is non empty set
[:(dom c₄),B:] is non empty Relation-like set
A is non empty set
B is non empty set
C is non empty set
Funcs (B,C) is non empty functional FUNCTION_DOMAIN of B,C
[:A,(Funcs (B,C)):] is non empty Relation-like set
bool [:A,(Funcs (B,C)):] is non empty set
c₄ is non empty Relation-like A -defined Funcs (B,C) -valued Function-like total quasi_total Element of bool [:A,(Funcs (B,C)):]
(A,B,C,c₄) is non empty Relation-like [:A,B:] -defined C -valued Function-like total quasi_total Element of bool [:[:A,B:],C:]
[:A,B:] is non empty Relation-like set
[:[:A,B:],C:] is non empty Relation-like set
bool [:[:A,B:],C:] is non empty set
curry (A,B,C,c₄) is non empty Relation-like A -defined Funcs (B,C) -valued Function-like total quasi_total Element of bool [:A,(Funcs (B,C)):]
rng c₄ is non empty Element of bool (Funcs (B,C))
bool (Funcs (B,C)) is non empty set
A is non empty set
B is non empty set
C is non empty set
Funcs (B,C) is non empty functional FUNCTION_DOMAIN of B,C
[:A,(Funcs (B,C)):] is non empty Relation-like set
bool [:A,(Funcs (B,C)):] is non empty set
c₄ is non empty Relation-like A -defined Funcs (B,C) -valued Function-like total quasi_total Element of bool [:A,(Funcs (B,C)):]
(A,B,C,c₄) is non empty Relation-like [:A,B:] -defined C -valued Function-like total quasi_total Element of bool [:[:A,B:],C:]
[:A,B:] is non empty Relation-like set
[:[:A,B:],C:] is non empty Relation-like set
bool [:[:A,B:],C:] is non empty set
o1 is Element of A
c₄ . o1 is Relation-like B -defined C -valued Function-like total quasi_total Element of Funcs (B,C)
o2 is Element of B
(A,B,C,c₄) . (o1,o2) is Element of C
[o1,o2] is set
{o1,o2} is non empty set
{o1} is non empty set
{{o1,o2},{o1}} is non empty set
(A,B,C,c₄) . [o1,o2] is set
(c₄ . o1) . o2 is Element of C
dom c₄ is non empty Element of bool A
bool A is non empty set
dom (c₄ . o1) is Element of bool B
bool B is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is Element of the carrier' of A
cod B is Element of the carrier of A
the carrier of A is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Target of A . B is Element of the carrier of A
id (cod B) is Morphism of cod B, cod B
(id (cod B)) (*) B is Element of the carrier' of A
dom B is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Source of A . B is Element of the carrier of A
Hom ((dom B),(cod B)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom B & cod b₁ = cod B ) } is set
Hom ((cod B),(cod B)) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod B & cod b₁ = cod B ) } is set
C is Morphism of dom B, cod B
(id (cod B)) * C is Morphism of dom B, cod B
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is Element of the carrier' of A
dom B is Element of the carrier of A
the carrier of A is non empty set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of A . B is Element of the carrier of A
id (dom B) is Morphism of dom B, dom B
B (*) (id (dom B)) is Element of the carrier' of A
cod B is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of A . B is Element of the carrier of A
Hom ((dom B),(cod B)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom B & cod b₁ = cod B ) } is set
Hom ((dom B),(dom B)) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom B & cod b₁ = dom B ) } is set
C is Morphism of dom B, cod B
C * (id (dom B)) is Morphism of dom B, cod B
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Functors (A,B) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier of (Functors (A,B)) is non empty set
the carrier' of B is non empty set
C is set
Funct (A,B) is non empty FUNCTOR-DOMAIN of A,B
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Functors (A,B) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,B)) is non empty set
the carrier' of B is non empty set
C is Element of the carrier' of (Functors (A,B))
dom C is Element of the carrier of (Functors (A,B))
the carrier of (Functors (A,B)) is non empty set
the Source of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
[: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty set
the Source of (Functors (A,B)) . C is Element of the carrier of (Functors (A,B))
cod C is Element of the carrier of (Functors (A,B))
the Target of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
the Target of (Functors (A,B)) . C is Element of the carrier of (Functors (A,B))
Hom ((dom C),(cod C)) is Element of bool the carrier' of (Functors (A,B))
bool the carrier' of (Functors (A,B)) is non empty set
{ b₁ where b₁ is Element of the carrier' of (Functors (A,B)) : ( dom b₁ = dom C & cod b₁ = cod C ) } is set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[c₄,o1] is set
{c₄,o1} is non empty set
{c₄} is non empty set
{{c₄,o1},{c₄}} is non empty set
o2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1
[[c₄,o1],o2] is set
{[c₄,o1],o2} is non empty set
{[c₄,o1]} is non empty Relation-like set
{{[c₄,o1],o2},{[c₄,o1]}} is non empty set
NatTrans (A,B) is non empty NatTrans-DOMAIN of A,B
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Functors (A,B) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,B)) is non empty set
the carrier' of B is non empty set
the carrier' of A is non empty set
C is Element of the carrier of A
NatTrans (A,B) is non empty NatTrans-DOMAIN of A,B
c₄ is Element of NatTrans (A,B)
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[o1,o2] is set
{o1,o2} is non empty set
{o1} is non empty set
{{o1,o2},{o1}} is non empty set
G1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of o1,o2
[[o1,o2],G1] is set
{[o1,o2],G1} is non empty set
{[o1,o2]} is non empty Relation-like set
{{[o1,o2],G1},{[o1,o2]}} is non empty set
G1 . C is Morphism of o1 . C,o2 . C
o1 . C is Element of the carrier of B
the carrier of B is non empty set
Obj o1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj o1) . C is Element of the carrier of B
o2 . C is Element of the carrier of B
Obj o2 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj o2) . C is Element of the carrier of B
G2 is Element of the carrier' of B
t is Element of the carrier' of B
F1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
F2 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
s is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of F1,F2
[[F1,F2],s] is set
{[F1,F2],s} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],s},{[F1,F2]}} is non empty set
s . C is Morphism of F1 . C,F2 . C
F1 . C is Element of the carrier of B
Obj F1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj F1) . C is Element of the carrier of B
F2 . C is Element of the carrier of B
Obj F2 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj F2) . C is Element of the carrier of B
[:(NatTrans (A,B)), the carrier' of B:] is non empty Relation-like set
bool [:(NatTrans (A,B)), the carrier' of B:] is non empty set
c₄ is non empty Relation-like NatTrans (A,B) -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:(NatTrans (A,B)), the carrier' of B:]
[: the carrier' of (Functors (A,B)), the carrier' of B:] is non empty Relation-like set
bool [: the carrier' of (Functors (A,B)), the carrier' of B:] is non empty set
the carrier of (Functors (A,B)) is non empty set
o2 is Element of the carrier of (Functors (A,B))
G1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
G1 . C is Element of the carrier of B
Obj G1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj G1) . C is Element of the carrier of B
[G1,G1] is set
{G1,G1} is non empty set
{G1} is non empty set
{{G1,G1},{G1}} is non empty set
id G1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of G1,G1
[[G1,G1],(id G1)] is set
{[G1,G1],(id G1)} is non empty set
{[G1,G1]} is non empty Relation-like set
{{[G1,G1],(id G1)},{[G1,G1]}} is non empty set
id o2 is Morphism of o2,o2
c₄ . (id o2) is set
c₄ . [[G1,G1],(id G1)] is set
(id G1) . C is Morphism of G1 . C,G1 . C
G2 is Element of the carrier of B
id G2 is Morphism of G2,G2
G1 is Element of the carrier' of (Functors (A,B))
o2 is Element of the carrier' of (Functors (A,B))
[G1,o2] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,B)):]
[:(Functors (A,B)),(Functors (A,B)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty Relation-like set
[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] is non empty Relation-like set
the Source of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
[: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty set
[: the Source of (Functors (A,B)), the Source of (Functors (A,B)):] is non empty Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] -defined [: the carrier of (Functors (A,B)), the carrier of (Functors (A,B)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,B)):]:]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,B)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,B)):]:] is non empty set
the Target of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
[: the Target of (Functors (A,B)), the Target of (Functors (A,B)):] is non empty Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] -defined [: the carrier of (Functors (A,B)), the carrier of (Functors (A,B)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,B)):]:]
the Comp of (Functors (A,B)) is Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] -defined the carrier' of (Functors (A,B)) -valued Function-like Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):] is non empty set
K209( the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)), the Comp of (Functors (A,B)), the Comp of (Functors (A,B))) is Relation-like [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]:] -defined [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]:]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]:] is non empty set
CatStr(# [: the carrier of (Functors (A,B)), the carrier of (Functors (A,B)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):],[: the Source of (Functors (A,B)), the Source of (Functors (A,B)):],[: the Target of (Functors (A,B)), the Target of (Functors (A,B)):],K209( the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)), the Comp of (Functors (A,B)), the Comp of (Functors (A,B))) #) is strict CatStr
the carrier' of [:(Functors (A,B)),(Functors (A,B)):] is non empty set
{G1,o2} is non empty set
{G1} is non empty set
{{G1,o2},{G1}} is non empty set
dom the Comp of (Functors (A,B)) is Relation-like the carrier' of (Functors (A,B)) -defined the carrier' of (Functors (A,B)) -valued Element of bool [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):]
bool [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] is non empty set
dom o2 is Element of the carrier of (Functors (A,B))
the Source of (Functors (A,B)) . o2 is Element of the carrier of (Functors (A,B))
cod o2 is Element of the carrier of (Functors (A,B))
the Target of (Functors (A,B)) . o2 is Element of the carrier of (Functors (A,B))
F1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
F2 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
s is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of F1,F2
[[F1,F2],s] is set
{[F1,F2],s} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],s},{[F1,F2]}} is non empty set
F1 . C is Element of the carrier of B
Obj F1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj F1) . C is Element of the carrier of B
F2 . C is Element of the carrier of B
Obj F2 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj F2) . C is Element of the carrier of B
Hom ((F1 . C),(F2 . C)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = F1 . C & cod b₁ = F2 . C ) } is set
G2 is Element of NatTrans (A,B)
c₄ . G2 is Element of the carrier' of B
s . C is Morphism of F1 . C,F2 . C
dom G1 is Element of the carrier of (Functors (A,B))
the Source of (Functors (A,B)) . G1 is Element of the carrier of (Functors (A,B))
cod G1 is Element of the carrier of (Functors (A,B))
the Target of (Functors (A,B)) . G1 is Element of the carrier of (Functors (A,B))
f is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
f is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
f2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of f,f
[[f,f],f2] is set
{[f,f],f2} is non empty set
{[f,f]} is non empty Relation-like set
{{[f,f],f2},{[f,f]}} is non empty set
f . C is Element of the carrier of B
Obj f is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj f) . C is Element of the carrier of B
Hom ((F2 . C),(f . C)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = F2 . C & cod b₁ = f . C ) } is set
t is Element of NatTrans (A,B)
c₄ . t is Element of the carrier' of B
g1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of F2,f
g1 . C is Morphism of F2 . C,f . C
G1 (*) o2 is Element of the carrier' of (Functors (A,B))
[F1,f] is set
{F1,f} is non empty set
{{F1,f},{F1}} is non empty set
g1 `*` s is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of F1,f
[[F1,f],(g1 `*` s)] is set
{[F1,f],(g1 `*` s)} is non empty set
{[F1,f]} is non empty Relation-like set
{{[F1,f],(g1 `*` s)},{[F1,f]}} is non empty set
o1 is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier' of B:]
o1 . (G1 (*) o2) is Element of the carrier' of B
(g1 `*` s) . C is Morphism of F1 . C,f . C
(g1 . C) * (s . C) is Morphism of F1 . C,f . C
(g1 . C) (*) (s . C) is Element of the carrier' of B
o1 . o2 is Element of the carrier' of B
o1 . G1 is Element of the carrier' of B
(o1 . G1) (*) (o1 . o2) is Element of the carrier' of B
o2 is Element of the carrier' of (Functors (A,B))
dom o2 is Element of the carrier of (Functors (A,B))
the Source of (Functors (A,B)) . o2 is Element of the carrier of (Functors (A,B))
cod o2 is Element of the carrier of (Functors (A,B))
the Target of (Functors (A,B)) . o2 is Element of the carrier of (Functors (A,B))
G2 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
t is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[G2,t] is set
{G2,t} is non empty set
{G2} is non empty set
{{G2,t},{G2}} is non empty set
F1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of G2,t
[[G2,t],F1] is set
{[G2,t],F1} is non empty set
{[G2,t]} is non empty Relation-like set
{{[G2,t],F1},{[G2,t]}} is non empty set
G2 . C is Element of the carrier of B
Obj G2 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj G2) . C is Element of the carrier of B
t . C is Element of the carrier of B
Obj t is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj t) . C is Element of the carrier of B
Hom ((G2 . C),(t . C)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = G2 . C & cod b₁ = t . C ) } is set
[G2,G2] is set
{G2,G2} is non empty set
{{G2,G2},{G2}} is non empty set
id G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of G2,G2
[[G2,G2],(id G2)] is set
{[G2,G2],(id G2)} is non empty set
{[G2,G2]} is non empty Relation-like set
{{[G2,G2],(id G2)},{[G2,G2]}} is non empty set
id (dom o2) is Morphism of dom o2, dom o2
c₄ . (id (dom o2)) is set
c₄ . [[G2,G2],(id G2)] is set
(id G2) . C is Morphism of G2 . C,G2 . C
id (G2 . C) is Morphism of G2 . C,G2 . C
F1 . C is Morphism of G2 . C,t . C
dom (F1 . C) is Element of the carrier of B
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of B . (F1 . C) is Element of the carrier of B
id (dom (F1 . C)) is Morphism of dom (F1 . C), dom (F1 . C)
G1 is Element of NatTrans (A,B)
c₄ . G1 is Element of the carrier' of B
dom (c₄ . G1) is Element of the carrier of B
the Source of B . (c₄ . G1) is Element of the carrier of B
id (dom (c₄ . G1)) is Morphism of dom (c₄ . G1), dom (c₄ . G1)
o1 . o2 is Element of the carrier' of B
dom (o1 . o2) is Element of the carrier of B
the Source of B . (o1 . o2) is Element of the carrier of B
id (dom (o1 . o2)) is Morphism of dom (o1 . o2), dom (o1 . o2)
[t,t] is set
{t,t} is non empty set
{t} is non empty set
{{t,t},{t}} is non empty set
id t is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of t,t
[[t,t],(id t)] is set
{[t,t],(id t)} is non empty set
{[t,t]} is non empty Relation-like set
{{[t,t],(id t)},{[t,t]}} is non empty set
id (cod o2) is Morphism of cod o2, cod o2
c₄ . (id (cod o2)) is set
c₄ . [[t,t],(id t)] is set
(id t) . C is Morphism of t . C,t . C
id (t . C) is Morphism of t . C,t . C
cod (F1 . C) is Element of the carrier of B
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of B . (F1 . C) is Element of the carrier of B
id (cod (F1 . C)) is Morphism of cod (F1 . C), cod (F1 . C)
cod (c₄ . G1) is Element of the carrier of B
the Target of B . (c₄ . G1) is Element of the carrier of B
id (cod (c₄ . G1)) is Morphism of cod (c₄ . G1), cod (c₄ . G1)
cod (o1 . o2) is Element of the carrier of B
the Target of B . (o1 . o2) is Element of the carrier of B
id (cod (o1 . o2)) is Morphism of cod (o1 . o2), cod (o1 . o2)
o2 is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier' of B -valued Function-like total quasi_total Functor of Functors (A,B),B
G1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
G2 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
o2 . [[G1,G2],t] is set
t . C is Morphism of G1 . C,G2 . C
G1 . C is Element of the carrier of B
Obj G1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj G1) . C is Element of the carrier of B
G2 . C is Element of the carrier of B
Obj G2 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj G2) . C is Element of the carrier of B
c₄ is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier' of B -valued Function-like total quasi_total Functor of Functors (A,B),B
o1 is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier' of B -valued Function-like total quasi_total Functor of Functors (A,B),B
NatTrans (A,B) is non empty NatTrans-DOMAIN of A,B
o2 is Element of the carrier' of (Functors (A,B))
G1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
G2 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
c₄ . o2 is Element of the carrier' of B
t . C is Morphism of G1 . C,G2 . C
G1 . C is Element of the carrier of B
the carrier of B is non empty set
Obj G1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj G1) . C is Element of the carrier of B
G2 . C is Element of the carrier of B
Obj G2 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj G2) . C is Element of the carrier of B
o1 . o2 is Element of the carrier' of B
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is set
C is set
1Cat (B,C) is non empty trivial V49() non void V54(1) V55() trivial' strict Category-like V68() V69() V70() with_identities CatStr
{B} is non empty set
{C} is non empty set
C :-> B is non empty Relation-like {C} -defined {B} -valued Function-like total quasi_total Element of bool [:{C},{B}:]
[:{C},{B}:] is non empty Relation-like set
bool [:{C},{B}:] is non empty set
(C,C) :-> C is non empty Relation-like [:{C},{C}:] -defined {C} -valued Function-like total quasi_total Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is non empty Relation-like set
[:[:{C},{C}:],{C}:] is non empty Relation-like set
bool [:[:{C},{C}:],{C}:] is non empty set
CatStr(# {B},{C},(C :-> B),(C :-> B),((C,C) :-> C) #) is strict CatStr
Functors ((1Cat (B,C)),A) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier of (1Cat (B,C)) is non empty trivial V31() set
the carrier' of (Functors ((1Cat (B,C)),A)) is non empty set
the carrier' of A is non empty set
c₄ is Element of the carrier of (1Cat (B,C))
((1Cat (B,C)),A,c₄) is non empty Relation-like the carrier' of (Functors ((1Cat (B,C)),A)) -defined the carrier' of A -valued Function-like total quasi_total Functor of Functors ((1Cat (B,C)),A),A
o1 is non empty Relation-like the carrier' of (Functors ((1Cat (B,C)),A)) -defined the carrier' of A -valued Function-like total quasi_total Functor of Functors ((1Cat (B,C)),A),A
NatTrans ((1Cat (B,C)),A) is non empty NatTrans-DOMAIN of 1Cat (B,C),A
o2 is set
the carrier' of (1Cat (B,C)) is non empty trivial set
G2 is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Functor of 1Cat (B,C),A
t is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Functor of 1Cat (B,C),A
[G2,t] is set
{G2,t} is non empty set
{G2} is non empty set
{{G2,t},{G2}} is non empty set
F1 is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total natural_transformation of G2,t
[[G2,t],F1] is set
{[G2,t],F1} is non empty set
{[G2,t]} is non empty Relation-like set
{{[G2,t],F1},{[G2,t]}} is non empty set
G1 is set
F2 is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Functor of 1Cat (B,C),A
s is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Functor of 1Cat (B,C),A
[F2,s] is set
{F2,s} is non empty set
{F2} is non empty set
{{F2,s},{F2}} is non empty set
f is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total natural_transformation of F2,s
[[F2,s],f] is set
{[F2,s],f} is non empty set
{[F2,s]} is non empty Relation-like set
{{[F2,s],f},{[F2,s]}} is non empty set
o1 . o2 is set
o1 . G1 is set
F1 . c₄ is Morphism of G2 . c₄,t . c₄
G2 . c₄ is Element of the carrier of A
the carrier of A is non empty set
Obj G2 is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier of A:]
[: the carrier of (1Cat (B,C)), the carrier of A:] is non empty Relation-like set
bool [: the carrier of (1Cat (B,C)), the carrier of A:] is non empty set
(Obj G2) . c₄ is Element of the carrier of A
t . c₄ is Element of the carrier of A
Obj t is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier of A:]
(Obj t) . c₄ is Element of the carrier of A
f . c₄ is Morphism of F2 . c₄,s . c₄
F2 . c₄ is Element of the carrier of A
Obj F2 is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier of A:]
(Obj F2) . c₄ is Element of the carrier of A
s . c₄ is Element of the carrier of A
Obj s is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier of A:]
(Obj s) . c₄ is Element of the carrier of A
[:{C}, the carrier' of A:] is non empty Relation-like set
bool [:{C}, the carrier' of A:] is non empty set
{c₄} is non empty set
[:{c₄}, the carrier' of A:] is non empty Relation-like set
bool [:{c₄}, the carrier' of A:] is non empty set
id c₄ is Morphism of c₄,c₄
Hom ((G2 . c₄),(t . c₄)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = G2 . c₄ & cod b₁ = t . c₄ ) } is set
Hom ((F2 . c₄),(s . c₄)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F2 . c₄ & cod b₁ = s . c₄ ) } is set
f is non empty Relation-like {C} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{C}, the carrier' of A:]
f . (id c₄) is set
id (F2 . c₄) is Morphism of F2 . c₄,F2 . c₄
f2 is non empty Relation-like {C} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{C}, the carrier' of A:]
f2 . (id c₄) is set
g1 is non empty Relation-like {C} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{C}, the carrier' of A:]
g1 . (id c₄) is set
id (s . c₄) is Morphism of s . c₄,s . c₄
f1 is non empty Relation-like {C} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{C}, the carrier' of A:]
f1 . (id c₄) is set
t2 is non empty Relation-like {c₄} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{c₄}, the carrier' of A:]
t2 . c₄ is set
a1 is non empty Relation-like {c₄} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{c₄}, the carrier' of A:]
a1 . c₄ is set
rng o1 is non empty Element of bool the carrier' of A
o2 is set
[: the carrier' of (1Cat (B,C)), the carrier' of A:] is non empty Relation-like set
bool [: the carrier' of (1Cat (B,C)), the carrier' of A:] is non empty set
G1 is Element of the carrier' of A
dom G1 is Element of the carrier of A
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of A . G1 is Element of the carrier of A
id (dom G1) is Morphism of dom G1, dom G1
{C} --> (id (dom G1)) is non empty Relation-like {C} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{C}, the carrier' of A:]
cod G1 is Element of the carrier of A
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of A . G1 is Element of the carrier of A
id (cod G1) is Morphism of cod G1, cod G1
{C} --> (id (cod G1)) is non empty Relation-like {C} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{C}, the carrier' of A:]
G2 is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Element of bool [: the carrier' of (1Cat (B,C)), the carrier' of A:]
F1 is Element of the carrier' of (1Cat (B,C))
dom F1 is Element of the carrier of (1Cat (B,C))
the Source of (1Cat (B,C)) is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier of (1Cat (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (1Cat (B,C)), the carrier of (1Cat (B,C)):]
[: the carrier' of (1Cat (B,C)), the carrier of (1Cat (B,C)):] is non empty Relation-like set
bool [: the carrier' of (1Cat (B,C)), the carrier of (1Cat (B,C)):] is non empty set
the Source of (1Cat (B,C)) . F1 is Element of the carrier of (1Cat (B,C))
id (dom F1) is Morphism of dom F1, dom F1
G2 . (id (dom F1)) is Element of the carrier' of A
dom (id (dom G1)) is Element of the carrier of A
the Source of A . (id (dom G1)) is Element of the carrier of A
id (dom (id (dom G1))) is Morphism of dom (id (dom G1)), dom (id (dom G1))
G2 . F1 is Element of the carrier' of A
dom (G2 . F1) is Element of the carrier of A
the Source of A . (G2 . F1) is Element of the carrier of A
id (dom (G2 . F1)) is Morphism of dom (G2 . F1), dom (G2 . F1)
cod F1 is Element of the carrier of (1Cat (B,C))
the Target of (1Cat (B,C)) is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier of (1Cat (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (1Cat (B,C)), the carrier of (1Cat (B,C)):]
the Target of (1Cat (B,C)) . F1 is Element of the carrier of (1Cat (B,C))
id (cod F1) is Morphism of cod F1, cod F1
G2 . (id (cod F1)) is Element of the carrier' of A
cod (id (dom G1)) is Element of the carrier of A
the Target of A . (id (dom G1)) is Element of the carrier of A
id (cod (id (dom G1))) is Morphism of cod (id (dom G1)), cod (id (dom G1))
cod (G2 . F1) is Element of the carrier of A
the Target of A . (G2 . F1) is Element of the carrier of A
id (cod (G2 . F1)) is Morphism of cod (G2 . F1), cod (G2 . F1)
F2 is Element of the carrier' of (1Cat (B,C))
dom F2 is Element of the carrier of (1Cat (B,C))
the Source of (1Cat (B,C)) . F2 is Element of the carrier of (1Cat (B,C))
F1 is Element of the carrier' of (1Cat (B,C))
cod F1 is Element of the carrier of (1Cat (B,C))
the Target of (1Cat (B,C)) . F1 is Element of the carrier of (1Cat (B,C))
Hom ((dom G1),(dom G1)) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom G1 & cod b₁ = dom G1 ) } is set
F2 (*) F1 is Element of the carrier' of (1Cat (B,C))
G2 . (F2 (*) F1) is Element of the carrier' of A
(id (dom G1)) * (id (dom G1)) is Morphism of dom G1, dom G1
(id (dom G1)) (*) (id (dom G1)) is Element of the carrier' of A
G2 . F1 is Element of the carrier' of A
(id (dom G1)) (*) (G2 . F1) is Element of the carrier' of A
G2 . F2 is Element of the carrier' of A
(G2 . F2) (*) (G2 . F1) is Element of the carrier' of A
F2 is Element of the carrier' of (1Cat (B,C))
dom F2 is Element of the carrier of (1Cat (B,C))
the Source of (1Cat (B,C)) . F2 is Element of the carrier of (1Cat (B,C))
F1 is Element of the carrier' of (1Cat (B,C))
cod F1 is Element of the carrier of (1Cat (B,C))
the Target of (1Cat (B,C)) . F1 is Element of the carrier of (1Cat (B,C))
Hom ((cod G1),(cod G1)) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = cod G1 & cod b₁ = cod G1 ) } is set
t is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Element of bool [: the carrier' of (1Cat (B,C)), the carrier' of A:]
F2 (*) F1 is Element of the carrier' of (1Cat (B,C))
t . (F2 (*) F1) is Element of the carrier' of A
(id (cod G1)) * (id (cod G1)) is Morphism of cod G1, cod G1
(id (cod G1)) (*) (id (cod G1)) is Element of the carrier' of A
t . F1 is Element of the carrier' of A
(id (cod G1)) (*) (t . F1) is Element of the carrier' of A
t . F2 is Element of the carrier' of A
(t . F2) (*) (t . F1) is Element of the carrier' of A
F1 is Element of the carrier' of (1Cat (B,C))
dom F1 is Element of the carrier of (1Cat (B,C))
the Source of (1Cat (B,C)) . F1 is Element of the carrier of (1Cat (B,C))
id (dom F1) is Morphism of dom F1, dom F1
t . (id (dom F1)) is Element of the carrier' of A
dom (id (cod G1)) is Element of the carrier of A
the Source of A . (id (cod G1)) is Element of the carrier of A
id (dom (id (cod G1))) is Morphism of dom (id (cod G1)), dom (id (cod G1))
t . F1 is Element of the carrier' of A
dom (t . F1) is Element of the carrier of A
the Source of A . (t . F1) is Element of the carrier of A
id (dom (t . F1)) is Morphism of dom (t . F1), dom (t . F1)
cod F1 is Element of the carrier of (1Cat (B,C))
the Target of (1Cat (B,C)) . F1 is Element of the carrier of (1Cat (B,C))
id (cod F1) is Morphism of cod F1, cod F1
t . (id (cod F1)) is Element of the carrier' of A
cod (id (cod G1)) is Element of the carrier of A
the Target of A . (id (cod G1)) is Element of the carrier of A
id (cod (id (cod G1))) is Morphism of cod (id (cod G1)), cod (id (cod G1))
cod (t . F1) is Element of the carrier of A
the Target of A . (t . F1) is Element of the carrier of A
id (cod (t . F1)) is Morphism of cod (t . F1), cod (t . F1)
F1 is Element of the carrier of (1Cat (B,C))
id F1 is Morphism of F1,F1
G2 . (id F1) is Element of the carrier' of A
F2 is Element of the carrier of (1Cat (B,C))
id F2 is Morphism of F2,F2
t . (id F2) is Element of the carrier' of A
[: the carrier of (1Cat (B,C)), the carrier' of A:] is non empty Relation-like set
bool [: the carrier of (1Cat (B,C)), the carrier' of A:] is non empty set
{c₄} --> G1 is non empty Relation-like {c₄} -defined the carrier' of A -valued Function-like total quasi_total Element of bool [:{c₄}, the carrier' of A:]
F1 is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Functor of 1Cat (B,C),A
F2 is non empty Relation-like the carrier' of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Functor of 1Cat (B,C),A
f is Element of the carrier of (1Cat (B,C))
F1 . f is Element of the carrier of A
Obj F1 is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier of A:]
(Obj F1) . f is Element of the carrier of A
F2 . f is Element of the carrier of A
Obj F2 is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier of A:]
(Obj F2) . f is Element of the carrier of A
id f is Morphism of f,f
F2 . (id f) is Element of the carrier' of A
id (F2 . f) is Morphism of F2 . f,F2 . f
F1 . (id f) is Element of the carrier' of A
id (F1 . f) is Morphism of F1 . f,F1 . f
f is Element of the carrier of (1Cat (B,C))
F2 . f is Element of the carrier of A
Obj F2 is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier of A:]
(Obj F2) . f is Element of the carrier of A
s is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier' of A:]
s . f is Element of the carrier' of A
F1 . f is Element of the carrier of A
Obj F1 is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier of (1Cat (B,C)), the carrier of A:]
(Obj F1) . f is Element of the carrier of A
Hom ((F1 . f),(F2 . f)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 . f & cod b₁ = F2 . f ) } is set
f is Element of the carrier of (1Cat (B,C))
F1 . f is Element of the carrier of A
(Obj F1) . f is Element of the carrier of A
F2 . f is Element of the carrier of A
(Obj F2) . f is Element of the carrier of A
Hom ((F1 . f),(F2 . f)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 . f & cod b₁ = F2 . f ) } is set
f is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total transformation of F1,F2
f is Element of the carrier of (1Cat (B,C))
f . f is Morphism of F1 . f,F2 . f
F1 . f is Element of the carrier of A
(Obj F1) . f is Element of the carrier of A
F2 . f is Element of the carrier of A
(Obj F2) . f is Element of the carrier of A
({c₄} --> G1) . f is set
f is Element of the carrier of (1Cat (B,C))
f2 is Element of the carrier of (1Cat (B,C))
Hom (f,f2) is trivial Element of bool the carrier' of (1Cat (B,C))
bool the carrier' of (1Cat (B,C)) is non empty set
{ b₁ where b₁ is Element of the carrier' of (1Cat (B,C)) : ( dom b₁ = f & cod b₁ = f2 ) } is set
F2 . f is Element of the carrier of A
(Obj F2) . f is Element of the carrier of A
F2 . f2 is Element of the carrier of A
(Obj F2) . f2 is Element of the carrier of A
Hom ((F2 . f),(F2 . f2)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F2 . f & cod b₁ = F2 . f2 ) } is set
f . f is Morphism of F1 . f,F2 . f
F1 . f is Element of the carrier of A
(Obj F1) . f is Element of the carrier of A
Hom ((F1 . f),(F2 . f)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 . f & cod b₁ = F2 . f ) } is set
F1 . f2 is Element of the carrier of A
(Obj F1) . f2 is Element of the carrier of A
Hom ((F1 . f),(F1 . f2)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 . f & cod b₁ = F1 . f2 ) } is set
g1 is Morphism of f,f2
F2 /. g1 is Morphism of F2 . f,F2 . f2
F2 . C is set
F1 /. g1 is Morphism of F1 . f,F1 . f2
F1 . C is set
f . f2 is Morphism of F1 . f2,F2 . f2
Hom ((F1 . f2),(F2 . f2)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 . f2 & cod b₁ = F2 . f2 ) } is set
(f . f2) * (F1 /. g1) is Morphism of F1 . f,F2 . f2
G1 (*) (F1 /. g1) is Element of the carrier' of A
(F2 /. g1) (*) G1 is Element of the carrier' of A
(F2 /. g1) * (f . f) is Morphism of F1 . f,F2 . f2
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
f is non empty Relation-like the carrier of (1Cat (B,C)) -defined the carrier' of A -valued Function-like total quasi_total natural_transformation of F1,F2
[[F1,F2],f] is set
{[F1,F2],f} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],f},{[F1,F2]}} is non empty set
o1 . [[F1,F2],f] is set
f . c₄ is Morphism of F1 . c₄,F2 . c₄
F1 . c₄ is Element of the carrier of A
(Obj F1) . c₄ is Element of the carrier of A
F2 . c₄ is Element of the carrier of A
(Obj F2) . c₄ is Element of the carrier of A
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is Element of the carrier of A
c₄ ?- o1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id o1 is Morphism of o1,o1
(curry c₄) . (id o1) is set
o2 is Element of the carrier of B
(c₄ ?- o1) . o2 is Element of the carrier of C
the carrier of C is non empty set
Obj (c₄ ?- o1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- o1)) . o2 is Element of the carrier of C
[o1,o2] is Element of the carrier of [:A,B:]
the carrier of [:A,B:] is non empty set
{o1,o2} is non empty set
{o1} is non empty set
{{o1,o2},{o1}} is non empty set
c₄ . [o1,o2] is Element of the carrier of C
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . [o1,o2] is Element of the carrier of C
(Obj c₄) . (o1,o2) is set
[o1,o2] is set
(Obj c₄) . [o1,o2] is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
C is Element of the carrier of A
c₄ is Element of the carrier of A
Hom (C,c₄) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = C & cod b₁ = c₄ ) } is set
o1 is Element of the carrier of B
o2 is Element of the carrier of B
Hom (o1,o2) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = o1 & cod b₁ = o2 ) } is set
[C,o1] is Element of the carrier of [:A,B:]
the carrier of [:A,B:] is non empty set
{C,o1} is non empty set
{C} is non empty set
{{C,o1},{C}} is non empty set
[c₄,o2] is Element of the carrier of [:A,B:]
{c₄,o2} is non empty set
{c₄} is non empty set
{{c₄,o2},{c₄}} is non empty set
Hom ([C,o1],[c₄,o2]) is Element of bool the carrier' of [:A,B:]
the carrier' of [:A,B:] is non empty set
bool the carrier' of [:A,B:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:A,B:] : ( dom b₁ = [C,o1] & cod b₁ = [c₄,o2] ) } is set
[:(Hom (C,c₄)),(Hom (o1,o2)):] is Relation-like set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
C is Element of the carrier of A
c₄ is Element of the carrier of A
o1 is Element of the carrier of B
[C,o1] is Element of the carrier of [:A,B:]
the carrier of [:A,B:] is non empty set
{C,o1} is non empty set
{C} is non empty set
{{C,o1},{C}} is non empty set
o2 is Element of the carrier of B
[c₄,o2] is Element of the carrier of [:A,B:]
{c₄,o2} is non empty set
{c₄} is non empty set
{{c₄,o2},{c₄}} is non empty set
Hom ([C,o1],[c₄,o2]) is Element of bool the carrier' of [:A,B:]
the carrier' of [:A,B:] is non empty set
bool the carrier' of [:A,B:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:A,B:] : ( dom b₁ = [C,o1] & cod b₁ = [c₄,o2] ) } is set
G1 is Element of the carrier' of A
G2 is Element of the carrier' of B
[G1,G2] is Element of the carrier' of [:A,B:]
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
Hom (C,c₄) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = C & cod b₁ = c₄ ) } is set
Hom (o1,o2) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = o1 & cod b₁ = o2 ) } is set
[:(Hom (C,c₄)),(Hom (o1,o2)):] is Relation-like set
Hom (C,c₄) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = C & cod b₁ = c₄ ) } is set
Hom (o1,o2) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = o1 & cod b₁ = o2 ) } is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
the carrier of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,o1
curry o2 is Relation-like Function-like set
G1 is Element of the carrier of A
c₄ ?- G1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id G1 is Morphism of G1,G1
(curry c₄) . (id G1) is set
o1 ?- G1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry o1 is Relation-like Function-like set
(curry o1) . (id G1) is set
(curry o2) . G1 is set
[:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty set
t is Element of the carrier of B
(c₄ ?- G1) . t is Element of the carrier of C
the carrier of C is non empty set
Obj (c₄ ?- G1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- G1)) . t is Element of the carrier of C
(o1 ?- G1) . t is Element of the carrier of C
Obj (o1 ?- G1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o1 ?- G1)) . t is Element of the carrier of C
Hom (((c₄ ?- G1) . t),((o1 ?- G1) . t)) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- G1) . t & cod b₁ = (o1 ?- G1) . t ) } is set
[G1,t] is Element of the carrier of [:A,B:]
{G1,t} is non empty set
{G1} is non empty set
{{G1,t},{G1}} is non empty set
c₄ . [G1,t] is Element of the carrier of C
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . [G1,t] is Element of the carrier of C
o1 . [G1,t] is Element of the carrier of C
Obj o1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
(Obj o1) . [G1,t] is Element of the carrier of C
t is Element of the carrier of B
(c₄ ?- G1) . t is Element of the carrier of C
the carrier of C is non empty set
Obj (c₄ ?- G1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- G1)) . t is Element of the carrier of C
[G1,t] is Element of the carrier of [:A,B:]
{G1,t} is non empty set
{G1} is non empty set
{{G1,t},{G1}} is non empty set
c₄ . [G1,t] is Element of the carrier of C
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . [G1,t] is Element of the carrier of C
(o1 ?- G1) . t is Element of the carrier of C
Obj (o1 ?- G1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o1 ?- G1)) . t is Element of the carrier of C
o1 . [G1,t] is Element of the carrier of C
Obj o1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
(Obj o1) . [G1,t] is Element of the carrier of C
Hom (((c₄ ?- G1) . t),((o1 ?- G1) . t)) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- G1) . t & cod b₁ = (o1 ?- G1) . t ) } is set
Funcs ( the carrier of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier of B, the carrier' of C
G2 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry G2 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
[: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty set
(curry G2) . G1 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
((curry G2) . G1) . t is Element of the carrier' of C
G2 . (G1,t) is Element of the carrier' of C
[G1,t] is set
G2 . [G1,t] is set
o2 . [G1,t] is Morphism of c₄ . [G1,t],o1 . [G1,t]
t is Element of the carrier of B
((curry G2) . G1) . t is Element of the carrier' of C
(c₄ ?- G1) . t is Element of the carrier of C
(Obj (c₄ ?- G1)) . t is Element of the carrier of C
(o1 ?- G1) . t is Element of the carrier of C
(Obj (o1 ?- G1)) . t is Element of the carrier of C
Hom (((c₄ ?- G1) . t),((o1 ?- G1) . t)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- G1) . t & cod b₁ = (o1 ?- G1) . t ) } is set
F1 is Element of the carrier of B
F2 is Element of the carrier of B
Hom (F1,F2) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = F1 & cod b₁ = F2 ) } is set
(c₄ ?- G1) . F1 is Element of the carrier of C
(Obj (c₄ ?- G1)) . F1 is Element of the carrier of C
(c₄ ?- G1) . F2 is Element of the carrier of C
(Obj (c₄ ?- G1)) . F2 is Element of the carrier of C
Hom (((c₄ ?- G1) . F1),((c₄ ?- G1) . F2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- G1) . F1 & cod b₁ = (c₄ ?- G1) . F2 ) } is set
Hom (G1,G1) is non empty Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = G1 & cod b₁ = G1 ) } is set
[G1,F1] is Element of the carrier of [:A,B:]
{G1,F1} is non empty set
{{G1,F1},{G1}} is non empty set
[G1,F2] is Element of the carrier of [:A,B:]
{G1,F2} is non empty set
{{G1,F2},{G1}} is non empty set
s is Morphism of F1,F2
[(id G1),s] is Element of the carrier' of [:A,B:]
{(id G1),s} is non empty set
{(id G1)} is non empty set
{{(id G1),s},{(id G1)}} is non empty set
Hom ([G1,F1],[G1,F2]) is Element of bool the carrier' of [:A,B:]
bool the carrier' of [:A,B:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:A,B:] : ( dom b₁ = [G1,F1] & cod b₁ = [G1,F2] ) } is set
c₄ . [G1,F1] is Element of the carrier of C
(Obj c₄) . [G1,F1] is Element of the carrier of C
c₄ . [G1,F2] is Element of the carrier of C
(Obj c₄) . [G1,F2] is Element of the carrier of C
Hom ((c₄ . [G1,F1]),(c₄ . [G1,F2])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [G1,F1] & cod b₁ = c₄ . [G1,F2] ) } is set
t is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of c₄ ?- G1,o1 ?- G1
t . F1 is Morphism of (c₄ ?- G1) . F1,(o1 ?- G1) . F1
(o1 ?- G1) . F1 is Element of the carrier of C
(Obj (o1 ?- G1)) . F1 is Element of the carrier of C
((curry G2) . G1) . F1 is Element of the carrier' of C
G2 . (G1,F1) is Element of the carrier' of C
[G1,F1] is set
G2 . [G1,F1] is set
o2 . [G1,F1] is Morphism of c₄ . [G1,F1],o1 . [G1,F1]
o1 . [G1,F1] is Element of the carrier of C
(Obj o1) . [G1,F1] is Element of the carrier of C
o1 . [G1,F2] is Element of the carrier of C
(Obj o1) . [G1,F2] is Element of the carrier of C
Hom ((c₄ . [G1,F2]),(o1 . [G1,F2])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [G1,F2] & cod b₁ = o1 . [G1,F2] ) } is set
(o1 ?- G1) . F2 is Element of the carrier of C
(Obj (o1 ?- G1)) . F2 is Element of the carrier of C
Hom (((o1 ?- G1) . F1),((o1 ?- G1) . F2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (o1 ?- G1) . F1 & cod b₁ = (o1 ?- G1) . F2 ) } is set
Hom ((c₄ . [G1,F1]),(o1 . [G1,F1])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [G1,F1] & cod b₁ = o1 . [G1,F1] ) } is set
Hom ((o1 . [G1,F1]),(o1 . [G1,F2])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o1 . [G1,F1] & cod b₁ = o1 . [G1,F2] ) } is set
t . F2 is Morphism of (c₄ ?- G1) . F2,(o1 ?- G1) . F2
((curry G2) . G1) . F2 is Element of the carrier' of C
G2 . (G1,F2) is Element of the carrier' of C
[G1,F2] is set
G2 . [G1,F2] is set
o2 . [G1,F2] is Morphism of c₄ . [G1,F2],o1 . [G1,F2]
(c₄ ?- G1) /. s is Morphism of (c₄ ?- G1) . F1,(c₄ ?- G1) . F2
(t . F2) * ((c₄ ?- G1) /. s) is Morphism of (c₄ ?- G1) . F1,(o1 ?- G1) . F2
(o2 . [G1,F2]) (*) ((c₄ ?- G1) /. s) is Element of the carrier' of C
(c₄ ?- G1) . s is Element of the carrier' of C
(o2 . [G1,F2]) (*) ((c₄ ?- G1) . s) is Element of the carrier' of C
c₄ . ((id G1),s) is Element of the carrier' of C
[(id G1),s] is set
c₄ . [(id G1),s] is set
(o2 . [G1,F2]) (*) (c₄ . ((id G1),s)) is Element of the carrier' of C
f is Morphism of [G1,F1],[G1,F2]
c₄ /. f is Morphism of c₄ . [G1,F1],c₄ . [G1,F2]
(o2 . [G1,F2]) (*) (c₄ /. f) is Element of the carrier' of C
(o2 . [G1,F2]) * (c₄ /. f) is Morphism of c₄ . [G1,F1],o1 . [G1,F2]
o1 /. f is Morphism of o1 . [G1,F1],o1 . [G1,F2]
(o1 /. f) * (o2 . [G1,F1]) is Morphism of c₄ . [G1,F1],o1 . [G1,F2]
(o1 /. f) (*) (o2 . [G1,F1]) is Element of the carrier' of C
o1 . ((id G1),s) is Element of the carrier' of C
o1 . [(id G1),s] is set
(o1 . ((id G1),s)) (*) (o2 . [G1,F1]) is Element of the carrier' of C
(o1 ?- G1) . s is Element of the carrier' of C
((o1 ?- G1) . s) (*) (o2 . [G1,F1]) is Element of the carrier' of C
(o1 ?- G1) /. s is Morphism of (o1 ?- G1) . F1,(o1 ?- G1) . F2
((o1 ?- G1) /. s) (*) (t . F1) is Element of the carrier' of C
((o1 ?- G1) /. s) * (t . F1) is Morphism of (c₄ ?- G1) . F1,(o1 ?- G1) . F2
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
curry c₄ is Relation-like Function-like set
o1 is Element of the carrier' of A
(curry c₄) . o1 is set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
[:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty set
Funcs ( the carrier' of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier' of B, the carrier' of C
o2 is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:]
curry o2 is non empty Relation-like the carrier' of A -defined Funcs ( the carrier' of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):]
[: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty set
(curry o2) . o1 is Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier' of B, the carrier' of C)
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier' of B is non empty set
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of A, the carrier of B:] is non empty Relation-like set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
C is Element of the carrier of A
c₄ is Element of the carrier of A
Hom (C,c₄) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = C & cod b₁ = c₄ ) } is set
o1 is Element of the carrier of B
o2 is Element of the carrier of B
Hom (o1,o2) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = o1 & cod b₁ = o2 ) } is set
[C,o1] is Element of the carrier of [:A,B:]
the carrier of [:A,B:] is non empty set
{C,o1} is non empty set
{C} is non empty set
{{C,o1},{C}} is non empty set
[c₄,o2] is Element of the carrier of [:A,B:]
{c₄,o2} is non empty set
{c₄} is non empty set
{{c₄,o2},{c₄}} is non empty set
Hom ([C,o1],[c₄,o2]) is Element of bool the carrier' of [:A,B:]
the carrier' of [:A,B:] is non empty set
bool the carrier' of [:A,B:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:A,B:] : ( dom b₁ = [C,o1] & cod b₁ = [c₄,o2] ) } is set
G1 is Element of the carrier' of A
G2 is Element of the carrier' of B
[G1,G2] is Element of the carrier' of [:A,B:]
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
[:(Hom (C,c₄)),(Hom (o1,o2)):] is Relation-like set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is Element of the carrier of A
o2 is Element of the carrier of A
Hom (o1,o2) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = o1 & cod b₁ = o2 ) } is set
c₄ ?- o1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id o1 is Morphism of o1,o1
(curry c₄) . (id o1) is set
c₄ ?- o2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id o2 is Morphism of o2,o2
(curry c₄) . (id o2) is set
[:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty set
G2 is Morphism of o1,o2
(A,B,C,c₄,G2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry c₄) . G2 is set
(A,B,C,c₄,G2) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
Funcs ( the carrier' of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier' of B, the carrier' of C
G1 is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:]
curry G1 is non empty Relation-like the carrier' of A -defined Funcs ( the carrier' of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):]
[: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty set
(curry G1) . G2 is Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier' of B, the carrier' of C)
F1 is Element of the carrier of B
id F1 is Morphism of F1,F1
Hom (F1,F1) is non empty Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = F1 & cod b₁ = F1 ) } is set
[G2,(id F1)] is Element of the carrier' of [:A,B:]
{G2,(id F1)} is non empty set
{G2} is non empty set
{{G2,(id F1)},{G2}} is non empty set
[o1,F1] is Element of the carrier of [:A,B:]
the carrier of [:A,B:] is non empty set
{o1,F1} is non empty set
{o1} is non empty set
{{o1,F1},{o1}} is non empty set
[o2,F1] is Element of the carrier of [:A,B:]
{o2,F1} is non empty set
{o2} is non empty set
{{o2,F1},{o2}} is non empty set
Hom ([o1,F1],[o2,F1]) is Element of bool the carrier' of [:A,B:]
bool the carrier' of [:A,B:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:A,B:] : ( dom b₁ = [o1,F1] & cod b₁ = [o2,F1] ) } is set
c₄ . (G2,(id F1)) is Element of the carrier' of C
[G2,(id F1)] is set
c₄ . [G2,(id F1)] is set
c₄ . [o1,F1] is Element of the carrier of C
the carrier of C is non empty set
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . [o1,F1] is Element of the carrier of C
c₄ . [o2,F1] is Element of the carrier of C
(Obj c₄) . [o2,F1] is Element of the carrier of C
Hom ((c₄ . [o1,F1]),(c₄ . [o2,F1])) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [o1,F1] & cod b₁ = c₄ . [o2,F1] ) } is set
(IdMap B) . F1 is Element of the carrier' of B
(c₄ ?- o1) . F1 is Element of the carrier of C
Obj (c₄ ?- o1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- o1)) . F1 is Element of the carrier of C
(c₄ ?- o2) . F1 is Element of the carrier of C
Obj (c₄ ?- o2) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- o2)) . F1 is Element of the carrier of C
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
t . (id F1) is Element of the carrier' of C
Hom (((c₄ ?- o1) . F1),((c₄ ?- o2) . F1)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- o1) . F1 & cod b₁ = (c₄ ?- o2) . F1 ) } is set
((A,B,C,c₄,G2) * (IdMap B)) . F1 is Element of the carrier' of C
F1 is Element of the carrier of B
(c₄ ?- o1) . F1 is Element of the carrier of C
(Obj (c₄ ?- o1)) . F1 is Element of the carrier of C
(c₄ ?- o2) . F1 is Element of the carrier of C
(Obj (c₄ ?- o2)) . F1 is Element of the carrier of C
Hom (((c₄ ?- o1) . F1),((c₄ ?- o2) . F1)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- o1) . F1 & cod b₁ = (c₄ ?- o2) . F1 ) } is set
F2 is Element of the carrier of B
((A,B,C,c₄,G2) * (IdMap B)) . F2 is Element of the carrier' of C
(c₄ ?- o1) . F2 is Element of the carrier of C
(Obj (c₄ ?- o1)) . F2 is Element of the carrier of C
(c₄ ?- o2) . F2 is Element of the carrier of C
(Obj (c₄ ?- o2)) . F2 is Element of the carrier of C
Hom (((c₄ ?- o1) . F2),((c₄ ?- o2) . F2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- o1) . F2 & cod b₁ = (c₄ ?- o2) . F2 ) } is set
F1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
F1 . F2 is Element of the carrier' of C
Hom (o1,o1) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = o1 & cod b₁ = o1 ) } is set
Hom (o2,o2) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = o2 & cod b₁ = o2 ) } is set
f is Element of the carrier of B
f2 is Element of the carrier of B
Hom (f,f2) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f & cod b₁ = f2 ) } is set
(c₄ ?- o2) . f is Element of the carrier of C
(Obj (c₄ ?- o2)) . f is Element of the carrier of C
(c₄ ?- o2) . f2 is Element of the carrier of C
(Obj (c₄ ?- o2)) . f2 is Element of the carrier of C
Hom (((c₄ ?- o2) . f),((c₄ ?- o2) . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- o2) . f & cod b₁ = (c₄ ?- o2) . f2 ) } is set
id f is Morphism of f,f
id f2 is Morphism of f2,f2
Hom (f,f) is non empty Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f & cod b₁ = f ) } is set
dom (id f2) is Element of the carrier of B
the Source of B . (id f2) is Element of the carrier of B
g1 is Morphism of f,f2
cod g1 is Element of the carrier of B
the Target of B . g1 is Element of the carrier of B
Hom (f2,f2) is non empty Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f2 & cod b₁ = f2 ) } is set
s is Element of the carrier' of A
G2 (*) s is Element of the carrier' of A
t2 is Element of the carrier' of B
t2 (*) g1 is Element of the carrier' of B
[(G2 (*) s),(t2 (*) g1)] is Element of the carrier' of [:A,B:]
{(G2 (*) s),(t2 (*) g1)} is non empty set
{(G2 (*) s)} is non empty set
{{(G2 (*) s),(t2 (*) g1)},{(G2 (*) s)}} is non empty set
(id f2) * g1 is Morphism of f,f2
[(G2 (*) s),((id f2) * g1)] is Element of the carrier' of [:A,B:]
{(G2 (*) s),((id f2) * g1)} is non empty set
{{(G2 (*) s),((id f2) * g1)},{(G2 (*) s)}} is non empty set
[(G2 (*) s),g1] is Element of the carrier' of [:A,B:]
{(G2 (*) s),g1} is non empty set
{{(G2 (*) s),g1},{(G2 (*) s)}} is non empty set
G2 * (id o1) is Morphism of o1,o2
[(G2 * (id o1)),g1] is Element of the carrier' of [:A,B:]
{(G2 * (id o1)),g1} is non empty set
{(G2 * (id o1))} is non empty set
{{(G2 * (id o1)),g1},{(G2 * (id o1))}} is non empty set
[G2,g1] is Element of the carrier' of [:A,B:]
{G2,g1} is non empty set
{{G2,g1},{G2}} is non empty set
(id o2) * G2 is Morphism of o1,o2
[((id o2) * G2),g1] is Element of the carrier' of [:A,B:]
{((id o2) * G2),g1} is non empty set
{((id o2) * G2)} is non empty set
{{((id o2) * G2),g1},{((id o2) * G2)}} is non empty set
f is Element of the carrier' of A
f (*) G2 is Element of the carrier' of A
[(f (*) G2),g1] is Element of the carrier' of [:A,B:]
{(f (*) G2),g1} is non empty set
{(f (*) G2)} is non empty set
{{(f (*) G2),g1},{(f (*) G2)}} is non empty set
g1 * (id f) is Morphism of f,f2
[(f (*) G2),(g1 * (id f))] is Element of the carrier' of [:A,B:]
{(f (*) G2),(g1 * (id f))} is non empty set
{{(f (*) G2),(g1 * (id f))},{(f (*) G2)}} is non empty set
f1 is Element of the carrier' of B
g1 (*) f1 is Element of the carrier' of B
[(f (*) G2),(g1 (*) f1)] is Element of the carrier' of [:A,B:]
{(f (*) G2),(g1 (*) f1)} is non empty set
{{(f (*) G2),(g1 (*) f1)},{(f (*) G2)}} is non empty set
(c₄ ?- o1) . f2 is Element of the carrier of C
(Obj (c₄ ?- o1)) . f2 is Element of the carrier of C
Hom (((c₄ ?- o1) . f2),((c₄ ?- o2) . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- o1) . f2 & cod b₁ = (c₄ ?- o2) . f2 ) } is set
F2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of c₄ ?- o1,c₄ ?- o2
F2 . f2 is Morphism of (c₄ ?- o1) . f2,(c₄ ?- o2) . f2
F1 . f2 is Element of the carrier' of C
cod (id o1) is Element of the carrier of A
the Target of A . (id o1) is Element of the carrier of A
dom G2 is Element of the carrier of A
the Source of A . G2 is Element of the carrier of A
[(id o1),g1] is Element of the carrier' of [:A,B:]
{(id o1),g1} is non empty set
{(id o1)} is non empty set
{{(id o1),g1},{(id o1)}} is non empty set
cod [(id o1),g1] is Element of the carrier of [:A,B:]
the Target of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
[: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty Relation-like set
bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty set
the Target of [:A,B:] . [(id o1),g1] is Element of the carrier of [:A,B:]
[(dom G2),(cod g1)] is Element of the carrier of [:A,B:]
{(dom G2),(cod g1)} is non empty set
{(dom G2)} is non empty set
{{(dom G2),(cod g1)},{(dom G2)}} is non empty set
[G2,(id f2)] is Element of the carrier' of [:A,B:]
{G2,(id f2)} is non empty set
{{G2,(id f2)},{G2}} is non empty set
dom [G2,(id f2)] is Element of the carrier of [:A,B:]
the Source of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
the Source of [:A,B:] . [G2,(id f2)] is Element of the carrier of [:A,B:]
(c₄ ?- o1) . f is Element of the carrier of C
(Obj (c₄ ?- o1)) . f is Element of the carrier of C
Hom (((c₄ ?- o1) . f),((c₄ ?- o2) . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- o1) . f & cod b₁ = (c₄ ?- o2) . f ) } is set
F2 . f is Morphism of (c₄ ?- o1) . f,(c₄ ?- o2) . f
F1 . f is Element of the carrier' of C
dom g1 is Element of the carrier of B
the Source of B . g1 is Element of the carrier of B
cod (id f) is Element of the carrier of B
the Target of B . (id f) is Element of the carrier of B
dom (id o2) is Element of the carrier of A
the Source of A . (id o2) is Element of the carrier of A
cod G2 is Element of the carrier of A
the Target of A . G2 is Element of the carrier of A
[(id o2),g1] is Element of the carrier' of [:A,B:]
{(id o2),g1} is non empty set
{(id o2)} is non empty set
{{(id o2),g1},{(id o2)}} is non empty set
dom [(id o2),g1] is Element of the carrier of [:A,B:]
the Source of [:A,B:] . [(id o2),g1] is Element of the carrier of [:A,B:]
[(cod G2),(dom g1)] is Element of the carrier of [:A,B:]
{(cod G2),(dom g1)} is non empty set
{(cod G2)} is non empty set
{{(cod G2),(dom g1)},{(cod G2)}} is non empty set
[G2,(id f)] is Element of the carrier' of [:A,B:]
{G2,(id f)} is non empty set
{{G2,(id f)},{G2}} is non empty set
cod [G2,(id f)] is Element of the carrier of [:A,B:]
the Target of [:A,B:] . [G2,(id f)] is Element of the carrier of [:A,B:]
(IdMap B) . f2 is Element of the carrier' of B
(IdMap B) . f is Element of the carrier' of B
Hom (((c₄ ?- o1) . f),((c₄ ?- o1) . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- o1) . f & cod b₁ = (c₄ ?- o1) . f2 ) } is set
(c₄ ?- o1) /. g1 is Morphism of (c₄ ?- o1) . f,(c₄ ?- o1) . f2
(F2 . f2) * ((c₄ ?- o1) /. g1) is Morphism of (c₄ ?- o1) . f,(c₄ ?- o2) . f2
(F1 . f2) (*) ((c₄ ?- o1) /. g1) is Element of the carrier' of C
t . (id f2) is Element of the carrier' of C
(t . (id f2)) (*) ((c₄ ?- o1) /. g1) is Element of the carrier' of C
c₄ . (G2,(id f2)) is Element of the carrier' of C
[G2,(id f2)] is set
c₄ . [G2,(id f2)] is set
(c₄ . (G2,(id f2))) (*) ((c₄ ?- o1) /. g1) is Element of the carrier' of C
(c₄ ?- o1) . g1 is Element of the carrier' of C
c₄ . [G2,(id f2)] is Element of the carrier' of C
(c₄ . [G2,(id f2)]) (*) ((c₄ ?- o1) . g1) is Element of the carrier' of C
c₄ . ((id o1),g1) is Element of the carrier' of C
[(id o1),g1] is set
c₄ . [(id o1),g1] is set
(c₄ . (G2,(id f2))) (*) (c₄ . ((id o1),g1)) is Element of the carrier' of C
[G2,(id f2)] (*) [(id o1),g1] is Element of the carrier' of [:A,B:]
c₄ . ([G2,(id f2)] (*) [(id o1),g1]) is Element of the carrier' of C
c₄ . [(G2 (*) s),(t2 (*) g1)] is Element of the carrier' of C
[G2,f1] is Element of the carrier' of [:A,B:]
{G2,f1} is non empty set
{{G2,f1},{G2}} is non empty set
[f,g1] is Element of the carrier' of [:A,B:]
{f,g1} is non empty set
{f} is non empty set
{{f,g1},{f}} is non empty set
[f,g1] (*) [G2,f1] is Element of the carrier' of [:A,B:]
c₄ . ([f,g1] (*) [G2,f1]) is Element of the carrier' of C
c₄ . [G2,(id f)] is Element of the carrier' of C
c₄ . ((id o2),g1) is Element of the carrier' of C
[(id o2),g1] is set
c₄ . [(id o2),g1] is set
(c₄ . ((id o2),g1)) (*) (c₄ . [G2,(id f)]) is Element of the carrier' of C
(c₄ ?- o2) . g1 is Element of the carrier' of C
((c₄ ?- o2) . g1) (*) (c₄ . [G2,(id f)]) is Element of the carrier' of C
c₄ . (G2,(id f)) is Element of the carrier' of C
[G2,(id f)] is set
c₄ . [G2,(id f)] is set
(c₄ ?- o2) /. g1 is Morphism of (c₄ ?- o2) . f,(c₄ ?- o2) . f2
((c₄ ?- o2) /. g1) (*) (c₄ . (G2,(id f))) is Element of the carrier' of C
t . (id f) is Element of the carrier' of C
((c₄ ?- o2) /. g1) (*) (t . (id f)) is Element of the carrier' of C
((c₄ ?- o2) /. g1) (*) (F1 . f) is Element of the carrier' of C
((c₄ ?- o2) /. g1) * (F2 . f) is Morphism of (c₄ ?- o1) . f,(c₄ ?- o2) . f2
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is Element of the carrier' of A
(A,B,C,c₄,o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
curry c₄ is Relation-like Function-like set
(curry c₄) . o1 is set
(A,B,C,c₄,o1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
dom o1 is Element of the carrier of A
the Source of A . o1 is Element of the carrier of A
c₄ ?- (dom o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom o1) is Morphism of dom o1, dom o1
(curry c₄) . (id (dom o1)) is set
cod o1 is Element of the carrier of A
the Target of A . o1 is Element of the carrier of A
c₄ ?- (cod o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod o1) is Morphism of cod o1, cod o1
(curry c₄) . (id (cod o1)) is set
Hom ((dom o1),(cod o1)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom o1 & cod b₁ = cod o1 ) } is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is Element of the carrier' of A
dom o1 is Element of the carrier of A
the Source of A . o1 is Element of the carrier of A
c₄ ?- (dom o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id (dom o1) is Morphism of dom o1, dom o1
(curry c₄) . (id (dom o1)) is set
cod o1 is Element of the carrier of A
the Target of A . o1 is Element of the carrier of A
c₄ ?- (cod o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod o1) is Morphism of cod o1, cod o1
(curry c₄) . (id (cod o1)) is set
Hom ((dom o1),(cod o1)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom o1 & cod b₁ = cod o1 ) } is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is Element of the carrier' of A
dom o1 is Element of the carrier of A
the Source of A . o1 is Element of the carrier of A
c₄ ?- (dom o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id (dom o1) is Morphism of dom o1, dom o1
(curry c₄) . (id (dom o1)) is set
cod o1 is Element of the carrier of A
the Target of A . o1 is Element of the carrier of A
c₄ ?- (cod o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod o1) is Morphism of cod o1, cod o1
(curry c₄) . (id (cod o1)) is set
(A,B,C,c₄,o1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o1),c₄ ?- (cod o1)
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,c₄,o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry c₄) . o1 is set
(A,B,C,c₄,o1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
o2 is Element of the carrier of B
(A,B,C,c₄,o1) . o2 is Morphism of (c₄ ?- (dom o1)) . o2,(c₄ ?- (cod o1)) . o2
(c₄ ?- (dom o1)) . o2 is Element of the carrier of C
the carrier of C is non empty set
Obj (c₄ ?- (dom o1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- (dom o1))) . o2 is Element of the carrier of C
(c₄ ?- (cod o1)) . o2 is Element of the carrier of C
Obj (c₄ ?- (cod o1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- (cod o1))) . o2 is Element of the carrier of C
id o2 is Morphism of o2,o2
c₄ . (o1,(id o2)) is Element of the carrier' of C
[o1,(id o2)] is set
{o1,(id o2)} is non empty set
{o1} is non empty set
{{o1,(id o2)},{o1}} is non empty set
c₄ . [o1,(id o2)] is set
[:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty set
Funcs ( the carrier' of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier' of B, the carrier' of C
G1 is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:]
curry G1 is non empty Relation-like the carrier' of A -defined Funcs ( the carrier' of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):]
[: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty set
(curry G1) . o1 is Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier' of B, the carrier' of C)
(IdMap B) . o2 is Element of the carrier' of B
((A,B,C,c₄,o1) * (IdMap B)) . o2 is Element of the carrier' of C
G2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
G2 . (id o2) is Element of the carrier' of C
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is Element of the carrier of A
c₄ ?- o1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id o1 is Morphism of o1,o1
(curry c₄) . (id o1) is set
id (c₄ ?- o1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- o1,c₄ ?- o1
(A,B,C,c₄,(id o1)) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom (id o1)),c₄ ?- (cod (id o1))
dom (id o1) is Element of the carrier of A
the Source of A . (id o1) is Element of the carrier of A
c₄ ?- (dom (id o1)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom (id o1)) is Morphism of dom (id o1), dom (id o1)
(curry c₄) . (id (dom (id o1))) is set
cod (id o1) is Element of the carrier of A
the Target of A . (id o1) is Element of the carrier of A
c₄ ?- (cod (id o1)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod (id o1)) is Morphism of cod (id o1), cod (id o1)
(curry c₄) . (id (cod (id o1))) is set
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,c₄,(id o1)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(A,B,C,c₄,(id o1)) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
[:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty set
Funcs ( the carrier' of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier' of B, the carrier' of C
o2 is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:]
curry o2 is non empty Relation-like the carrier' of A -defined Funcs ( the carrier' of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):]
[: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty set
(curry o2) . (id o1) is Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier' of B, the carrier' of C)
t is Element of the carrier of B
id t is Morphism of t,t
(IdMap B) . t is Element of the carrier' of B
G2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of c₄ ?- o1,c₄ ?- o1
G2 . t is Element of the carrier' of C
G1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
G1 . (id t) is Element of the carrier' of C
c₄ . ((id o1),(id t)) is Element of the carrier' of C
[(id o1),(id t)] is set
{(id o1),(id t)} is non empty set
{(id o1)} is non empty set
{{(id o1),(id t)},{(id o1)}} is non empty set
c₄ . [(id o1),(id t)] is set
[o1,t] is Element of the carrier of [:A,B:]
the carrier of [:A,B:] is non empty set
{o1,t} is non empty set
{o1} is non empty set
{{o1,t},{o1}} is non empty set
id [o1,t] is Morphism of [o1,t],[o1,t]
c₄ . (id [o1,t]) is Element of the carrier' of C
c₄ . [o1,t] is Element of the carrier of C
the carrier of C is non empty set
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . [o1,t] is Element of the carrier of C
id (c₄ . [o1,t]) is Morphism of c₄ . [o1,t],c₄ . [o1,t]
(c₄ ?- o1) . t is Element of the carrier of C
Obj (c₄ ?- o1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- o1)) . t is Element of the carrier of C
id ((c₄ ?- o1) . t) is Morphism of (c₄ ?- o1) . t,(c₄ ?- o1) . t
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is Element of the carrier' of A
dom o1 is Element of the carrier of A
the Source of A . o1 is Element of the carrier of A
o2 is Element of the carrier' of A
cod o2 is Element of the carrier of A
the Target of A . o2 is Element of the carrier of A
dom o2 is Element of the carrier of A
the Source of A . o2 is Element of the carrier of A
c₄ ?- (dom o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id (dom o2) is Morphism of dom o2, dom o2
(curry c₄) . (id (dom o2)) is set
c₄ ?- (dom o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom o1) is Morphism of dom o1, dom o1
(curry c₄) . (id (dom o1)) is set
(A,B,C,c₄,o2) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (cod o2)
c₄ ?- (cod o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod o2) is Morphism of cod o2, cod o2
(curry c₄) . (id (cod o2)) is set
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry c₄) . o2 is set
(A,B,C,c₄,o2) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
o1 (*) o2 is Element of the carrier' of A
(A,B,C,c₄,(o1 (*) o2)) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom (o1 (*) o2)),c₄ ?- (cod (o1 (*) o2))
dom (o1 (*) o2) is Element of the carrier of A
the Source of A . (o1 (*) o2) is Element of the carrier of A
c₄ ?- (dom (o1 (*) o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom (o1 (*) o2)) is Morphism of dom (o1 (*) o2), dom (o1 (*) o2)
(curry c₄) . (id (dom (o1 (*) o2))) is set
cod (o1 (*) o2) is Element of the carrier of A
the Target of A . (o1 (*) o2) is Element of the carrier of A
c₄ ?- (cod (o1 (*) o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod (o1 (*) o2)) is Morphism of cod (o1 (*) o2), cod (o1 (*) o2)
(curry c₄) . (id (cod (o1 (*) o2))) is set
(A,B,C,c₄,(o1 (*) o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . (o1 (*) o2) is set
(A,B,C,c₄,(o1 (*) o2)) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
cod o1 is Element of the carrier of A
the Target of A . o1 is Element of the carrier of A
c₄ ?- (cod o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod o1) is Morphism of cod o1, cod o1
(curry c₄) . (id (cod o1)) is set
(A,B,C,c₄,o1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o1),c₄ ?- (cod o1)
(A,B,C,c₄,o1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . o1 is set
(A,B,C,c₄,o1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty set
Funcs ( the carrier' of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier' of B, the carrier' of C
G1 is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:]
curry G1 is non empty Relation-like the carrier' of A -defined Funcs ( the carrier' of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):]
[: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier' of A,(Funcs ( the carrier' of B, the carrier' of C)):] is non empty set
(curry G1) . (o1 (*) o2) is Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier' of B, the carrier' of C)
(curry G1) . o2 is Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier' of B, the carrier' of C)
(curry G1) . o1 is Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier' of B, the carrier' of C)
F2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (dom o1)
(A,B,C,c₄,o1) `*` F2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (cod o1)
f is Element of the carrier of B
Hom (f,f) is non empty Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f & cod b₁ = f ) } is set
id f is Morphism of f,f
(IdMap B) . f is Element of the carrier' of B
(A,B,C,c₄,o1) . f is Morphism of (c₄ ?- (dom o1)) . f,(c₄ ?- (cod o1)) . f
(c₄ ?- (dom o1)) . f is Element of the carrier of C
the carrier of C is non empty set
Obj (c₄ ?- (dom o1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- (dom o1))) . f is Element of the carrier of C
(c₄ ?- (cod o1)) . f is Element of the carrier of C
Obj (c₄ ?- (cod o1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- (cod o1))) . f is Element of the carrier of C
((A,B,C,c₄,o1) * (IdMap B)) . f is Element of the carrier' of C
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
F1 . (id f) is Element of the carrier' of C
c₄ . (o1,(id f)) is Element of the carrier' of C
[o1,(id f)] is set
{o1,(id f)} is non empty set
{o1} is non empty set
{{o1,(id f)},{o1}} is non empty set
c₄ . [o1,(id f)] is set
dom (id f) is Element of the carrier of B
the Source of B . (id f) is Element of the carrier of B
cod (id f) is Element of the carrier of B
the Target of B . (id f) is Element of the carrier of B
[o1,(id f)] is Element of the carrier' of [:A,B:]
dom [o1,(id f)] is Element of the carrier of [:A,B:]
the carrier of [:A,B:] is non empty set
the Source of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
[: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty Relation-like set
bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty set
the Source of [:A,B:] . [o1,(id f)] is Element of the carrier of [:A,B:]
[(cod o2),(cod (id f))] is Element of the carrier of [:A,B:]
{(cod o2),(cod (id f))} is non empty set
{(cod o2)} is non empty set
{{(cod o2),(cod (id f))},{(cod o2)}} is non empty set
[o2,(id f)] is Element of the carrier' of [:A,B:]
{o2,(id f)} is non empty set
{o2} is non empty set
{{o2,(id f)},{o2}} is non empty set
cod [o2,(id f)] is Element of the carrier of [:A,B:]
the Target of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
the Target of [:A,B:] . [o2,(id f)] is Element of the carrier of [:A,B:]
Hom (((c₄ ?- (dom o1)) . f),((c₄ ?- (cod o1)) . f)) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- (dom o1)) . f & cod b₁ = (c₄ ?- (cod o1)) . f ) } is set
(c₄ ?- (dom o2)) . f is Element of the carrier of C
Obj (c₄ ?- (dom o2)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- (dom o2))) . f is Element of the carrier of C
Hom (((c₄ ?- (dom o2)) . f),((c₄ ?- (dom o1)) . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (c₄ ?- (dom o2)) . f & cod b₁ = (c₄ ?- (dom o1)) . f ) } is set
(A,B,C,c₄,o2) . f is Morphism of (c₄ ?- (dom o2)) . f,(c₄ ?- (cod o2)) . f
(c₄ ?- (cod o2)) . f is Element of the carrier of C
Obj (c₄ ?- (cod o2)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- (cod o2))) . f is Element of the carrier of C
((A,B,C,c₄,o2) * (IdMap B)) . f is Element of the carrier' of C
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
t . (id f) is Element of the carrier' of C
c₄ . (o2,(id f)) is Element of the carrier' of C
[o2,(id f)] is set
c₄ . [o2,(id f)] is set
(A,B,C,c₄,(o1 (*) o2)) . f is Morphism of (c₄ ?- (dom (o1 (*) o2))) . f,(c₄ ?- (cod (o1 (*) o2))) . f
(c₄ ?- (dom (o1 (*) o2))) . f is Element of the carrier of C
Obj (c₄ ?- (dom (o1 (*) o2))) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- (dom (o1 (*) o2)))) . f is Element of the carrier of C
(c₄ ?- (cod (o1 (*) o2))) . f is Element of the carrier of C
Obj (c₄ ?- (cod (o1 (*) o2))) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- (cod (o1 (*) o2)))) . f is Element of the carrier of C
((A,B,C,c₄,(o1 (*) o2)) * (IdMap B)) . f is Element of the carrier' of C
G2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
G2 . (id f) is Element of the carrier' of C
c₄ . ((o1 (*) o2),(id f)) is Element of the carrier' of C
[(o1 (*) o2),(id f)] is set
{(o1 (*) o2),(id f)} is non empty set
{(o1 (*) o2)} is non empty set
{{(o1 (*) o2),(id f)},{(o1 (*) o2)}} is non empty set
c₄ . [(o1 (*) o2),(id f)] is set
(id f) * (id f) is Morphism of f,f
[(o1 (*) o2),((id f) * (id f))] is Element of the carrier' of [:A,B:]
{(o1 (*) o2),((id f) * (id f))} is non empty set
{{(o1 (*) o2),((id f) * (id f))},{(o1 (*) o2)}} is non empty set
c₄ . [(o1 (*) o2),((id f) * (id f))] is Element of the carrier' of C
(id f) (*) (id f) is Element of the carrier' of B
[(o1 (*) o2),((id f) (*) (id f))] is Element of the carrier' of [:A,B:]
{(o1 (*) o2),((id f) (*) (id f))} is non empty set
{{(o1 (*) o2),((id f) (*) (id f))},{(o1 (*) o2)}} is non empty set
c₄ . [(o1 (*) o2),((id f) (*) (id f))] is Element of the carrier' of C
[o1,(id f)] (*) [o2,(id f)] is Element of the carrier' of [:A,B:]
c₄ . ([o1,(id f)] (*) [o2,(id f)]) is Element of the carrier' of C
s is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of c₄ ?- (dom o2),c₄ ?- (dom o1)
s . f is Morphism of (c₄ ?- (dom o2)) . f,(c₄ ?- (dom o1)) . f
((A,B,C,c₄,o1) . f) (*) (s . f) is Element of the carrier' of C
((A,B,C,c₄,o1) . f) * (s . f) is Morphism of (c₄ ?- (dom o2)) . f,(c₄ ?- (cod o1)) . f
(A,B,C,c₄,o1) `*` s is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of c₄ ?- (dom o2),c₄ ?- (cod o1)
((A,B,C,c₄,o1) `*` s) . f is Morphism of (c₄ ?- (dom o2)) . f,(c₄ ?- (cod o1)) . f
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is set
o2 is Element of the carrier' of A
dom o2 is Element of the carrier of A
the Source of A . o2 is Element of the carrier of A
c₄ ?- (dom o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id (dom o2) is Morphism of dom o2, dom o2
(curry c₄) . (id (dom o2)) is set
cod o2 is Element of the carrier of A
the Target of A . o2 is Element of the carrier of A
c₄ ?- (cod o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod o2) is Morphism of cod o2, cod o2
(curry c₄) . (id (cod o2)) is set
[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))] is set
{(c₄ ?- (dom o2)),(c₄ ?- (cod o2))} is non empty set
{(c₄ ?- (dom o2))} is non empty set
{{(c₄ ?- (dom o2)),(c₄ ?- (cod o2))},{(c₄ ?- (dom o2))}} is non empty set
(A,B,C,c₄,o2) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (cod o2)
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry c₄) . o2 is set
(A,B,C,c₄,o2) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
[[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)] is set
{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)} is non empty set
{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))]} is non empty Relation-like set
{{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)},{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))]}} is non empty set
G1 is set
NatTrans (B,C) is non empty NatTrans-DOMAIN of B,C
G2 is Element of the carrier' of A
dom G2 is Element of the carrier of A
the Source of A . G2 is Element of the carrier of A
c₄ ?- (dom G2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom G2) is Morphism of dom G2, dom G2
(curry c₄) . (id (dom G2)) is set
cod G2 is Element of the carrier of A
the Target of A . G2 is Element of the carrier of A
c₄ ?- (cod G2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod G2) is Morphism of cod G2, cod G2
(curry c₄) . (id (cod G2)) is set
[(c₄ ?- (dom G2)),(c₄ ?- (cod G2))] is set
{(c₄ ?- (dom G2)),(c₄ ?- (cod G2))} is non empty set
{(c₄ ?- (dom G2))} is non empty set
{{(c₄ ?- (dom G2)),(c₄ ?- (cod G2))},{(c₄ ?- (dom G2))}} is non empty set
(A,B,C,c₄,G2) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom G2),c₄ ?- (cod G2)
(A,B,C,c₄,G2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . G2 is set
(A,B,C,c₄,G2) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(c₄ ?- (dom G2)),(c₄ ?- (cod G2))],(A,B,C,c₄,G2)] is set
{[(c₄ ?- (dom G2)),(c₄ ?- (cod G2))],(A,B,C,c₄,G2)} is non empty set
{[(c₄ ?- (dom G2)),(c₄ ?- (cod G2))]} is non empty Relation-like set
{{[(c₄ ?- (dom G2)),(c₄ ?- (cod G2))],(A,B,C,c₄,G2)},{[(c₄ ?- (dom G2)),(c₄ ?- (cod G2))]}} is non empty set
[: the carrier' of A, the carrier' of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier' of A, the carrier' of (Functors (B,C)):] is non empty set
o1 is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier' of (Functors (B,C)):]
the carrier of (Functors (B,C)) is non empty set
o2 is Element of the carrier of A
id o2 is Morphism of o2,o2
o1 . (id o2) is Element of the carrier' of (Functors (B,C))
c₄ ?- o2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id o2) is set
G1 is Element of the carrier of (Functors (B,C))
id G1 is Morphism of G1,G1
[(c₄ ?- o2),(c₄ ?- o2)] is set
{(c₄ ?- o2),(c₄ ?- o2)} is non empty set
{(c₄ ?- o2)} is non empty set
{{(c₄ ?- o2),(c₄ ?- o2)},{(c₄ ?- o2)}} is non empty set
(A,B,C,c₄,(id o2)) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom (id o2)),c₄ ?- (cod (id o2))
dom (id o2) is Element of the carrier of A
the Source of A . (id o2) is Element of the carrier of A
c₄ ?- (dom (id o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom (id o2)) is Morphism of dom (id o2), dom (id o2)
(curry c₄) . (id (dom (id o2))) is set
cod (id o2) is Element of the carrier of A
the Target of A . (id o2) is Element of the carrier of A
c₄ ?- (cod (id o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod (id o2)) is Morphism of cod (id o2), cod (id o2)
(curry c₄) . (id (cod (id o2))) is set
(A,B,C,c₄,(id o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(A,B,C,c₄,(id o2)) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(c₄ ?- o2),(c₄ ?- o2)],(A,B,C,c₄,(id o2))] is set
{[(c₄ ?- o2),(c₄ ?- o2)],(A,B,C,c₄,(id o2))} is non empty set
{[(c₄ ?- o2),(c₄ ?- o2)]} is non empty Relation-like set
{{[(c₄ ?- o2),(c₄ ?- o2)],(A,B,C,c₄,(id o2))},{[(c₄ ?- o2),(c₄ ?- o2)]}} is non empty set
id (c₄ ?- o2) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- o2,c₄ ?- o2
[[(c₄ ?- o2),(c₄ ?- o2)],(id (c₄ ?- o2))] is set
{[(c₄ ?- o2),(c₄ ?- o2)],(id (c₄ ?- o2))} is non empty set
{{[(c₄ ?- o2),(c₄ ?- o2)],(id (c₄ ?- o2))},{[(c₄ ?- o2),(c₄ ?- o2)]}} is non empty set
o2 is Element of the carrier' of A
dom o2 is Element of the carrier of A
the Source of A . o2 is Element of the carrier of A
id (dom o2) is Morphism of dom o2, dom o2
o1 . (id (dom o2)) is Element of the carrier' of (Functors (B,C))
o1 . o2 is Element of the carrier' of (Functors (B,C))
dom (o1 . o2) is Element of the carrier of (Functors (B,C))
the Source of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty set
the Source of (Functors (B,C)) . (o1 . o2) is Element of the carrier of (Functors (B,C))
id (dom (o1 . o2)) is Morphism of dom (o1 . o2), dom (o1 . o2)
cod o2 is Element of the carrier of A
the Target of A . o2 is Element of the carrier of A
id (cod o2) is Morphism of cod o2, cod o2
o1 . (id (cod o2)) is Element of the carrier' of (Functors (B,C))
cod (o1 . o2) is Element of the carrier of (Functors (B,C))
the Target of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
the Target of (Functors (B,C)) . (o1 . o2) is Element of the carrier of (Functors (B,C))
id (cod (o1 . o2)) is Morphism of cod (o1 . o2), cod (o1 . o2)
c₄ ?- (dom o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id (dom o2)) is set
c₄ ?- (cod o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id (cod o2)) is set
[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))] is set
{(c₄ ?- (dom o2)),(c₄ ?- (cod o2))} is non empty set
{(c₄ ?- (dom o2))} is non empty set
{{(c₄ ?- (dom o2)),(c₄ ?- (cod o2))},{(c₄ ?- (dom o2))}} is non empty set
(A,B,C,c₄,o2) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (cod o2)
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . o2 is set
(A,B,C,c₄,o2) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)] is set
{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)} is non empty set
{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))]} is non empty Relation-like set
{{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)},{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))]}} is non empty set
[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))] is set
{(c₄ ?- (dom o2)),(c₄ ?- (dom o2))} is non empty set
{{(c₄ ?- (dom o2)),(c₄ ?- (dom o2))},{(c₄ ?- (dom o2))}} is non empty set
(A,B,C,c₄,(id (dom o2))) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom (id (dom o2))),c₄ ?- (cod (id (dom o2)))
dom (id (dom o2)) is Element of the carrier of A
the Source of A . (id (dom o2)) is Element of the carrier of A
c₄ ?- (dom (id (dom o2))) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom (id (dom o2))) is Morphism of dom (id (dom o2)), dom (id (dom o2))
(curry c₄) . (id (dom (id (dom o2)))) is set
cod (id (dom o2)) is Element of the carrier of A
the Target of A . (id (dom o2)) is Element of the carrier of A
c₄ ?- (cod (id (dom o2))) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod (id (dom o2))) is Morphism of cod (id (dom o2)), cod (id (dom o2))
(curry c₄) . (id (cod (id (dom o2)))) is set
(A,B,C,c₄,(id (dom o2))) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(A,B,C,c₄,(id (dom o2))) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))],(A,B,C,c₄,(id (dom o2)))] is set
{[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))],(A,B,C,c₄,(id (dom o2)))} is non empty set
{[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))]} is non empty Relation-like set
{{[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))],(A,B,C,c₄,(id (dom o2)))},{[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))]}} is non empty set
id (c₄ ?- (dom o2)) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (dom o2)
[[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))],(id (c₄ ?- (dom o2)))] is set
{[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))],(id (c₄ ?- (dom o2)))} is non empty set
{{[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))],(id (c₄ ?- (dom o2)))},{[(c₄ ?- (dom o2)),(c₄ ?- (dom o2))]}} is non empty set
G1 is Element of the carrier of (Functors (B,C))
id G1 is Morphism of G1,G1
[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))] is set
{(c₄ ?- (cod o2)),(c₄ ?- (cod o2))} is non empty set
{(c₄ ?- (cod o2))} is non empty set
{{(c₄ ?- (cod o2)),(c₄ ?- (cod o2))},{(c₄ ?- (cod o2))}} is non empty set
(A,B,C,c₄,(id (cod o2))) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom (id (cod o2))),c₄ ?- (cod (id (cod o2)))
dom (id (cod o2)) is Element of the carrier of A
the Source of A . (id (cod o2)) is Element of the carrier of A
c₄ ?- (dom (id (cod o2))) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom (id (cod o2))) is Morphism of dom (id (cod o2)), dom (id (cod o2))
(curry c₄) . (id (dom (id (cod o2)))) is set
cod (id (cod o2)) is Element of the carrier of A
the Target of A . (id (cod o2)) is Element of the carrier of A
c₄ ?- (cod (id (cod o2))) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod (id (cod o2))) is Morphism of cod (id (cod o2)), cod (id (cod o2))
(curry c₄) . (id (cod (id (cod o2)))) is set
(A,B,C,c₄,(id (cod o2))) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(A,B,C,c₄,(id (cod o2))) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,(id (cod o2)))] is set
{[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,(id (cod o2)))} is non empty set
{[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))]} is non empty Relation-like set
{{[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,(id (cod o2)))},{[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))]}} is non empty set
id (c₄ ?- (cod o2)) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (cod o2),c₄ ?- (cod o2)
[[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))],(id (c₄ ?- (cod o2)))] is set
{[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))],(id (c₄ ?- (cod o2)))} is non empty set
{{[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))],(id (c₄ ?- (cod o2)))},{[(c₄ ?- (cod o2)),(c₄ ?- (cod o2))]}} is non empty set
G2 is Element of the carrier of (Functors (B,C))
id G2 is Morphism of G2,G2
G1 is Element of the carrier' of A
dom G1 is Element of the carrier of A
the Source of A . G1 is Element of the carrier of A
o2 is Element of the carrier' of A
cod o2 is Element of the carrier of A
the Target of A . o2 is Element of the carrier of A
G1 (*) o2 is Element of the carrier' of A
o1 . (G1 (*) o2) is Element of the carrier' of (Functors (B,C))
o1 . o2 is Element of the carrier' of (Functors (B,C))
o1 . G1 is Element of the carrier' of (Functors (B,C))
(o1 . G1) (*) (o1 . o2) is Element of the carrier' of (Functors (B,C))
dom o2 is Element of the carrier of A
the Source of A . o2 is Element of the carrier of A
c₄ ?- (dom o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom o2) is Morphism of dom o2, dom o2
(curry c₄) . (id (dom o2)) is set
c₄ ?- (dom G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom G1) is Morphism of dom G1, dom G1
(curry c₄) . (id (dom G1)) is set
(A,B,C,c₄,o2) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (cod o2)
c₄ ?- (cod o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod o2) is Morphism of cod o2, cod o2
(curry c₄) . (id (cod o2)) is set
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . o2 is set
(A,B,C,c₄,o2) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
cod (G1 (*) o2) is Element of the carrier of A
the Target of A . (G1 (*) o2) is Element of the carrier of A
cod G1 is Element of the carrier of A
the Target of A . G1 is Element of the carrier of A
dom (G1 (*) o2) is Element of the carrier of A
the Source of A . (G1 (*) o2) is Element of the carrier of A
c₄ ?- (cod G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod G1) is Morphism of cod G1, cod G1
(curry c₄) . (id (cod G1)) is set
[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))] is set
{(c₄ ?- (dom G1)),(c₄ ?- (cod G1))} is non empty set
{(c₄ ?- (dom G1))} is non empty set
{{(c₄ ?- (dom G1)),(c₄ ?- (cod G1))},{(c₄ ?- (dom G1))}} is non empty set
(A,B,C,c₄,G1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom G1),c₄ ?- (cod G1)
(A,B,C,c₄,G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . G1 is set
(A,B,C,c₄,G1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)] is set
{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)} is non empty set
{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))]} is non empty Relation-like set
{{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)},{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))]}} is non empty set
[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))] is set
{(c₄ ?- (dom o2)),(c₄ ?- (cod o2))} is non empty set
{(c₄ ?- (dom o2))} is non empty set
{{(c₄ ?- (dom o2)),(c₄ ?- (cod o2))},{(c₄ ?- (dom o2))}} is non empty set
[[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)] is set
{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)} is non empty set
{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))]} is non empty Relation-like set
{{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))],(A,B,C,c₄,o2)},{[(c₄ ?- (dom o2)),(c₄ ?- (cod o2))]}} is non empty set
F1 is Element of the carrier' of (Functors (B,C))
c₄ ?- (dom (G1 (*) o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom (G1 (*) o2)) is Morphism of dom (G1 (*) o2), dom (G1 (*) o2)
(curry c₄) . (id (dom (G1 (*) o2))) is set
c₄ ?- (cod (G1 (*) o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod (G1 (*) o2)) is Morphism of cod (G1 (*) o2), cod (G1 (*) o2)
(curry c₄) . (id (cod (G1 (*) o2))) is set
[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))] is set
{(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))} is non empty set
{(c₄ ?- (dom (G1 (*) o2)))} is non empty set
{{(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))},{(c₄ ?- (dom (G1 (*) o2)))}} is non empty set
(A,B,C,c₄,(G1 (*) o2)) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom (G1 (*) o2)),c₄ ?- (cod (G1 (*) o2))
(A,B,C,c₄,(G1 (*) o2)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . (G1 (*) o2) is set
(A,B,C,c₄,(G1 (*) o2)) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))],(A,B,C,c₄,(G1 (*) o2))] is set
{[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))],(A,B,C,c₄,(G1 (*) o2))} is non empty set
{[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))]} is non empty Relation-like set
{{[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))],(A,B,C,c₄,(G1 (*) o2))},{[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))]}} is non empty set
G2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (dom G1)
(A,B,C,c₄,G1) `*` G2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom o2),c₄ ?- (cod G1)
[[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))],((A,B,C,c₄,G1) `*` G2)] is set
{[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))],((A,B,C,c₄,G1) `*` G2)} is non empty set
{{[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))],((A,B,C,c₄,G1) `*` G2)},{[(c₄ ?- (dom (G1 (*) o2))),(c₄ ?- (cod (G1 (*) o2)))]}} is non empty set
t is Element of the carrier' of (Functors (B,C))
t (*) F1 is Element of the carrier' of (Functors (B,C))
o2 is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
G1 is Element of the carrier' of A
o2 . G1 is Element of the carrier' of (Functors (B,C))
dom G1 is Element of the carrier of A
the Source of A . G1 is Element of the carrier of A
c₄ ?- (dom G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom G1) is Morphism of dom G1, dom G1
(curry c₄) . (id (dom G1)) is set
cod G1 is Element of the carrier of A
the Target of A . G1 is Element of the carrier of A
c₄ ?- (cod G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod G1) is Morphism of cod G1, cod G1
(curry c₄) . (id (cod G1)) is set
[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))] is set
{(c₄ ?- (dom G1)),(c₄ ?- (cod G1))} is non empty set
{(c₄ ?- (dom G1))} is non empty set
{{(c₄ ?- (dom G1)),(c₄ ?- (cod G1))},{(c₄ ?- (dom G1))}} is non empty set
(A,B,C,c₄,G1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom G1),c₄ ?- (cod G1)
(A,B,C,c₄,G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . G1 is set
(A,B,C,c₄,G1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)] is set
{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)} is non empty set
{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))]} is non empty Relation-like set
{{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)},{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))]}} is non empty set
o1 is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
o2 is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
G1 is Element of the carrier' of A
o1 . G1 is Element of the carrier' of (Functors (B,C))
dom G1 is Element of the carrier of A
the Source of A . G1 is Element of the carrier of A
c₄ ?- (dom G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id (dom G1) is Morphism of dom G1, dom G1
(curry c₄) . (id (dom G1)) is set
cod G1 is Element of the carrier of A
the Target of A . G1 is Element of the carrier of A
c₄ ?- (cod G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod G1) is Morphism of cod G1, cod G1
(curry c₄) . (id (cod G1)) is set
[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))] is set
{(c₄ ?- (dom G1)),(c₄ ?- (cod G1))} is non empty set
{(c₄ ?- (dom G1))} is non empty set
{{(c₄ ?- (dom G1)),(c₄ ?- (cod G1))},{(c₄ ?- (dom G1))}} is non empty set
(A,B,C,c₄,G1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom G1),c₄ ?- (cod G1)
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,c₄,G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry c₄) . G1 is set
(A,B,C,c₄,G1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
[[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)] is set
{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)} is non empty set
{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))]} is non empty Relation-like set
{{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)},{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))]}} is non empty set
o2 . G1 is Element of the carrier' of (Functors (B,C))
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total transformation of C,c₄
o2 is Element of the carrier of A
o1 . o2 is Morphism of C . o2,c₄ . o2
C . o2 is Element of the carrier of B
the carrier of B is non empty set
Obj C is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj C) . o2 is Element of the carrier of B
c₄ . o2 is Element of the carrier of B
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj c₄) . o2 is Element of the carrier of B
Hom ((C . o2),(c₄ . o2)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = C . o2 & cod b₁ = c₄ . o2 ) } is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
the carrier' of (Functors (B,C)) is non empty set
o1 is Element of the carrier of A
(A,B,C,c₄) . o1 is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
Obj (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj (A,B,C,c₄)) . o1 is Element of the carrier of (Functors (B,C))
c₄ ?- o1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id o1 is Morphism of o1,o1
(curry c₄) . (id o1) is set
G1 is Element of the carrier' of A
(A,B,C,c₄) . G1 is Element of the carrier' of (Functors (B,C))
[(c₄ ?- o1),(c₄ ?- o1)] is set
{(c₄ ?- o1),(c₄ ?- o1)} is non empty set
{(c₄ ?- o1)} is non empty set
{{(c₄ ?- o1),(c₄ ?- o1)},{(c₄ ?- o1)}} is non empty set
(A,B,C,c₄,(id o1)) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom (id o1)),c₄ ?- (cod (id o1))
dom (id o1) is Element of the carrier of A
the Source of A . (id o1) is Element of the carrier of A
c₄ ?- (dom (id o1)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom (id o1)) is Morphism of dom (id o1), dom (id o1)
(curry c₄) . (id (dom (id o1))) is set
cod (id o1) is Element of the carrier of A
the Target of A . (id o1) is Element of the carrier of A
c₄ ?- (cod (id o1)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod (id o1)) is Morphism of cod (id o1), cod (id o1)
(curry c₄) . (id (cod (id o1))) is set
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,c₄,(id o1)) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(A,B,C,c₄,(id o1)) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
[[(c₄ ?- o1),(c₄ ?- o1)],(A,B,C,c₄,(id o1))] is set
{[(c₄ ?- o1),(c₄ ?- o1)],(A,B,C,c₄,(id o1))} is non empty set
{[(c₄ ?- o1),(c₄ ?- o1)]} is non empty Relation-like set
{{[(c₄ ?- o1),(c₄ ?- o1)],(A,B,C,c₄,(id o1))},{[(c₄ ?- o1),(c₄ ?- o1)]}} is non empty set
id (c₄ ?- o1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- o1,c₄ ?- o1
[[(c₄ ?- o1),(c₄ ?- o1)],(id (c₄ ?- o1))] is set
{[(c₄ ?- o1),(c₄ ?- o1)],(id (c₄ ?- o1))} is non empty set
{{[(c₄ ?- o1),(c₄ ?- o1)],(id (c₄ ?- o1))},{[(c₄ ?- o1),(c₄ ?- o1)]}} is non empty set
o2 is Element of the carrier of (Functors (B,C))
id o2 is Morphism of o2,o2
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
the carrier' of (Functors (B,C)) is non empty set
o1 is Element of the carrier of A
(A,B,C,c₄) . o1 is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
Obj (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj (A,B,C,c₄)) . o1 is Element of the carrier of (Functors (B,C))
c₄ ?- o1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id o1 is Morphism of o1,o1
(curry c₄) . (id o1) is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
o2 is Element of the carrier' of [:A,B:]
G1 is Element of the carrier' of A
G2 is Element of the carrier' of B
[G1,G2] is Element of the carrier' of [:A,B:]
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
cod G1 is Element of the carrier of A
the Target of A . G1 is Element of the carrier of A
id (cod G1) is Morphism of cod G1, cod G1
dom (id (cod G1)) is Element of the carrier of A
the Source of A . (id (cod G1)) is Element of the carrier of A
dom G2 is Element of the carrier of B
the Source of B . G2 is Element of the carrier of B
id (dom G2) is Morphism of dom G2, dom G2
cod (id (dom G2)) is Element of the carrier of B
the Target of B . (id (dom G2)) is Element of the carrier of B
(id (cod G1)) (*) G1 is Element of the carrier' of A
[((id (cod G1)) (*) G1),G2] is Element of the carrier' of [:A,B:]
{((id (cod G1)) (*) G1),G2} is non empty set
{((id (cod G1)) (*) G1)} is non empty set
{{((id (cod G1)) (*) G1),G2},{((id (cod G1)) (*) G1)}} is non empty set
G2 (*) (id (dom G2)) is Element of the carrier' of B
[((id (cod G1)) (*) G1),(G2 (*) (id (dom G2)))] is Element of the carrier' of [:A,B:]
{((id (cod G1)) (*) G1),(G2 (*) (id (dom G2)))} is non empty set
{{((id (cod G1)) (*) G1),(G2 (*) (id (dom G2)))},{((id (cod G1)) (*) G1)}} is non empty set
[G1,(id (dom G2))] is Element of the carrier' of [:A,B:]
{G1,(id (dom G2))} is non empty set
{{G1,(id (dom G2))},{G1}} is non empty set
[(id (cod G1)),G2] is Element of the carrier' of [:A,B:]
{(id (cod G1)),G2} is non empty set
{(id (cod G1))} is non empty set
{{(id (cod G1)),G2},{(id (cod G1))}} is non empty set
[(id (cod G1)),G2] (*) [G1,(id (dom G2))] is Element of the carrier' of [:A,B:]
dom G1 is Element of the carrier of A
the Source of A . G1 is Element of the carrier of A
c₄ ?- (dom G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id (dom G1) is Morphism of dom G1, dom G1
(curry c₄) . (id (dom G1)) is set
c₄ ?- (cod G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id (cod G1)) is set
[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))] is set
{(c₄ ?- (dom G1)),(c₄ ?- (cod G1))} is non empty set
{(c₄ ?- (dom G1))} is non empty set
{{(c₄ ?- (dom G1)),(c₄ ?- (cod G1))},{(c₄ ?- (dom G1))}} is non empty set
(A,B,C,c₄,G1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom G1),c₄ ?- (cod G1)
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,c₄,G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry c₄) . G1 is set
(A,B,C,c₄,G1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
[[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)] is set
{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)} is non empty set
{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))]} is non empty Relation-like set
{{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))],(A,B,C,c₄,G1)},{[(c₄ ?- (dom G1)),(c₄ ?- (cod G1))]}} is non empty set
(A,B,C,o1) . G1 is Element of the carrier' of (Functors (B,C))
o1 ?- (dom G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry o1 is Relation-like Function-like set
(curry o1) . (id (dom G1)) is set
o1 ?- (cod G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry o1) . (id (cod G1)) is set
[(o1 ?- (dom G1)),(o1 ?- (cod G1))] is set
{(o1 ?- (dom G1)),(o1 ?- (cod G1))} is non empty set
{(o1 ?- (dom G1))} is non empty set
{{(o1 ?- (dom G1)),(o1 ?- (cod G1))},{(o1 ?- (dom G1))}} is non empty set
(A,B,C,o1,G1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o1 ?- (dom G1),o1 ?- (cod G1)
(A,B,C,o1,G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry o1) . G1 is set
(A,B,C,o1,G1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[[(o1 ?- (dom G1)),(o1 ?- (cod G1))],(A,B,C,o1,G1)] is set
{[(o1 ?- (dom G1)),(o1 ?- (cod G1))],(A,B,C,o1,G1)} is non empty set
{[(o1 ?- (dom G1)),(o1 ?- (cod G1))]} is non empty Relation-like set
{{[(o1 ?- (dom G1)),(o1 ?- (cod G1))],(A,B,C,o1,G1)},{[(o1 ?- (dom G1)),(o1 ?- (cod G1))]}} is non empty set
c₄ . ((id (cod G1)),G2) is Element of the carrier' of C
[(id (cod G1)),G2] is set
c₄ . [(id (cod G1)),G2] is set
(o1 ?- (cod G1)) . G2 is Element of the carrier' of C
o1 . ((id (cod G1)),G2) is Element of the carrier' of C
o1 . [(id (cod G1)),G2] is set
cod [G1,(id (dom G2))] is Element of the carrier of [:A,B:]
the carrier of [:A,B:] is non empty set
the Target of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
[: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty Relation-like set
bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty set
the Target of [:A,B:] . [G1,(id (dom G2))] is Element of the carrier of [:A,B:]
[(cod G1),(cod (id (dom G2)))] is Element of the carrier of [:A,B:]
{(cod G1),(cod (id (dom G2)))} is non empty set
{(cod G1)} is non empty set
{{(cod G1),(cod (id (dom G2)))},{(cod G1)}} is non empty set
[(cod G1),(dom G2)] is Element of the carrier of [:A,B:]
{(cod G1),(dom G2)} is non empty set
{{(cod G1),(dom G2)},{(cod G1)}} is non empty set
[(dom (id (cod G1))),(dom G2)] is Element of the carrier of [:A,B:]
{(dom (id (cod G1))),(dom G2)} is non empty set
{(dom (id (cod G1)))} is non empty set
{{(dom (id (cod G1))),(dom G2)},{(dom (id (cod G1)))}} is non empty set
dom [(id (cod G1)),G2] is Element of the carrier of [:A,B:]
the Source of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
the Source of [:A,B:] . [(id (cod G1)),G2] is Element of the carrier of [:A,B:]
c₄ . (G1,(id (dom G2))) is Element of the carrier' of C
[G1,(id (dom G2))] is set
c₄ . [G1,(id (dom G2))] is set
(A,B,C,c₄,G1) . (dom G2) is Morphism of (c₄ ?- (dom G1)) . (dom G2),(c₄ ?- (cod G1)) . (dom G2)
(c₄ ?- (dom G1)) . (dom G2) is Element of the carrier of C
the carrier of C is non empty set
Obj (c₄ ?- (dom G1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- (dom G1))) . (dom G2) is Element of the carrier of C
(c₄ ?- (cod G1)) . (dom G2) is Element of the carrier of C
Obj (c₄ ?- (cod G1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- (cod G1))) . (dom G2) is Element of the carrier of C
(A,B,C,o1,G1) . (dom G2) is Morphism of (o1 ?- (dom G1)) . (dom G2),(o1 ?- (cod G1)) . (dom G2)
(o1 ?- (dom G1)) . (dom G2) is Element of the carrier of C
Obj (o1 ?- (dom G1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o1 ?- (dom G1))) . (dom G2) is Element of the carrier of C
(o1 ?- (cod G1)) . (dom G2) is Element of the carrier of C
Obj (o1 ?- (cod G1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o1 ?- (cod G1))) . (dom G2) is Element of the carrier of C
o1 . (G1,(id (dom G2))) is Element of the carrier' of C
o1 . [G1,(id (dom G2))] is set
c₄ . o2 is Element of the carrier' of C
o1 . [G1,(id (dom G2))] is Element of the carrier' of C
o1 . [(id (cod G1)),G2] is Element of the carrier' of C
(o1 . [(id (cod G1)),G2]) (*) (o1 . [G1,(id (dom G2))]) is Element of the carrier' of C
o1 . o2 is Element of the carrier' of C
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
the carrier of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
[:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty set
Funcs ( the carrier of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier of B, the carrier' of C
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
o2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,o1
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
G2 is Element of the carrier of A
(A,B,C,c₄) . G2 is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
Obj (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj (A,B,C,c₄)) . G2 is Element of the carrier of (Functors (B,C))
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(A,B,C,o1) . G2 is Element of the carrier of (Functors (B,C))
Obj (A,B,C,o1) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
(Obj (A,B,C,o1)) . G2 is Element of the carrier of (Functors (B,C))
F2 is Element of the carrier of B
F1 . F2 is Element of the carrier of C
the carrier of C is non empty set
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj F1) . F2 is Element of the carrier of C
o1 ?- G2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry o1 is Relation-like Function-like set
id G2 is Morphism of G2,G2
(curry o1) . (id G2) is set
(o1 ?- G2) . F2 is Element of the carrier of C
Obj (o1 ?- G2) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o1 ?- G2)) . F2 is Element of the carrier of C
[G2,F2] is Element of the carrier of [:A,B:]
{G2,F2} is non empty set
{G2} is non empty set
{{G2,F2},{G2}} is non empty set
o1 . [G2,F2] is Element of the carrier of C
Obj o1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj o1) . [G2,F2] is Element of the carrier of C
G1 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry G1 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
[: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty set
(curry G1) . G2 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
((curry G1) . G2) . F2 is Element of the carrier' of C
G1 . (G2,F2) is Element of the carrier' of C
[G2,F2] is set
G1 . [G2,F2] is set
o2 . [G2,F2] is Morphism of c₄ . [G2,F2],o1 . [G2,F2]
c₄ . [G2,F2] is Element of the carrier of C
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
(Obj c₄) . [G2,F2] is Element of the carrier of C
t . F2 is Element of the carrier of C
Obj t is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj t) . F2 is Element of the carrier of C
c₄ ?- G2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
(curry c₄) . (id G2) is set
(c₄ ?- G2) . F2 is Element of the carrier of C
Obj (c₄ ?- G2) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- G2)) . F2 is Element of the carrier of C
Hom ((t . F2),(F1 . F2)) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = t . F2 & cod b₁ = F1 . F2 ) } is set
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
G2 is Element of the carrier of A
(A,B,C,c₄) . G2 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . G2 is Element of the carrier of (Functors (B,C))
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(A,B,C,o1) . G2 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . G2 is Element of the carrier of (Functors (B,C))
F2 is Element of the carrier of B
t . F2 is Element of the carrier of C
Obj t is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj t) . F2 is Element of the carrier of C
F1 . F2 is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F1) . F2 is Element of the carrier of C
Hom ((t . F2),(F1 . F2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = t . F2 & cod b₁ = F1 . F2 ) } is set
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
G2 is Element of the carrier of A
(A,B,C,c₄) . G2 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . G2 is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . G2 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . G2 is Element of the carrier of (Functors (B,C))
F2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of t,F1
(curry G1) . G2 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
s is Element of the carrier of B
f is Element of the carrier of B
Hom (s,f) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = s & cod b₁ = f ) } is set
t . s is Element of the carrier of C
Obj t is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj t) . s is Element of the carrier of C
t . f is Element of the carrier of C
(Obj t) . f is Element of the carrier of C
Hom ((t . s),(t . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = t . s & cod b₁ = t . f ) } is set
F2 . f is Morphism of t . f,F1 . f
F1 . f is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F1) . f is Element of the carrier of C
F2 . f is Element of the carrier' of C
G1 . (G2,f) is Element of the carrier' of C
[G2,f] is set
{G2,f} is non empty set
{G2} is non empty set
{{G2,f},{G2}} is non empty set
G1 . [G2,f] is set
[G2,f] is Element of the carrier of [:A,B:]
o2 . [G2,f] is Morphism of c₄ . [G2,f],o1 . [G2,f]
c₄ . [G2,f] is Element of the carrier of C
(Obj c₄) . [G2,f] is Element of the carrier of C
o1 . [G2,f] is Element of the carrier of C
(Obj o1) . [G2,f] is Element of the carrier of C
Hom ((c₄ . [G2,f]),(o1 . [G2,f])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [G2,f] & cod b₁ = o1 . [G2,f] ) } is set
Hom (G2,G2) is non empty Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = G2 & cod b₁ = G2 ) } is set
[G2,s] is Element of the carrier of [:A,B:]
{G2,s} is non empty set
{{G2,s},{G2}} is non empty set
id G2 is Morphism of G2,G2
f is Morphism of s,f
[(id G2),f] is Element of the carrier' of [:A,B:]
{(id G2),f} is non empty set
{(id G2)} is non empty set
{{(id G2),f},{(id G2)}} is non empty set
Hom ([G2,s],[G2,f]) is Element of bool the carrier' of [:A,B:]
bool the carrier' of [:A,B:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:A,B:] : ( dom b₁ = [G2,s] & cod b₁ = [G2,f] ) } is set
c₄ . [G2,s] is Element of the carrier of C
(Obj c₄) . [G2,s] is Element of the carrier of C
Hom ((c₄ . [G2,s]),(c₄ . [G2,f])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [G2,s] & cod b₁ = c₄ . [G2,f] ) } is set
F1 . s is Element of the carrier of C
(Obj F1) . s is Element of the carrier of C
Hom ((t . s),(F1 . s)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = t . s & cod b₁ = F1 . s ) } is set
F2 . s is Morphism of t . s,F1 . s
F2 . s is Element of the carrier' of C
G1 . (G2,s) is Element of the carrier' of C
[G2,s] is set
G1 . [G2,s] is set
o2 . [G2,s] is Morphism of c₄ . [G2,s],o1 . [G2,s]
o1 . [G2,s] is Element of the carrier of C
(Obj o1) . [G2,s] is Element of the carrier of C
Hom ((c₄ . [G2,s]),(o1 . [G2,s])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [G2,s] & cod b₁ = o1 . [G2,s] ) } is set
Hom ((t . f),(F1 . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = t . f & cod b₁ = F1 . f ) } is set
Hom ((F1 . s),(F1 . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = F1 . s & cod b₁ = F1 . f ) } is set
F1 /. f is Morphism of F1 . s,F1 . f
o1 ?- G2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry o1) . (id G2) is set
(o1 ?- G2) /. f is Morphism of (o1 ?- G2) . s,(o1 ?- G2) . f
(o1 ?- G2) . s is Element of the carrier of C
Obj (o1 ?- G2) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o1 ?- G2)) . s is Element of the carrier of C
(o1 ?- G2) . f is Element of the carrier of C
(Obj (o1 ?- G2)) . f is Element of the carrier of C
(o1 ?- G2) /. f is Element of the carrier' of C
(o1 ?- G2) . f is Element of the carrier' of C
o1 . ((id G2),f) is Element of the carrier' of C
[(id G2),f] is set
o1 . [(id G2),f] is set
f2 is Morphism of [G2,s],[G2,f]
o1 /. f2 is Morphism of o1 . [G2,s],o1 . [G2,f]
Hom ((o1 . [G2,s]),(o1 . [G2,f])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o1 . [G2,s] & cod b₁ = o1 . [G2,f] ) } is set
t /. f is Morphism of t . s,t . f
c₄ ?- G2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id G2) is set
(c₄ ?- G2) /. f is Morphism of (c₄ ?- G2) . s,(c₄ ?- G2) . f
(c₄ ?- G2) . s is Element of the carrier of C
Obj (c₄ ?- G2) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (c₄ ?- G2)) . s is Element of the carrier of C
(c₄ ?- G2) . f is Element of the carrier of C
(Obj (c₄ ?- G2)) . f is Element of the carrier of C
(c₄ ?- G2) /. f is Element of the carrier' of C
(c₄ ?- G2) . f is Element of the carrier' of C
c₄ . ((id G2),f) is Element of the carrier' of C
c₄ . [(id G2),f] is set
c₄ /. f2 is Morphism of c₄ . [G2,s],c₄ . [G2,f]
(F2 . f) * (t /. f) is Morphism of t . s,F1 . f
(F2 . f) (*) (t /. f) is Element of the carrier' of C
(o2 . [G2,f]) * (c₄ /. f2) is Morphism of c₄ . [G2,s],o1 . [G2,f]
(o1 /. f2) * (o2 . [G2,s]) is Morphism of c₄ . [G2,s],o1 . [G2,f]
(F1 /. f) (*) (F2 . s) is Element of the carrier' of C
(F1 /. f) * (F2 . s) is Morphism of t . s,F1 . f
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
G2 is Element of the carrier of A
(A,B,C,c₄) . G2 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . G2 is Element of the carrier of (Functors (B,C))
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(A,B,C,o1) . G2 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . G2 is Element of the carrier of (Functors (B,C))
(curry G1) . G2 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
F2 is Element of the carrier of B
((curry G1) . G2) . F2 is Element of the carrier' of C
t . F2 is Element of the carrier of C
Obj t is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj t) . F2 is Element of the carrier of C
F1 . F2 is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F1) . F2 is Element of the carrier of C
Hom ((t . F2),(F1 . F2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = t . F2 & cod b₁ = F1 . F2 ) } is set
G2 is set
t is Element of the carrier of A
(A,B,C,c₄) . t is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . t is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . t is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . t is Element of the carrier of (Functors (B,C))
[((A,B,C,c₄) . t),((A,B,C,o1) . t)] is Element of the carrier of [:(Functors (B,C)),(Functors (B,C)):]
[:(Functors (B,C)),(Functors (B,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] is non empty Relation-like set
the Source of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty set
[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty set
the Target of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
the Comp of (Functors (B,C)) is Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined the carrier' of (Functors (B,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty set
K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) is Relation-like [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] -defined [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):],[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):],K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) #) is strict CatStr
the carrier of [:(Functors (B,C)),(Functors (B,C)):] is non empty set
{((A,B,C,c₄) . t),((A,B,C,o1) . t)} is non empty set
{((A,B,C,c₄) . t)} is non empty set
{{((A,B,C,c₄) . t),((A,B,C,o1) . t)},{((A,B,C,c₄) . t)}} is non empty set
(curry G1) . t is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[((A,B,C,c₄) . t),((A,B,C,o1) . t)],((curry G1) . t)] is set
{[((A,B,C,c₄) . t),((A,B,C,o1) . t)],((curry G1) . t)} is non empty set
{[((A,B,C,c₄) . t),((A,B,C,o1) . t)]} is non empty Relation-like set
{{[((A,B,C,c₄) . t),((A,B,C,o1) . t)],((curry G1) . t)},{[((A,B,C,c₄) . t),((A,B,C,o1) . t)]}} is non empty set
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
F2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
f is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of F1,F2
f is Element of the carrier of B
f2 is Element of the carrier of B
Hom (f,f2) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f & cod b₁ = f2 ) } is set
F1 . f is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F1) . f is Element of the carrier of C
F1 . f2 is Element of the carrier of C
(Obj F1) . f2 is Element of the carrier of C
F2 . f2 is Element of the carrier of C
Obj F2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F2) . f2 is Element of the carrier of C
g1 is Morphism of f,f2
F1 /. g1 is Morphism of F1 . f,F1 . f2
f . f2 is Morphism of F1 . f2,F2 . f2
(f . f2) * (F1 /. g1) is Morphism of F1 . f,F2 . f2
F2 . f is Element of the carrier of C
(Obj F2) . f is Element of the carrier of C
f . f is Morphism of F1 . f,F2 . f
F2 /. g1 is Morphism of F2 . f,F2 . f2
(F2 /. g1) * (f . f) is Morphism of F1 . f,F2 . f2
f is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of F1,F2
f is Element of the carrier of B
f2 is Element of the carrier of B
Hom (f,f2) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f & cod b₁ = f2 ) } is set
F1 . f is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F1) . f is Element of the carrier of C
F1 . f2 is Element of the carrier of C
(Obj F1) . f2 is Element of the carrier of C
F2 . f2 is Element of the carrier of C
Obj F2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F2) . f2 is Element of the carrier of C
g1 is Morphism of f,f2
F1 /. g1 is Morphism of F1 . f,F1 . f2
f . f2 is Morphism of F1 . f2,F2 . f2
(f . f2) * (F1 /. g1) is Morphism of F1 . f,F2 . f2
F2 . f is Element of the carrier of C
(Obj F2) . f is Element of the carrier of C
f . f is Morphism of F1 . f,F2 . f
F2 /. g1 is Morphism of F2 . f,F2 . f2
(F2 /. g1) * (f . f) is Morphism of F1 . f,F2 . f2
s is set
NatTrans (B,C) is non empty NatTrans-DOMAIN of B,C
f2 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
f is Element of the carrier of A
(A,B,C,c₄) . f is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . f is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . f is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . f is Element of the carrier of (Functors (B,C))
[((A,B,C,c₄) . f),((A,B,C,o1) . f)] is Element of the carrier of [:(Functors (B,C)),(Functors (B,C)):]
{((A,B,C,c₄) . f),((A,B,C,o1) . f)} is non empty set
{((A,B,C,c₄) . f)} is non empty set
{{((A,B,C,c₄) . f),((A,B,C,o1) . f)},{((A,B,C,c₄) . f)}} is non empty set
curry f2 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
(curry f2) . f is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[((A,B,C,c₄) . f),((A,B,C,o1) . f)],((curry f2) . f)] is set
{[((A,B,C,c₄) . f),((A,B,C,o1) . f)],((curry f2) . f)} is non empty set
{[((A,B,C,c₄) . f),((A,B,C,o1) . f)]} is non empty Relation-like set
{{[((A,B,C,c₄) . f),((A,B,C,o1) . f)],((curry f2) . f)},{[((A,B,C,c₄) . f),((A,B,C,o1) . f)]}} is non empty set
[: the carrier of A, the carrier' of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier' of (Functors (B,C)):] is non empty set
G2 is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of (Functors (B,C)):]
t is Element of the carrier of A
(A,B,C,c₄) . t is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . t is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . t is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . t is Element of the carrier of (Functors (B,C))
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
F2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry G1) . t is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
G2 . t is Element of the carrier' of (Functors (B,C))
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
s is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total transformation of F1,F2
[[F1,F2],s] is set
{[F1,F2],s} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],s},{[F1,F2]}} is non empty set
f is Element of the carrier of B
f is Element of the carrier of B
Hom (f,f) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f & cod b₁ = f ) } is set
F1 . f is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F1) . f is Element of the carrier of C
F1 . f is Element of the carrier of C
(Obj F1) . f is Element of the carrier of C
F2 . f is Element of the carrier of C
Obj F2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F2) . f is Element of the carrier of C
f2 is Morphism of f,f
F1 /. f2 is Morphism of F1 . f,F1 . f
s . f is Morphism of F1 . f,F2 . f
(s . f) * (F1 /. f2) is Morphism of F1 . f,F2 . f
F2 . f is Element of the carrier of C
(Obj F2) . f is Element of the carrier of C
s . f is Morphism of F1 . f,F2 . f
F2 /. f2 is Morphism of F2 . f,F2 . f
(F2 /. f2) * (s . f) is Morphism of F1 . f,F2 . f
f is Element of the carrier of B
f is Element of the carrier of B
Hom (f,f) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f & cod b₁ = f ) } is set
F1 . f is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F1) . f is Element of the carrier of C
F1 . f is Element of the carrier of C
(Obj F1) . f is Element of the carrier of C
F2 . f is Element of the carrier of C
Obj F2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F2) . f is Element of the carrier of C
f2 is Morphism of f,f
F1 /. f2 is Morphism of F1 . f,F1 . f
s . f is Morphism of F1 . f,F2 . f
(s . f) * (F1 /. f2) is Morphism of F1 . f,F2 . f
F2 . f is Element of the carrier of C
(Obj F2) . f is Element of the carrier of C
s . f is Morphism of F1 . f,F2 . f
F2 /. f2 is Morphism of F2 . f,F2 . f
(F2 /. f2) * (s . f) is Morphism of F1 . f,F2 . f
dom (G2 . t) is Element of the carrier of (Functors (B,C))
the Source of (Functors (B,C)) . (G2 . t) is Element of the carrier of (Functors (B,C))
cod (G2 . t) is Element of the carrier of (Functors (B,C))
the Target of (Functors (B,C)) . (G2 . t) is Element of the carrier of (Functors (B,C))
Hom (((A,B,C,c₄) . t),((A,B,C,o1) . t)) is Element of bool the carrier' of (Functors (B,C))
bool the carrier' of (Functors (B,C)) is non empty set
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . t & cod b₁ = (A,B,C,o1) . t ) } is set
t is Element of the carrier of A
(A,B,C,c₄) . t is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . t is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . t is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . t is Element of the carrier of (Functors (B,C))
Hom (((A,B,C,c₄) . t),((A,B,C,o1) . t)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . t & cod b₁ = (A,B,C,o1) . t ) } is set
t is Element of the carrier of A
G2 . t is Element of the carrier' of (Functors (B,C))
(A,B,C,c₄) . t is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . t is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . t is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . t is Element of the carrier of (Functors (B,C))
Hom (((A,B,C,c₄) . t),((A,B,C,o1) . t)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . t & cod b₁ = (A,B,C,o1) . t ) } is set
F1 is Element of the carrier of A
F2 is Element of the carrier of A
Hom (F1,F2) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 & cod b₁ = F2 ) } is set
(A,B,C,o1) . F1 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . F1 is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . F2 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . F2 is Element of the carrier of (Functors (B,C))
Hom (((A,B,C,o1) . F1),((A,B,C,o1) . F2)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,o1) . F1 & cod b₁ = (A,B,C,o1) . F2 ) } is set
(A,B,C,c₄) . F1 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . F1 is Element of the carrier of (Functors (B,C))
(A,B,C,c₄) . F2 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . F2 is Element of the carrier of (Functors (B,C))
o1 ?- F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id F1 is Morphism of F1,F1
(curry o1) . (id F1) is set
c₄ ?- F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id F1) is set
s is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
f is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry G1) . F1 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
o1 ?- F2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id F2 is Morphism of F2,F2
(curry o1) . (id F2) is set
g1 is Morphism of F1,F2
cod g1 is Element of the carrier of A
the Target of A . g1 is Element of the carrier of A
o1 ?- (cod g1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod g1) is Morphism of cod g1, cod g1
(curry o1) . (id (cod g1)) is set
f2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(A,B,C,o1,g1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o1 ?- (dom g1),o1 ?- (cod g1)
dom g1 is Element of the carrier of A
the Source of A . g1 is Element of the carrier of A
o1 ?- (dom g1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom g1) is Morphism of dom g1, dom g1
(curry o1) . (id (dom g1)) is set
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,o1,g1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry o1) . g1 is set
(A,B,C,o1,g1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total transformation of (A,B,C,c₄),(A,B,C,o1)
t . F1 is Morphism of (A,B,C,c₄) . F1,(A,B,C,o1) . F1
t . F1 is set
[s,f] is set
{s,f} is non empty set
{s} is non empty set
{{s,f},{s}} is non empty set
f1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of s,f
[[s,f],f1] is set
{[s,f],f1} is non empty set
{[s,f]} is non empty Relation-like set
{{[s,f],f1},{[s,f]}} is non empty set
c₄ ?- F2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id F2) is set
f is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry G1) . F2 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
c₄ ?- (cod g1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id (cod g1)) is set
(A,B,C,c₄,g1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom g1),c₄ ?- (cod g1)
c₄ ?- (dom g1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry c₄) . (id (dom g1)) is set
(A,B,C,c₄,g1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry c₄) . g1 is set
(A,B,C,c₄,g1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
t . F2 is Morphism of (A,B,C,c₄) . F2,(A,B,C,o1) . F2
t . F2 is set
[f,f2] is set
{f,f2} is non empty set
{f} is non empty set
{{f,f2},{f}} is non empty set
a1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of f,f2
[[f,f2],a1] is set
{[f,f2],a1} is non empty set
{[f,f2]} is non empty Relation-like set
{{[f,f2],a1},{[f,f2]}} is non empty set
Hom (((A,B,C,c₄) . F1),((A,B,C,o1) . F1)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . F1 & cod b₁ = (A,B,C,o1) . F1 ) } is set
G1 is Element of the carrier' of A
(A,B,C,o1) . G1 is Element of the carrier' of (Functors (B,C))
[f,f2] is set
{f,f2} is non empty set
{f} is non empty set
{{f,f2},{f}} is non empty set
t2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of f,f2
[[f,f2],t2] is set
{[f,f2],t2} is non empty set
{[f,f2]} is non empty Relation-like set
{{[f,f2],t2},{[f,f2]}} is non empty set
Hom (((A,B,C,c₄) . F1),((A,B,C,c₄) . F2)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . F1 & cod b₁ = (A,B,C,c₄) . F2 ) } is set
[:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty set
f is Element of the carrier of B
[F1,f] is Element of the carrier of [:A,B:]
{F1,f} is non empty set
{F1} is non empty set
{{F1,f},{F1}} is non empty set
c₄ . [F1,f] is Element of the carrier of C
(Obj c₄) . [F1,f] is Element of the carrier of C
o1 . [F1,f] is Element of the carrier of C
(Obj o1) . [F1,f] is Element of the carrier of C
Hom ((c₄ . [F1,f]),(o1 . [F1,f])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [F1,f] & cod b₁ = o1 . [F1,f] ) } is set
[F2,f] is Element of the carrier of [:A,B:]
{F2,f} is non empty set
{F2} is non empty set
{{F2,f},{F2}} is non empty set
c₄ . [F2,f] is Element of the carrier of C
(Obj c₄) . [F2,f] is Element of the carrier of C
o1 . [F2,f] is Element of the carrier of C
(Obj o1) . [F2,f] is Element of the carrier of C
Hom ((c₄ . [F2,f]),(o1 . [F2,f])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [F2,f] & cod b₁ = o1 . [F2,f] ) } is set
f . f is Element of the carrier of C
Obj f is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f) . f is Element of the carrier of C
f2 . f is Element of the carrier of C
Obj f2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f2) . f is Element of the carrier of C
Hom ((f . f),(f2 . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = f . f & cod b₁ = f2 . f ) } is set
s . f is Element of the carrier of C
Obj s is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj s) . f is Element of the carrier of C
Hom ((s . f),(f . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s . f & cod b₁ = f . f ) } is set
f . f is Element of the carrier of C
Obj f is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f) . f is Element of the carrier of C
Hom ((f . f),(f2 . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = f . f & cod b₁ = f2 . f ) } is set
Hom ((s . f),(f . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s . f & cod b₁ = f . f ) } is set
o2 . [F2,f] is Morphism of c₄ . [F2,f],o1 . [F2,f]
G1 . (F2,f) is Element of the carrier' of C
[F2,f] is set
G1 . [F2,f] is set
((curry G1) . F2) . f is Element of the carrier' of C
a1 . f is Morphism of f . f,f2 . f
o2 . [F1,f] is Morphism of c₄ . [F1,f],o1 . [F1,f]
G1 . (F1,f) is Element of the carrier' of C
[F1,f] is set
G1 . [F1,f] is set
((curry G1) . F1) . f is Element of the carrier' of C
f1 . f is Morphism of s . f,f . f
Hom (f,f) is non empty Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f & cod b₁ = f ) } is set
id f is Morphism of f,f
[g1,(id f)] is Element of the carrier' of [:A,B:]
{g1,(id f)} is non empty set
{g1} is non empty set
{{g1,(id f)},{g1}} is non empty set
Hom ([F1,f],[F2,f]) is Element of bool the carrier' of [:A,B:]
{ b₁ where b₁ is Element of the carrier' of [:A,B:] : ( dom b₁ = [F1,f] & cod b₁ = [F2,f] ) } is set
Hom ((o1 . [F1,f]),(o1 . [F2,f])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o1 . [F1,f] & cod b₁ = o1 . [F2,f] ) } is set
(IdMap B) . f is Element of the carrier' of B
g is Morphism of [F1,f],[F2,f]
c₄ /. g is Morphism of c₄ . [F1,f],c₄ . [F2,f]
H1 is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:]
H1 . (g1,(id f)) is Element of the carrier' of C
[g1,(id f)] is set
H1 . [g1,(id f)] is set
(A,B,C,c₄,g1) . (id f) is Element of the carrier' of C
(A,B,C,c₄,g1) . f is Element of the carrier' of C
b1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of s,f
b1 . f is Morphism of s . f,f . f
o1 /. g is Morphism of o1 . [F1,f],o1 . [F2,f]
t1 is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:]
t1 . (g1,(id f)) is Element of the carrier' of C
t1 . [g1,(id f)] is set
(A,B,C,o1,g1) . (id f) is Element of the carrier' of C
(A,B,C,o1,g1) . f is Element of the carrier' of C
t2 . f is Morphism of f . f,f2 . f
Hom ((c₄ . [F1,f]),(c₄ . [F2,f])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [F1,f] & cod b₁ = c₄ . [F2,f] ) } is set
a1 `*` b1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of s,f2
(a1 `*` b1) . f is Morphism of s . f,f2 . f
(a1 . f) * (b1 . f) is Morphism of s . f,f2 . f
(o2 . [F2,f]) (*) (c₄ /. g) is Element of the carrier' of C
(o2 . [F2,f]) * (c₄ /. g) is Morphism of c₄ . [F1,f],o1 . [F2,f]
(o1 /. g) * (o2 . [F1,f]) is Morphism of c₄ . [F1,f],o1 . [F2,f]
(o1 /. g) (*) (o2 . [F1,f]) is Element of the carrier' of C
(t2 . f) * (f1 . f) is Morphism of s . f,f2 . f
t2 `*` f1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of s,f2
(t2 `*` f1) . f is Morphism of s . f,f2 . f
(A,B,C,c₄) . G1 is Element of the carrier' of (Functors (B,C))
[s,f] is set
{s,f} is non empty set
{{s,f},{s}} is non empty set
[[s,f],b1] is set
{[s,f],b1} is non empty set
{[s,f]} is non empty Relation-like set
{{[s,f],b1},{[s,f]}} is non empty set
Hom (((A,B,C,c₄) . F2),((A,B,C,o1) . F2)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . F2 & cod b₁ = (A,B,C,o1) . F2 ) } is set
(A,B,C,c₄) /. g1 is Morphism of (A,B,C,c₄) . F1,(A,B,C,c₄) . F2
(t . F2) * ((A,B,C,c₄) /. g1) is Morphism of (A,B,C,c₄) . F1,(A,B,C,o1) . F2
(t . F2) (*) ((A,B,C,c₄) /. g1) is Element of the carrier' of (Functors (B,C))
(t . F2) (*) ((A,B,C,c₄) . G1) is Element of the carrier' of (Functors (B,C))
[s,f2] is set
{s,f2} is non empty set
{{s,f2},{s}} is non empty set
[[s,f2],(a1 `*` b1)] is set
{[s,f2],(a1 `*` b1)} is non empty set
{[s,f2]} is non empty Relation-like set
{{[s,f2],(a1 `*` b1)},{[s,f2]}} is non empty set
(A,B,C,o1) /. G1 is Element of the carrier' of (Functors (B,C))
((A,B,C,o1) /. G1) (*) (t . F1) is Element of the carrier' of (Functors (B,C))
(A,B,C,o1) /. g1 is Morphism of (A,B,C,o1) . F1,(A,B,C,o1) . F2
((A,B,C,o1) /. g1) (*) (t . F1) is Element of the carrier' of (Functors (B,C))
((A,B,C,o1) /. g1) * (t . F1) is Morphism of (A,B,C,c₄) . F1,(A,B,C,o1) . F2
F1 is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
F2 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry F2 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
s is Element of the carrier of A
F1 . s is Morphism of (A,B,C,c₄) . s,(A,B,C,o1) . s
(A,B,C,c₄) . s is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . s is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . s is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . s is Element of the carrier of (Functors (B,C))
[((A,B,C,c₄) . s),((A,B,C,o1) . s)] is Element of the carrier of [:(Functors (B,C)),(Functors (B,C)):]
{((A,B,C,c₄) . s),((A,B,C,o1) . s)} is non empty set
{((A,B,C,c₄) . s)} is non empty set
{{((A,B,C,c₄) . s),((A,B,C,o1) . s)},{((A,B,C,c₄) . s)}} is non empty set
(curry F2) . s is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[((A,B,C,c₄) . s),((A,B,C,o1) . s)],((curry F2) . s)] is set
{[((A,B,C,c₄) . s),((A,B,C,o1) . s)],((curry F2) . s)} is non empty set
{[((A,B,C,c₄) . s),((A,B,C,o1) . s)]} is non empty Relation-like set
{{[((A,B,C,c₄) . s),((A,B,C,o1) . s)],((curry F2) . s)},{[((A,B,C,c₄) . s),((A,B,C,o1) . s)]}} is non empty set
F1 . s is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
the carrier of [:A,B:] is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty set
o2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,o1
Funcs ( the carrier of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier of B, the carrier' of C
G2 is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
t is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
F1 is Element of the carrier of A
G2 . F1 is Morphism of (A,B,C,c₄) . F1,(A,B,C,o1) . F1
(A,B,C,c₄) . F1 is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
Obj (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj (A,B,C,c₄)) . F1 is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . F1 is Element of the carrier of (Functors (B,C))
Obj (A,B,C,o1) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
(Obj (A,B,C,o1)) . F1 is Element of the carrier of (Functors (B,C))
[((A,B,C,c₄) . F1),((A,B,C,o1) . F1)] is Element of the carrier of [:(Functors (B,C)),(Functors (B,C)):]
[:(Functors (B,C)),(Functors (B,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] is non empty Relation-like set
the Source of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty set
[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty set
the Target of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
the Comp of (Functors (B,C)) is Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined the carrier' of (Functors (B,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty set
K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) is Relation-like [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] -defined [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):],[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):],K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) #) is strict CatStr
the carrier of [:(Functors (B,C)),(Functors (B,C)):] is non empty set
{((A,B,C,c₄) . F1),((A,B,C,o1) . F1)} is non empty set
{((A,B,C,c₄) . F1)} is non empty set
{{((A,B,C,c₄) . F1),((A,B,C,o1) . F1)},{((A,B,C,c₄) . F1)}} is non empty set
G1 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry G1 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
[: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty set
(curry G1) . F1 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[((A,B,C,c₄) . F1),((A,B,C,o1) . F1)],((curry G1) . F1)] is set
{[((A,B,C,c₄) . F1),((A,B,C,o1) . F1)],((curry G1) . F1)} is non empty set
{[((A,B,C,c₄) . F1),((A,B,C,o1) . F1)]} is non empty Relation-like set
{{[((A,B,C,c₄) . F1),((A,B,C,o1) . F1)],((curry G1) . F1)},{[((A,B,C,c₄) . F1),((A,B,C,o1) . F1)]}} is non empty set
t . F1 is Morphism of (A,B,C,c₄) . F1,(A,B,C,o1) . F1
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
id (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,c₄)
id c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,c₄
the carrier of [:A,B:] is non empty set
(A,B,C,c₄,c₄,(id c₄)) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,c₄)
[:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty set
o2 is Element of the carrier of A
(A,B,C,c₄) . o2 is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
Obj (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj (A,B,C,c₄)) . o2 is Element of the carrier of (Functors (B,C))
G1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id G1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,G1
G2 is Element of the carrier of B
(id G1) . G2 is Element of the carrier' of C
(id G1) . G2 is Morphism of G1 . G2,G1 . G2
G1 . G2 is Element of the carrier of C
the carrier of C is non empty set
Obj G1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj G1) . G2 is Element of the carrier of C
id (G1 . G2) is Morphism of G1 . G2,G1 . G2
id G2 is Morphism of G2,G2
G1 . (id G2) is Element of the carrier' of C
c₄ ?- o2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id o2 is Morphism of o2,o2
(curry c₄) . (id o2) is set
(c₄ ?- o2) . (id G2) is Element of the carrier' of C
c₄ . ((id o2),(id G2)) is Element of the carrier' of C
[(id o2),(id G2)] is set
{(id o2),(id G2)} is non empty set
{(id o2)} is non empty set
{{(id o2),(id G2)},{(id o2)}} is non empty set
c₄ . [(id o2),(id G2)] is set
[o2,G2] is Element of the carrier of [:A,B:]
{o2,G2} is non empty set
{o2} is non empty set
{{o2,G2},{o2}} is non empty set
id [o2,G2] is Morphism of [o2,G2],[o2,G2]
c₄ . (id [o2,G2]) is Element of the carrier' of C
c₄ . [o2,G2] is Element of the carrier of C
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . [o2,G2] is Element of the carrier of C
id (c₄ . [o2,G2]) is Morphism of c₄ . [o2,G2],c₄ . [o2,G2]
(id c₄) . [o2,G2] is Morphism of c₄ . [o2,G2],c₄ . [o2,G2]
(id c₄) . (o2,G2) is set
[o2,G2] is set
(id c₄) . [o2,G2] is set
Funcs ( the carrier of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier of B, the carrier' of C
o1 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry o1 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
[: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty set
(curry o1) . o2 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
((curry o1) . o2) . G2 is Element of the carrier' of C
(id (A,B,C,c₄)) . o2 is Morphism of (A,B,C,c₄) . o2,(A,B,C,c₄) . o2
id ((A,B,C,c₄) . o2) is Morphism of (A,B,C,c₄) . o2,(A,B,C,c₄) . o2
[G1,G1] is set
{G1,G1} is non empty set
{G1} is non empty set
{{G1,G1},{G1}} is non empty set
[[G1,G1],(id G1)] is set
{[G1,G1],(id G1)} is non empty set
{[G1,G1]} is non empty Relation-like set
{{[G1,G1],(id G1)},{[G1,G1]}} is non empty set
[((A,B,C,c₄) . o2),((A,B,C,c₄) . o2)] is Element of the carrier of [:(Functors (B,C)),(Functors (B,C)):]
[:(Functors (B,C)),(Functors (B,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] is non empty Relation-like set
the Source of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty set
[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty set
the Target of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
the Comp of (Functors (B,C)) is Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined the carrier' of (Functors (B,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty set
K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) is Relation-like [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] -defined [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):],[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):],K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) #) is strict CatStr
the carrier of [:(Functors (B,C)),(Functors (B,C)):] is non empty set
{((A,B,C,c₄) . o2),((A,B,C,c₄) . o2)} is non empty set
{((A,B,C,c₄) . o2)} is non empty set
{{((A,B,C,c₄) . o2),((A,B,C,c₄) . o2)},{((A,B,C,c₄) . o2)}} is non empty set
[[((A,B,C,c₄) . o2),((A,B,C,c₄) . o2)],((curry o1) . o2)] is set
{[((A,B,C,c₄) . o2),((A,B,C,c₄) . o2)],((curry o1) . o2)} is non empty set
{[((A,B,C,c₄) . o2),((A,B,C,c₄) . o2)]} is non empty Relation-like set
{{[((A,B,C,c₄) . o2),((A,B,C,c₄) . o2)],((curry o1) . o2)},{[((A,B,C,c₄) . o2),((A,B,C,c₄) . o2)]}} is non empty set
(A,B,C,c₄,c₄,(id c₄)) . o2 is Morphism of (A,B,C,c₄) . o2,(A,B,C,c₄) . o2
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
the carrier of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
G1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,o1
(A,B,C,c₄,o1,G1) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
G2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o1,o2
G2 `*` G1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,o2
(A,B,C,c₄,o2,(G2 `*` G1)) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o2)
(A,B,C,o1,o2,G2) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,o1),(A,B,C,o2)
(A,B,C,o1,o2,G2) `*` (A,B,C,c₄,o1,G1) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o2)
t is Element of the carrier of A
(A,B,C,c₄) . t is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
Obj (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj (A,B,C,c₄)) . t is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . t is Element of the carrier of (Functors (B,C))
Obj (A,B,C,o1) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
(Obj (A,B,C,o1)) . t is Element of the carrier of (Functors (B,C))
(A,B,C,o2) . t is Element of the carrier of (Functors (B,C))
Obj (A,B,C,o2) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
(Obj (A,B,C,o2)) . t is Element of the carrier of (Functors (B,C))
[:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty set
F2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
o1 ?- t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry o1 is Relation-like Function-like set
id t is Morphism of t,t
(curry o1) . (id t) is set
s is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
o2 ?- t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry o2 is Relation-like Function-like set
(curry o2) . (id t) is set
Funcs ( the carrier of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier of B, the carrier' of C
f is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry f is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
[: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty set
(curry f) . t is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
c₄ ?- t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
(curry c₄) . (id t) is set
f is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry f is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
(curry f) . t is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
(A,B,C,o1,o2,G2) . t is Morphism of (A,B,C,o1) . t,(A,B,C,o2) . t
[F2,s] is set
{F2,s} is non empty set
{F2} is non empty set
{{F2,s},{F2}} is non empty set
g1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of F2,s
[[F2,s],g1] is set
{[F2,s],g1} is non empty set
{[F2,s]} is non empty Relation-like set
{{[F2,s],g1},{[F2,s]}} is non empty set
(A,B,C,c₄,o1,G1) . t is Morphism of (A,B,C,c₄) . t,(A,B,C,o1) . t
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
f1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of F1,F2
[[F1,F2],f1] is set
{[F1,F2],f1} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],f1},{[F1,F2]}} is non empty set
f2 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry f2 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
(curry f2) . t is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
Hom (((A,B,C,c₄) . t),((A,B,C,o1) . t)) is Element of bool the carrier' of (Functors (B,C))
bool the carrier' of (Functors (B,C)) is non empty set
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . t & cod b₁ = (A,B,C,o1) . t ) } is set
Hom (((A,B,C,o1) . t),((A,B,C,o2) . t)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,o1) . t & cod b₁ = (A,B,C,o2) . t ) } is set
a1 is Element of the carrier of B
[t,a1] is Element of the carrier of [:A,B:]
{t,a1} is non empty set
{t} is non empty set
{{t,a1},{t}} is non empty set
c₄ . [t,a1] is Element of the carrier of C
the carrier of C is non empty set
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . [t,a1] is Element of the carrier of C
o1 . [t,a1] is Element of the carrier of C
Obj o1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
(Obj o1) . [t,a1] is Element of the carrier of C
Hom ((c₄ . [t,a1]),(o1 . [t,a1])) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . [t,a1] & cod b₁ = o1 . [t,a1] ) } is set
o2 . [t,a1] is Element of the carrier of C
Obj o2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
(Obj o2) . [t,a1] is Element of the carrier of C
Hom ((o1 . [t,a1]),(o2 . [t,a1])) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o1 . [t,a1] & cod b₁ = o2 . [t,a1] ) } is set
F1 . a1 is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj F1) . a1 is Element of the carrier of C
F2 . a1 is Element of the carrier of C
Obj F2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F2) . a1 is Element of the carrier of C
Hom ((F1 . a1),(F2 . a1)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = F1 . a1 & cod b₁ = F2 . a1 ) } is set
s . a1 is Element of the carrier of C
Obj s is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj s) . a1 is Element of the carrier of C
Hom ((F2 . a1),(s . a1)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = F2 . a1 & cod b₁ = s . a1 ) } is set
f1 . a1 is Morphism of F1 . a1,F2 . a1
f1 . a1 is Element of the carrier' of C
f . (t,a1) is Element of the carrier' of C
[t,a1] is set
f . [t,a1] is set
G1 . [t,a1] is Morphism of c₄ . [t,a1],o1 . [t,a1]
g1 . a1 is Morphism of F2 . a1,s . a1
g1 . a1 is Element of the carrier' of C
f . (t,a1) is Element of the carrier' of C
f . [t,a1] is set
G2 . [t,a1] is Morphism of o1 . [t,a1],o2 . [t,a1]
t2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of F1,s
t2 . a1 is Morphism of F1 . a1,s . a1
t2 . a1 is Element of the carrier' of C
f2 . (t,a1) is Element of the carrier' of C
f2 . [t,a1] is set
(G2 `*` G1) . [t,a1] is Morphism of c₄ . [t,a1],o2 . [t,a1]
(G2 . [t,a1]) * (G1 . [t,a1]) is Morphism of c₄ . [t,a1],o2 . [t,a1]
(g1 . a1) (*) (f1 . a1) is Element of the carrier' of C
(g1 . a1) * (f1 . a1) is Morphism of F1 . a1,s . a1
g1 `*` f1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of F1,s
(g1 `*` f1) . a1 is Morphism of F1 . a1,s . a1
(A,B,C,c₄,o2,(G2 `*` G1)) . t is Morphism of (A,B,C,c₄) . t,(A,B,C,o2) . t
[F1,s] is set
{F1,s} is non empty set
{{F1,s},{F1}} is non empty set
[[F1,s],t2] is set
{[F1,s],t2} is non empty set
{[F1,s]} is non empty Relation-like set
{{[F1,s],t2},{[F1,s]}} is non empty set
((A,B,C,o1,o2,G2) . t) (*) ((A,B,C,c₄,o1,G1) . t) is Element of the carrier' of (Functors (B,C))
((A,B,C,o1,o2,G2) . t) * ((A,B,C,c₄,o1,G1) . t) is Morphism of (A,B,C,c₄) . t,(A,B,C,o2) . t
((A,B,C,o1,o2,G2) `*` (A,B,C,c₄,o1,G1)) . t is Morphism of (A,B,C,c₄) . t,(A,B,C,o2) . t
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
the carrier of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,o1
(A,B,C,c₄,o1,o2) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
G1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,o1
(A,B,C,c₄,o1,G1) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
[:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty set
F1 is Element of the carrier of [:A,B:]
F2 is Element of the carrier of A
s is Element of the carrier of B
[F2,s] is Element of the carrier of [:A,B:]
{F2,s} is non empty set
{F2} is non empty set
{{F2,s},{F2}} is non empty set
(A,B,C,c₄) . F2 is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
Obj (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj (A,B,C,c₄)) . F2 is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . F2 is Element of the carrier of (Functors (B,C))
Obj (A,B,C,o1) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
(Obj (A,B,C,o1)) . F2 is Element of the carrier of (Functors (B,C))
[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)] is Element of the carrier of [:(Functors (B,C)),(Functors (B,C)):]
[:(Functors (B,C)),(Functors (B,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] is non empty Relation-like set
the Source of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty set
[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty set
the Target of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
the Comp of (Functors (B,C)) is Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined the carrier' of (Functors (B,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty set
K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) is Relation-like [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] -defined [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):],[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):],K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) #) is strict CatStr
the carrier of [:(Functors (B,C)),(Functors (B,C)):] is non empty set
{((A,B,C,c₄) . F2),((A,B,C,o1) . F2)} is non empty set
{((A,B,C,c₄) . F2)} is non empty set
{{((A,B,C,c₄) . F2),((A,B,C,o1) . F2)},{((A,B,C,c₄) . F2)}} is non empty set
Funcs ( the carrier of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier of B, the carrier' of C
G2 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry G2 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
[: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty set
(curry G2) . F2 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)],((curry G2) . F2)] is set
{[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)],((curry G2) . F2)} is non empty set
{[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)]} is non empty Relation-like set
{{[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)],((curry G2) . F2)},{[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)]}} is non empty set
(A,B,C,c₄,o1,o2) . F2 is Morphism of (A,B,C,c₄) . F2,(A,B,C,o1) . F2
t is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry t is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
(curry t) . F2 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)],((curry t) . F2)] is set
{[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)],((curry t) . F2)} is non empty set
{{[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)],((curry t) . F2)},{[((A,B,C,c₄) . F2),((A,B,C,o1) . F2)]}} is non empty set
o2 . F1 is Morphism of c₄ . F1,o1 . F1
c₄ . F1 is Element of the carrier of C
the carrier of C is non empty set
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . F1 is Element of the carrier of C
o1 . F1 is Element of the carrier of C
Obj o1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
(Obj o1) . F1 is Element of the carrier of C
G2 . (F2,s) is Element of the carrier' of C
[F2,s] is set
G2 . [F2,s] is set
((curry t) . F2) . s is Element of the carrier' of C
t . (F2,s) is Element of the carrier' of C
t . [F2,s] is set
G1 . F1 is Morphism of c₄ . F1,o1 . F1
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
o1 is set
o2 is Element of the carrier' of A
G1 is Element of the carrier' of B
[o2,G1] is Element of the carrier' of [:A,B:]
{o2,G1} is non empty set
{o2} is non empty set
{{o2,G1},{o2}} is non empty set
c₄ . o2 is Element of the carrier' of (Functors (B,C))
dom (c₄ . o2) is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
the Source of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty set
the Source of (Functors (B,C)) . (c₄ . o2) is Element of the carrier of (Functors (B,C))
cod (c₄ . o2) is Element of the carrier of (Functors (B,C))
the Target of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
the Target of (Functors (B,C)) . (c₄ . o2) is Element of the carrier of (Functors (B,C))
G2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[G2,t] is set
{G2,t} is non empty set
{G2} is non empty set
{{G2,t},{G2}} is non empty set
F1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G2,t
[[G2,t],F1] is set
{[G2,t],F1} is non empty set
{[G2,t]} is non empty Relation-like set
{{[G2,t],F1},{[G2,t]}} is non empty set
G2 . G1 is Element of the carrier' of C
cod G1 is Element of the carrier of B
the Target of B . G1 is Element of the carrier of B
F1 . (cod G1) is Morphism of G2 . (cod G1),t . (cod G1)
G2 . (cod G1) is Element of the carrier of C
the carrier of C is non empty set
Obj G2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj G2) . (cod G1) is Element of the carrier of C
t . (cod G1) is Element of the carrier of C
Obj t is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj t) . (cod G1) is Element of the carrier of C
(F1 . (cod G1)) (*) (G2 . G1) is Element of the carrier' of C
F2 is set
s is set
f is Element of the carrier' of A
c₄ . f is Element of the carrier' of (Functors (B,C))
f is Element of the carrier' of B
[f,f] is Element of the carrier' of [:A,B:]
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
cod f is Element of the carrier of B
the Target of B . f is Element of the carrier of B
f2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
g1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[f2,g1] is set
{f2,g1} is non empty set
{f2} is non empty set
{{f2,g1},{f2}} is non empty set
f2 . f is Element of the carrier' of C
f1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of f2,g1
[[f2,g1],f1] is set
{[f2,g1],f1} is non empty set
{[f2,g1]} is non empty Relation-like set
{{[f2,g1],f1},{[f2,g1]}} is non empty set
f1 . (cod f) is Morphism of f2 . (cod f),g1 . (cod f)
f2 . (cod f) is Element of the carrier of C
Obj f2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f2) . (cod f) is Element of the carrier of C
g1 . (cod f) is Element of the carrier of C
Obj g1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj g1) . (cod f) is Element of the carrier of C
(f1 . (cod f)) (*) (f2 . f) is Element of the carrier' of C
[: the carrier' of [:A,B:], the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of [:A,B:], the carrier' of C:] is non empty set
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier' of C:]
the carrier of [:A,B:] is non empty set
o2 is Element of the carrier of [:A,B:]
id o2 is Morphism of o2,o2
o1 . (id o2) is Element of the carrier' of C
G1 is Element of the carrier of A
G2 is Element of the carrier of B
[G1,G2] is Element of the carrier of [:A,B:]
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
c₄ . G1 is Element of the carrier of (Functors (B,C))
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj c₄) . G1 is Element of the carrier of (Functors (B,C))
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
t . G2 is Element of the carrier of C
Obj t is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj t) . G2 is Element of the carrier of C
id (t . G2) is Morphism of t . G2,t . G2
Hom ((t . G2),(t . G2)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = t . G2 & cod b₁ = t . G2 ) } is set
id G1 is Morphism of G1,G1
c₄ . (id G1) is Element of the carrier' of (Functors (B,C))
id (c₄ . G1) is Morphism of c₄ . G1,c₄ . G1
[t,t] is set
{t,t} is non empty set
{t} is non empty set
{{t,t},{t}} is non empty set
id t is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of t,t
[[t,t],(id t)] is set
{[t,t],(id t)} is non empty set
{[t,t]} is non empty Relation-like set
{{[t,t],(id t)},{[t,t]}} is non empty set
id G2 is Morphism of G2,G2
[(id G1),(id G2)] is Element of the carrier' of [:A,B:]
{(id G1),(id G2)} is non empty set
{(id G1)} is non empty set
{{(id G1),(id G2)},{(id G1)}} is non empty set
t . (id G2) is Element of the carrier' of C
cod (id G2) is Element of the carrier of B
the Target of B . (id G2) is Element of the carrier of B
(id t) . (cod (id G2)) is Morphism of t . (cod (id G2)),t . (cod (id G2))
t . (cod (id G2)) is Element of the carrier of C
(Obj t) . (cod (id G2)) is Element of the carrier of C
((id t) . (cod (id G2))) (*) (t . (id G2)) is Element of the carrier' of C
((id t) . (cod (id G2))) (*) (id (t . G2)) is Element of the carrier' of C
(id t) . G2 is Morphism of t . G2,t . G2
((id t) . G2) (*) (id (t . G2)) is Element of the carrier' of C
(id (t . G2)) (*) (id (t . G2)) is Element of the carrier' of C
(id (t . G2)) * (id (t . G2)) is Morphism of t . G2,t . G2
o2 is Element of the carrier' of [:A,B:]
dom o2 is Element of the carrier of [:A,B:]
the Source of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
[: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty Relation-like set
bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty set
the Source of [:A,B:] . o2 is Element of the carrier of [:A,B:]
id (dom o2) is Morphism of dom o2, dom o2
o1 . (id (dom o2)) is Element of the carrier' of C
o1 . o2 is Element of the carrier' of C
dom (o1 . o2) is Element of the carrier of C
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
the Source of C . (o1 . o2) is Element of the carrier of C
id (dom (o1 . o2)) is Morphism of dom (o1 . o2), dom (o1 . o2)
cod o2 is Element of the carrier of [:A,B:]
the Target of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
the Target of [:A,B:] . o2 is Element of the carrier of [:A,B:]
id (cod o2) is Morphism of cod o2, cod o2
o1 . (id (cod o2)) is Element of the carrier' of C
cod (o1 . o2) is Element of the carrier of C
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (o1 . o2) is Element of the carrier of C
id (cod (o1 . o2)) is Morphism of cod (o1 . o2), cod (o1 . o2)
G1 is Element of the carrier' of A
G2 is Element of the carrier' of B
[G1,G2] is Element of the carrier' of [:A,B:]
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
dom G1 is Element of the carrier of A
the Source of A . G1 is Element of the carrier of A
c₄ . (dom G1) is Element of the carrier of (Functors (B,C))
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj c₄) . (dom G1) is Element of the carrier of (Functors (B,C))
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
t . G2 is Element of the carrier' of C
dom (t . G2) is Element of the carrier of C
the Source of C . (t . G2) is Element of the carrier of C
Hom ((dom (t . G2)),(dom (t . G2))) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = dom (t . G2) & cod b₁ = dom (t . G2) ) } is set
id (c₄ . (dom G1)) is Morphism of c₄ . (dom G1),c₄ . (dom G1)
[t,t] is set
{t,t} is non empty set
{t} is non empty set
{{t,t},{t}} is non empty set
id t is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of t,t
[[t,t],(id t)] is set
{[t,t],(id t)} is non empty set
{[t,t]} is non empty Relation-like set
{{[t,t],(id t)},{[t,t]}} is non empty set
id (dom G1) is Morphism of dom G1, dom G1
c₄ . (id (dom G1)) is Element of the carrier' of (Functors (B,C))
c₄ . G1 is Element of the carrier' of (Functors (B,C))
dom (c₄ . G1) is Element of the carrier of (Functors (B,C))
the Source of (Functors (B,C)) . (c₄ . G1) is Element of the carrier of (Functors (B,C))
cod (c₄ . G1) is Element of the carrier of (Functors (B,C))
the Target of (Functors (B,C)) . (c₄ . G1) is Element of the carrier of (Functors (B,C))
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
F2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
s is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of F1,F2
[[F1,F2],s] is set
{[F1,F2],s} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],s},{[F1,F2]}} is non empty set
cod G2 is Element of the carrier of B
the Target of B . G2 is Element of the carrier of B
F1 . (cod G2) is Element of the carrier of C
Obj F1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F1) . (cod G2) is Element of the carrier of C
F1 . G2 is Element of the carrier' of C
cod (F1 . G2) is Element of the carrier of C
the Target of C . (F1 . G2) is Element of the carrier of C
F2 . (cod G2) is Element of the carrier of C
Obj F2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj F2) . (cod G2) is Element of the carrier of C
Hom ((F1 . (cod G2)),(F2 . (cod G2))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = F1 . (cod G2) & cod b₁ = F2 . (cod G2) ) } is set
s . (cod G2) is Morphism of F1 . (cod G2),F2 . (cod G2)
dom (s . (cod G2)) is Element of the carrier of C
the Source of C . (s . (cod G2)) is Element of the carrier of C
dom G2 is Element of the carrier of B
the Source of B . G2 is Element of the carrier of B
[(dom G1),(dom G2)] is Element of the carrier of [:A,B:]
{(dom G1),(dom G2)} is non empty set
{(dom G1)} is non empty set
{{(dom G1),(dom G2)},{(dom G1)}} is non empty set
id [(dom G1),(dom G2)] is Morphism of [(dom G1),(dom G2)],[(dom G1),(dom G2)]
id (dom G2) is Morphism of dom G2, dom G2
[(id (dom G1)),(id (dom G2))] is Element of the carrier' of [:A,B:]
{(id (dom G1)),(id (dom G2))} is non empty set
{(id (dom G1))} is non empty set
{{(id (dom G1)),(id (dom G2))},{(id (dom G1))}} is non empty set
t . (id (dom G2)) is Element of the carrier' of C
cod (id (dom G2)) is Element of the carrier of B
the Target of B . (id (dom G2)) is Element of the carrier of B
(id t) . (cod (id (dom G2))) is Morphism of t . (cod (id (dom G2))),t . (cod (id (dom G2)))
t . (cod (id (dom G2))) is Element of the carrier of C
Obj t is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj t) . (cod (id (dom G2))) is Element of the carrier of C
((id t) . (cod (id (dom G2)))) (*) (t . (id (dom G2))) is Element of the carrier' of C
t . (dom G2) is Element of the carrier of C
(Obj t) . (dom G2) is Element of the carrier of C
id (t . (dom G2)) is Morphism of t . (dom G2),t . (dom G2)
((id t) . (cod (id (dom G2)))) (*) (id (t . (dom G2))) is Element of the carrier' of C
id (dom (t . G2)) is Morphism of dom (t . G2), dom (t . G2)
((id t) . (cod (id (dom G2)))) (*) (id (dom (t . G2))) is Element of the carrier' of C
(id t) . (dom G2) is Morphism of t . (dom G2),t . (dom G2)
((id t) . (dom G2)) (*) (id (dom (t . G2))) is Element of the carrier' of C
(id (t . (dom G2))) (*) (id (dom (t . G2))) is Element of the carrier' of C
(id (dom (t . G2))) (*) (id (dom (t . G2))) is Element of the carrier' of C
(id (dom (t . G2))) * (id (dom (t . G2))) is Morphism of dom (t . G2), dom (t . G2)
dom (F1 . G2) is Element of the carrier of C
the Source of C . (F1 . G2) is Element of the carrier of C
id (dom (F1 . G2)) is Morphism of dom (F1 . G2), dom (F1 . G2)
(s . (cod G2)) (*) (F1 . G2) is Element of the carrier' of C
dom ((s . (cod G2)) (*) (F1 . G2)) is Element of the carrier of C
the Source of C . ((s . (cod G2)) (*) (F1 . G2)) is Element of the carrier of C
id (dom ((s . (cod G2)) (*) (F1 . G2))) is Morphism of dom ((s . (cod G2)) (*) (F1 . G2)), dom ((s . (cod G2)) (*) (F1 . G2))
cod G1 is Element of the carrier of A
the Target of A . G1 is Element of the carrier of A
c₄ . (cod G1) is Element of the carrier of (Functors (B,C))
(Obj c₄) . (cod G1) is Element of the carrier of (Functors (B,C))
f is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
f . G2 is Element of the carrier' of C
cod (f . G2) is Element of the carrier of C
the Target of C . (f . G2) is Element of the carrier of C
Hom ((cod (f . G2)),(cod (f . G2))) is non empty Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = cod (f . G2) & cod b₁ = cod (f . G2) ) } is set
[(cod G1),(cod G2)] is Element of the carrier of [:A,B:]
{(cod G1),(cod G2)} is non empty set
{(cod G1)} is non empty set
{{(cod G1),(cod G2)},{(cod G1)}} is non empty set
id [(cod G1),(cod G2)] is Morphism of [(cod G1),(cod G2)],[(cod G1),(cod G2)]
id (cod G1) is Morphism of cod G1, cod G1
id (cod G2) is Morphism of cod G2, cod G2
[(id (cod G1)),(id (cod G2))] is Element of the carrier' of [:A,B:]
{(id (cod G1)),(id (cod G2))} is non empty set
{(id (cod G1))} is non empty set
{{(id (cod G1)),(id (cod G2))},{(id (cod G1))}} is non empty set
id (c₄ . (cod G1)) is Morphism of c₄ . (cod G1),c₄ . (cod G1)
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
id f is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of f,f
[[f,f],(id f)] is set
{[f,f],(id f)} is non empty set
{[f,f]} is non empty Relation-like set
{{[f,f],(id f)},{[f,f]}} is non empty set
c₄ . (id (cod G1)) is Element of the carrier' of (Functors (B,C))
f . (id (cod G2)) is Element of the carrier' of C
cod (id (cod G2)) is Element of the carrier of B
the Target of B . (id (cod G2)) is Element of the carrier of B
(id f) . (cod (id (cod G2))) is Morphism of f . (cod (id (cod G2))),f . (cod (id (cod G2)))
f . (cod (id (cod G2))) is Element of the carrier of C
Obj f is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f) . (cod (id (cod G2))) is Element of the carrier of C
((id f) . (cod (id (cod G2)))) (*) (f . (id (cod G2))) is Element of the carrier' of C
f . (cod G2) is Element of the carrier of C
(Obj f) . (cod G2) is Element of the carrier of C
id (f . (cod G2)) is Morphism of f . (cod G2),f . (cod G2)
((id f) . (cod (id (cod G2)))) (*) (id (f . (cod G2))) is Element of the carrier' of C
id (cod (f . G2)) is Morphism of cod (f . G2), cod (f . G2)
((id f) . (cod (id (cod G2)))) (*) (id (cod (f . G2))) is Element of the carrier' of C
(id f) . (cod G2) is Morphism of f . (cod G2),f . (cod G2)
((id f) . (cod G2)) (*) (id (cod (f . G2))) is Element of the carrier' of C
(id (f . (cod G2))) (*) (id (cod (f . G2))) is Element of the carrier' of C
(id (cod (f . G2))) (*) (id (cod (f . G2))) is Element of the carrier' of C
(id (cod (f . G2))) * (id (cod (f . G2))) is Morphism of cod (f . G2), cod (f . G2)
id (F2 . (cod G2)) is Morphism of F2 . (cod G2),F2 . (cod G2)
cod (s . (cod G2)) is Element of the carrier of C
the Target of C . (s . (cod G2)) is Element of the carrier of C
id (cod (s . (cod G2))) is Morphism of cod (s . (cod G2)), cod (s . (cod G2))
cod ((s . (cod G2)) (*) (F1 . G2)) is Element of the carrier of C
the Target of C . ((s . (cod G2)) (*) (F1 . G2)) is Element of the carrier of C
id (cod ((s . (cod G2)) (*) (F1 . G2))) is Morphism of cod ((s . (cod G2)) (*) (F1 . G2)), cod ((s . (cod G2)) (*) (F1 . G2))
G1 is Element of the carrier' of [:A,B:]
dom G1 is Element of the carrier of [:A,B:]
the Source of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
[: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty Relation-like set
bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty set
the Source of [:A,B:] . G1 is Element of the carrier of [:A,B:]
o2 is Element of the carrier' of [:A,B:]
cod o2 is Element of the carrier of [:A,B:]
the Target of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
the Target of [:A,B:] . o2 is Element of the carrier of [:A,B:]
G1 (*) o2 is Element of the carrier' of [:A,B:]
o1 . (G1 (*) o2) is Element of the carrier' of C
o1 . o2 is Element of the carrier' of C
o1 . G1 is Element of the carrier' of C
(o1 . G1) (*) (o1 . o2) is Element of the carrier' of C
G2 is Element of the carrier' of A
t is Element of the carrier' of B
[G2,t] is Element of the carrier' of [:A,B:]
{G2,t} is non empty set
{G2} is non empty set
{{G2,t},{G2}} is non empty set
dom t is Element of the carrier of B
the Source of B . t is Element of the carrier of B
cod t is Element of the carrier of B
the Target of B . t is Element of the carrier of B
F2 is Element of the carrier' of A
s is Element of the carrier' of B
[F2,s] is Element of the carrier' of [:A,B:]
{F2,s} is non empty set
{F2} is non empty set
{{F2,s},{F2}} is non empty set
cod F2 is Element of the carrier of A
the Target of A . F2 is Element of the carrier of A
cod s is Element of the carrier of B
the Target of B . s is Element of the carrier of B
[(cod F2),(cod s)] is Element of the carrier of [:A,B:]
{(cod F2),(cod s)} is non empty set
{(cod F2)} is non empty set
{{(cod F2),(cod s)},{(cod F2)}} is non empty set
c₄ . G2 is Element of the carrier' of (Functors (B,C))
dom (c₄ . G2) is Element of the carrier of (Functors (B,C))
the Source of (Functors (B,C)) . (c₄ . G2) is Element of the carrier of (Functors (B,C))
cod (c₄ . G2) is Element of the carrier of (Functors (B,C))
the Target of (Functors (B,C)) . (c₄ . G2) is Element of the carrier of (Functors (B,C))
f is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
f is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
f2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of f,f
[[f,f],f2] is set
{[f,f],f2} is non empty set
{[f,f]} is non empty Relation-like set
{{[f,f],f2},{[f,f]}} is non empty set
c₄ . F2 is Element of the carrier' of (Functors (B,C))
dom (c₄ . F2) is Element of the carrier of (Functors (B,C))
the Source of (Functors (B,C)) . (c₄ . F2) is Element of the carrier of (Functors (B,C))
cod (c₄ . F2) is Element of the carrier of (Functors (B,C))
the Target of (Functors (B,C)) . (c₄ . F2) is Element of the carrier of (Functors (B,C))
g1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
f1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[g1,f1] is set
{g1,f1} is non empty set
{g1} is non empty set
{{g1,f1},{g1}} is non empty set
t2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of g1,f1
[[g1,f1],t2] is set
{[g1,f1],t2} is non empty set
{[g1,f1]} is non empty Relation-like set
{{[g1,f1],t2},{[g1,f1]}} is non empty set
g1 . s is Element of the carrier' of C
t2 . (cod s) is Morphism of g1 . (cod s),f1 . (cod s)
g1 . (cod s) is Element of the carrier of C
Obj g1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj g1) . (cod s) is Element of the carrier of C
f1 . (cod s) is Element of the carrier of C
Obj f1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f1) . (cod s) is Element of the carrier of C
(t2 . (cod s)) (*) (g1 . s) is Element of the carrier' of C
dom G2 is Element of the carrier of A
the Source of A . G2 is Element of the carrier of A
[(dom G2),(dom t)] is Element of the carrier of [:A,B:]
{(dom G2),(dom t)} is non empty set
{(dom G2)} is non empty set
{{(dom G2),(dom t)},{(dom G2)}} is non empty set
G2 (*) F2 is Element of the carrier' of A
t (*) s is Element of the carrier' of B
[(G2 (*) F2),(t (*) s)] is Element of the carrier' of [:A,B:]
{(G2 (*) F2),(t (*) s)} is non empty set
{(G2 (*) F2)} is non empty set
{{(G2 (*) F2),(t (*) s)},{(G2 (*) F2)}} is non empty set
dom s is Element of the carrier of B
the Source of B . s is Element of the carrier of B
cod (t (*) s) is Element of the carrier of B
the Target of B . (t (*) s) is Element of the carrier of B
Hom ((dom s),(dom t)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = dom s & cod b₁ = dom t ) } is set
g1 . (dom s) is Element of the carrier of C
(Obj g1) . (dom s) is Element of the carrier of C
g1 . (dom t) is Element of the carrier of C
(Obj g1) . (dom t) is Element of the carrier of C
Hom ((g1 . (dom s)),(g1 . (dom t))) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g1 . (dom s) & cod b₁ = g1 . (dom t) ) } is set
f1 . (dom t) is Element of the carrier of C
(Obj f1) . (dom t) is Element of the carrier of C
Hom ((g1 . (dom t)),(f1 . (dom t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g1 . (dom t) & cod b₁ = f1 . (dom t) ) } is set
Hom ((g1 . (dom s)),(f1 . (dom t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g1 . (dom s) & cod b₁ = f1 . (dom t) ) } is set
Hom ((dom t),(cod t)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = dom t & cod b₁ = cod t ) } is set
g1 /. t is Element of the carrier' of C
g1 . t is Element of the carrier' of C
F1 is Morphism of dom t, cod t
g1 /. F1 is Morphism of g1 . (dom t),g1 . (cod t)
g1 . (cod t) is Element of the carrier of C
(Obj g1) . (cod t) is Element of the carrier of C
f1 . (cod t) is Element of the carrier of C
(Obj f1) . (cod t) is Element of the carrier of C
f . (cod t) is Element of the carrier of C
Obj f is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f) . (cod t) is Element of the carrier of C
Hom ((f1 . (cod t)),(f . (cod t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = f1 . (cod t) & cod b₁ = f . (cod t) ) } is set
f /. t is Element of the carrier' of C
f . t is Element of the carrier' of C
f1 /. F1 is Morphism of f1 . (dom t),f1 . (cod t)
Hom ((f1 . (dom t)),(f1 . (cod t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = f1 . (dom t) & cod b₁ = f1 . (cod t) ) } is set
Hom ((f1 . (dom t)),(f . (cod t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = f1 . (dom t) & cod b₁ = f . (cod t) ) } is set
Hom ((g1 . (dom t)),(g1 . (cod t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g1 . (dom t) & cod b₁ = g1 . (cod t) ) } is set
Hom ((g1 . (dom s)),(g1 . (cod t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g1 . (dom s) & cod b₁ = g1 . (cod t) ) } is set
Hom ((g1 . (cod t)),(f1 . (cod t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g1 . (cod t) & cod b₁ = f1 . (cod t) ) } is set
Hom ((g1 . (cod t)),(f . (cod t))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g1 . (cod t) & cod b₁ = f . (cod t) ) } is set
g1 /. s is Element of the carrier' of C
b1 is Morphism of dom s, dom t
g1 /. b1 is Morphism of g1 . (dom s),g1 . (dom t)
c₄ . (G2 (*) F2) is Element of the carrier' of (Functors (B,C))
(c₄ . G2) (*) (c₄ . F2) is Element of the carrier' of (Functors (B,C))
[g1,f] is set
{g1,f} is non empty set
{{g1,f},{g1}} is non empty set
a1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of f1,f
a1 `*` t2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of g1,f
[[g1,f],(a1 `*` t2)] is set
{[g1,f],(a1 `*` t2)} is non empty set
{[g1,f]} is non empty Relation-like set
{{[g1,f],(a1 `*` t2)},{[g1,f]}} is non empty set
g1 . (t (*) s) is Element of the carrier' of C
(a1 `*` t2) . (cod (t (*) s)) is Morphism of g1 . (cod (t (*) s)),f . (cod (t (*) s))
g1 . (cod (t (*) s)) is Element of the carrier of C
(Obj g1) . (cod (t (*) s)) is Element of the carrier of C
f . (cod (t (*) s)) is Element of the carrier of C
(Obj f) . (cod (t (*) s)) is Element of the carrier of C
((a1 `*` t2) . (cod (t (*) s))) (*) (g1 . (t (*) s)) is Element of the carrier' of C
t2 . (cod t) is Morphism of g1 . (cod t),f1 . (cod t)
a1 . (cod t) is Morphism of f1 . (cod t),f . (cod t)
(a1 . (cod t)) * (t2 . (cod t)) is Morphism of g1 . (cod t),f . (cod t)
((a1 . (cod t)) * (t2 . (cod t))) (*) (g1 . (t (*) s)) is Element of the carrier' of C
(g1 /. t) (*) (g1 /. s) is Element of the carrier' of C
((a1 . (cod t)) * (t2 . (cod t))) (*) ((g1 /. t) (*) (g1 /. s)) is Element of the carrier' of C
(g1 /. F1) * (g1 /. b1) is Morphism of g1 . (dom s),g1 . (cod t)
((a1 . (cod t)) * (t2 . (cod t))) (*) ((g1 /. F1) * (g1 /. b1)) is Element of the carrier' of C
((a1 . (cod t)) * (t2 . (cod t))) * ((g1 /. F1) * (g1 /. b1)) is Morphism of g1 . (dom s),f . (cod t)
(t2 . (cod t)) * ((g1 /. F1) * (g1 /. b1)) is Morphism of g1 . (dom s),f1 . (cod t)
(a1 . (cod t)) * ((t2 . (cod t)) * ((g1 /. F1) * (g1 /. b1))) is Morphism of g1 . (dom s),f . (cod t)
(t2 . (cod t)) * (g1 /. F1) is Morphism of g1 . (dom t),f1 . (cod t)
((t2 . (cod t)) * (g1 /. F1)) * (g1 /. b1) is Morphism of g1 . (dom s),f1 . (cod t)
(a1 . (cod t)) * (((t2 . (cod t)) * (g1 /. F1)) * (g1 /. b1)) is Morphism of g1 . (dom s),f . (cod t)
t2 . (dom t) is Morphism of g1 . (dom t),f1 . (dom t)
(f1 /. F1) * (t2 . (dom t)) is Morphism of g1 . (dom t),f1 . (cod t)
((f1 /. F1) * (t2 . (dom t))) * (g1 /. b1) is Morphism of g1 . (dom s),f1 . (cod t)
(a1 . (cod t)) * (((f1 /. F1) * (t2 . (dom t))) * (g1 /. b1)) is Morphism of g1 . (dom s),f . (cod t)
(t2 . (dom t)) * (g1 /. b1) is Morphism of g1 . (dom s),f1 . (dom t)
(f1 /. F1) * ((t2 . (dom t)) * (g1 /. b1)) is Morphism of g1 . (dom s),f1 . (cod t)
(a1 . (cod t)) * ((f1 /. F1) * ((t2 . (dom t)) * (g1 /. b1))) is Morphism of g1 . (dom s),f . (cod t)
(a1 . (cod t)) * (f1 /. F1) is Morphism of f1 . (dom t),f . (cod t)
((a1 . (cod t)) * (f1 /. F1)) * ((t2 . (dom t)) * (g1 /. b1)) is Morphism of g1 . (dom s),f . (cod t)
((a1 . (cod t)) * (f1 /. F1)) (*) ((t2 . (dom t)) * (g1 /. b1)) is Element of the carrier' of C
((a1 . (cod t)) * (f1 /. F1)) (*) ((t2 . (cod s)) (*) (g1 . s)) is Element of the carrier' of C
(a1 . (cod t)) (*) (f /. t) is Element of the carrier' of C
((a1 . (cod t)) (*) (f /. t)) (*) ((t2 . (cod s)) (*) (g1 . s)) is Element of the carrier' of C
o2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
G1 is Element of the carrier' of A
c₄ . G1 is Element of the carrier' of (Functors (B,C))
dom (c₄ . G1) is Element of the carrier of (Functors (B,C))
the Source of (Functors (B,C)) . (c₄ . G1) is Element of the carrier of (Functors (B,C))
cod (c₄ . G1) is Element of the carrier of (Functors (B,C))
the Target of (Functors (B,C)) . (c₄ . G1) is Element of the carrier of (Functors (B,C))
G2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[G2,t] is set
{G2,t} is non empty set
{G2} is non empty set
{{G2,t},{G2}} is non empty set
F1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G2,t
[[G2,t],F1] is set
{[G2,t],F1} is non empty set
{[G2,t]} is non empty Relation-like set
{{[G2,t],F1},{[G2,t]}} is non empty set
F2 is Element of the carrier' of B
cod F2 is Element of the carrier of B
the Target of B . F2 is Element of the carrier of B
id (cod F2) is Morphism of cod F2, cod F2
dom (id (cod F2)) is Element of the carrier of B
the Source of B . (id (cod F2)) is Element of the carrier of B
dom G1 is Element of the carrier of A
the Source of A . G1 is Element of the carrier of A
c₄ . (dom G1) is Element of the carrier of (Functors (B,C))
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj c₄) . (dom G1) is Element of the carrier of (Functors (B,C))
id (dom G1) is Morphism of dom G1, dom G1
c₄ . (id (dom G1)) is Element of the carrier' of (Functors (B,C))
id (c₄ . (dom G1)) is Morphism of c₄ . (dom G1),c₄ . (dom G1)
[G2,G2] is set
{G2,G2} is non empty set
{{G2,G2},{G2}} is non empty set
id G2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G2,G2
[[G2,G2],(id G2)] is set
{[G2,G2],(id G2)} is non empty set
{[G2,G2]} is non empty Relation-like set
{{[G2,G2],(id G2)},{[G2,G2]}} is non empty set
o2 ?- (dom G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry o2 is Relation-like Function-like set
(curry o2) . (id (dom G1)) is set
(o2 ?- (dom G1)) . F2 is Element of the carrier' of C
o2 . ((id (dom G1)),F2) is Element of the carrier' of C
[(id (dom G1)),F2] is set
{(id (dom G1)),F2} is non empty set
{(id (dom G1))} is non empty set
{{(id (dom G1)),F2},{(id (dom G1))}} is non empty set
o2 . [(id (dom G1)),F2] is set
[(id (dom G1)),F2] is Element of the carrier' of [:A,B:]
o2 . [(id (dom G1)),F2] is Element of the carrier' of C
G2 . F2 is Element of the carrier' of C
(id G2) . (cod F2) is Morphism of G2 . (cod F2),G2 . (cod F2)
G2 . (cod F2) is Element of the carrier of C
Obj G2 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj G2) . (cod F2) is Element of the carrier of C
((id G2) . (cod F2)) (*) (G2 . F2) is Element of the carrier' of C
id (G2 . (cod F2)) is Morphism of G2 . (cod F2),G2 . (cod F2)
(id (G2 . (cod F2))) (*) (G2 . F2) is Element of the carrier' of C
G2 . (id (cod F2)) is Element of the carrier' of C
(G2 . (id (cod F2))) (*) (G2 . F2) is Element of the carrier' of C
(id (cod F2)) (*) F2 is Element of the carrier' of B
G2 . ((id (cod F2)) (*) F2) is Element of the carrier' of C
F2 is Element of the carrier' of B
cod F2 is Element of the carrier of B
the Target of B . F2 is Element of the carrier of B
id (cod F2) is Morphism of cod F2, cod F2
dom (id (cod F2)) is Element of the carrier of B
the Source of B . (id (cod F2)) is Element of the carrier of B
cod G1 is Element of the carrier of A
the Target of A . G1 is Element of the carrier of A
c₄ . (cod G1) is Element of the carrier of (Functors (B,C))
(Obj c₄) . (cod G1) is Element of the carrier of (Functors (B,C))
id (cod G1) is Morphism of cod G1, cod G1
c₄ . (id (cod G1)) is Element of the carrier' of (Functors (B,C))
id (c₄ . (cod G1)) is Morphism of c₄ . (cod G1),c₄ . (cod G1)
[t,t] is set
{t,t} is non empty set
{t} is non empty set
{{t,t},{t}} is non empty set
id t is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of t,t
[[t,t],(id t)] is set
{[t,t],(id t)} is non empty set
{[t,t]} is non empty Relation-like set
{{[t,t],(id t)},{[t,t]}} is non empty set
o2 ?- (cod G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry o2) . (id (cod G1)) is set
(o2 ?- (cod G1)) . F2 is Element of the carrier' of C
o2 . ((id (cod G1)),F2) is Element of the carrier' of C
[(id (cod G1)),F2] is set
{(id (cod G1)),F2} is non empty set
{(id (cod G1))} is non empty set
{{(id (cod G1)),F2},{(id (cod G1))}} is non empty set
o2 . [(id (cod G1)),F2] is set
[(id (cod G1)),F2] is Element of the carrier' of [:A,B:]
o2 . [(id (cod G1)),F2] is Element of the carrier' of C
t . F2 is Element of the carrier' of C
(id t) . (cod F2) is Morphism of t . (cod F2),t . (cod F2)
t . (cod F2) is Element of the carrier of C
Obj t is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj t) . (cod F2) is Element of the carrier of C
((id t) . (cod F2)) (*) (t . F2) is Element of the carrier' of C
id (t . (cod F2)) is Morphism of t . (cod F2),t . (cod F2)
(id (t . (cod F2))) (*) (t . F2) is Element of the carrier' of C
t . (id (cod F2)) is Element of the carrier' of C
(t . (id (cod F2))) (*) (t . F2) is Element of the carrier' of C
(id (cod F2)) (*) F2 is Element of the carrier' of B
t . ((id (cod F2)) (*) F2) is Element of the carrier' of C
F2 is Element of the carrier of B
G2 . F2 is Element of the carrier of C
(Obj G2) . F2 is Element of the carrier of C
Hom ((G2 . F2),(G2 . F2)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = G2 . F2 & cod b₁ = G2 . F2 ) } is set
t . F2 is Element of the carrier of C
(Obj t) . F2 is Element of the carrier of C
Hom ((G2 . F2),(t . F2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = G2 . F2 & cod b₁ = t . F2 ) } is set
(A,B,C,o2,G1) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2 ?- (dom G1),o2 ?- (cod G1)
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,o2,G1) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry o2) . G1 is set
(A,B,C,o2,G1) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
(A,B,C,o2,G1) . F2 is Morphism of (o2 ?- (dom G1)) . F2,(o2 ?- (cod G1)) . F2
(o2 ?- (dom G1)) . F2 is Element of the carrier of C
Obj (o2 ?- (dom G1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o2 ?- (dom G1))) . F2 is Element of the carrier of C
(o2 ?- (cod G1)) . F2 is Element of the carrier of C
Obj (o2 ?- (cod G1)) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o2 ?- (cod G1))) . F2 is Element of the carrier of C
id F2 is Morphism of F2,F2
o2 . (G1,(id F2)) is Element of the carrier' of C
[G1,(id F2)] is set
{G1,(id F2)} is non empty set
{G1} is non empty set
{{G1,(id F2)},{G1}} is non empty set
o2 . [G1,(id F2)] is set
[G1,(id F2)] is Element of the carrier' of [:A,B:]
o2 . [G1,(id F2)] is Element of the carrier' of C
G2 . (id F2) is Element of the carrier' of C
cod (id F2) is Element of the carrier of B
the Target of B . (id F2) is Element of the carrier of B
F1 . (cod (id F2)) is Morphism of G2 . (cod (id F2)),t . (cod (id F2))
G2 . (cod (id F2)) is Element of the carrier of C
(Obj G2) . (cod (id F2)) is Element of the carrier of C
t . (cod (id F2)) is Element of the carrier of C
(Obj t) . (cod (id F2)) is Element of the carrier of C
(F1 . (cod (id F2))) (*) (G2 . (id F2)) is Element of the carrier' of C
id (G2 . F2) is Morphism of G2 . F2,G2 . F2
(F1 . (cod (id F2))) (*) (id (G2 . F2)) is Element of the carrier' of C
F1 . F2 is Morphism of G2 . F2,t . F2
(F1 . F2) (*) (id (G2 . F2)) is Element of the carrier' of C
(F1 . F2) * (id (G2 . F2)) is Morphism of G2 . F2,t . F2
[(o2 ?- (dom G1)),(o2 ?- (cod G1))] is set
{(o2 ?- (dom G1)),(o2 ?- (cod G1))} is non empty set
{(o2 ?- (dom G1))} is non empty set
{{(o2 ?- (dom G1)),(o2 ?- (cod G1))},{(o2 ?- (dom G1))}} is non empty set
[[(o2 ?- (dom G1)),(o2 ?- (cod G1))],(A,B,C,o2,G1)] is set
{[(o2 ?- (dom G1)),(o2 ?- (cod G1))],(A,B,C,o2,G1)} is non empty set
{[(o2 ?- (dom G1)),(o2 ?- (cod G1))]} is non empty Relation-like set
{{[(o2 ?- (dom G1)),(o2 ?- (cod G1))],(A,B,C,o2,G1)},{[(o2 ?- (dom G1)),(o2 ?- (cod G1))]}} is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
the carrier' of [:A,B:] is non empty set
the carrier of [:A,B:] is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (B,C)) is non empty set
c₄ is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
o2 is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
G1 is set
G2 is Element of the carrier of A
o2 . G2 is Morphism of (A,B,C,c₄) . G2,(A,B,C,o1) . G2
(A,B,C,c₄) . G2 is Element of the carrier of (Functors (B,C))
the carrier of (Functors (B,C)) is non empty set
Obj (A,B,C,c₄) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
[: the carrier of A, the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier of A, the carrier of (Functors (B,C)):] is non empty set
(Obj (A,B,C,c₄)) . G2 is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . G2 is Element of the carrier of (Functors (B,C))
Obj (A,B,C,o1) is non empty Relation-like the carrier of A -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of (Functors (B,C)):]
(Obj (A,B,C,o1)) . G2 is Element of the carrier of (Functors (B,C))
dom (o2 . G2) is Element of the carrier of (Functors (B,C))
the Source of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
[: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty set
the Source of (Functors (B,C)) . (o2 . G2) is Element of the carrier of (Functors (B,C))
cod (o2 . G2) is Element of the carrier of (Functors (B,C))
the Target of (Functors (B,C)) is non empty Relation-like the carrier' of (Functors (B,C)) -defined the carrier of (Functors (B,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (B,C)), the carrier of (Functors (B,C)):]
the Target of (Functors (B,C)) . (o2 . G2) is Element of the carrier of (Functors (B,C))
t is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[t,F1] is set
{t,F1} is non empty set
{t} is non empty set
{{t,F1},{t}} is non empty set
F2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of t,F1
[[t,F1],F2] is set
{[t,F1],F2} is non empty set
{[t,F1]} is non empty Relation-like set
{{[t,F1],F2},{[t,F1]}} is non empty set
s is set
f is set
Funcs ( the carrier of B, the carrier' of C) is non empty functional FUNCTION_DOMAIN of the carrier of B, the carrier' of C
f is Element of the carrier of A
o2 . f is Morphism of (A,B,C,c₄) . f,(A,B,C,o1) . f
(A,B,C,c₄) . f is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . f is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . f is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . f is Element of the carrier of (Functors (B,C))
[((A,B,C,c₄) . f),((A,B,C,o1) . f)] is Element of the carrier of [:(Functors (B,C)),(Functors (B,C)):]
[:(Functors (B,C)),(Functors (B,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] is non empty Relation-like set
[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty set
[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
the Comp of (Functors (B,C)) is Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined the carrier' of (Functors (B,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty set
K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) is Relation-like [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] -defined [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):],[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):],K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) #) is strict CatStr
the carrier of [:(Functors (B,C)),(Functors (B,C)):] is non empty set
{((A,B,C,c₄) . f),((A,B,C,o1) . f)} is non empty set
{((A,B,C,c₄) . f)} is non empty set
{{((A,B,C,c₄) . f),((A,B,C,o1) . f)},{((A,B,C,c₄) . f)}} is non empty set
[[((A,B,C,c₄) . f),((A,B,C,o1) . f)],f] is set
{[((A,B,C,c₄) . f),((A,B,C,o1) . f)],f} is non empty set
{[((A,B,C,c₄) . f),((A,B,C,o1) . f)]} is non empty Relation-like set
{{[((A,B,C,c₄) . f),((A,B,C,o1) . f)],f},{[((A,B,C,c₄) . f),((A,B,C,o1) . f)]}} is non empty set
Hom (((A,B,C,c₄) . f),((A,B,C,o1) . f)) is Element of bool the carrier' of (Functors (B,C))
bool the carrier' of (Functors (B,C)) is non empty set
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . f & cod b₁ = (A,B,C,o1) . f ) } is set
[: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty Relation-like set
bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):] is non empty set
G1 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
[: the carrier of [:A,B:], the carrier' of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier' of C:] is non empty set
( the carrier of A, the carrier of B, the carrier' of C,G1) is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
[:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier of A, the carrier of B:], the carrier' of C:] is non empty set
t is Element of the carrier of [:A,B:]
F1 is Element of the carrier of A
F2 is Element of the carrier of B
[F1,F2] is Element of the carrier of [:A,B:]
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
(A,B,C,c₄) . F1 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . F1 is Element of the carrier of (Functors (B,C))
c₄ ?- F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry c₄ is Relation-like Function-like set
id F1 is Morphism of F1,F1
(curry c₄) . (id F1) is set
(A,B,C,o1) . F1 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . F1 is Element of the carrier of (Functors (B,C))
o1 ?- F1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
curry o1 is Relation-like Function-like set
(curry o1) . (id F1) is set
o2 . F1 is Morphism of (A,B,C,c₄) . F1,(A,B,C,o1) . F1
[(c₄ ?- F1),(o1 ?- F1)] is set
{(c₄ ?- F1),(o1 ?- F1)} is non empty set
{(c₄ ?- F1)} is non empty set
{{(c₄ ?- F1),(o1 ?- F1)},{(c₄ ?- F1)}} is non empty set
G1 . F1 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[(c₄ ?- F1),(o1 ?- F1)],(G1 . F1)] is set
{[(c₄ ?- F1),(o1 ?- F1)],(G1 . F1)} is non empty set
{[(c₄ ?- F1),(o1 ?- F1)]} is non empty Relation-like set
{{[(c₄ ?- F1),(o1 ?- F1)],(G1 . F1)},{[(c₄ ?- F1),(o1 ?- F1)]}} is non empty set
NatTrans (B,C) is non empty NatTrans-DOMAIN of B,C
s is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
f is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[s,f] is set
{s,f} is non empty set
{s} is non empty set
{{s,f},{s}} is non empty set
f is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of s,f
[[s,f],f] is set
{[s,f],f} is non empty set
{[s,f]} is non empty Relation-like set
{{[s,f],f},{[s,f]}} is non empty set
c₄ . [F1,F2] is Element of the carrier of C
the carrier of C is non empty set
Obj c₄ is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
[: the carrier of [:A,B:], the carrier of C:] is non empty Relation-like set
bool [: the carrier of [:A,B:], the carrier of C:] is non empty set
(Obj c₄) . [F1,F2] is Element of the carrier of C
(c₄ ?- F1) . F2 is Element of the carrier of C
Obj (c₄ ?- F1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
[: the carrier of B, the carrier of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier of C:] is non empty set
(Obj (c₄ ?- F1)) . F2 is Element of the carrier of C
s . F2 is Element of the carrier of C
Obj s is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj s) . F2 is Element of the carrier of C
f . F2 is Element of the carrier of C
Obj f is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f) . F2 is Element of the carrier of C
Hom ((s . F2),(f . F2)) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s . F2 & cod b₁ = f . F2 ) } is set
o1 . [F1,F2] is Element of the carrier of C
Obj o1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier of C:]
(Obj o1) . [F1,F2] is Element of the carrier of C
(o1 ?- F1) . F2 is Element of the carrier of C
Obj (o1 ?- F1) is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj (o1 ?- F1)) . F2 is Element of the carrier of C
G2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of [:A,B:], the carrier' of C:]
G2 . (F1,F2) is set
[F1,F2] is set
G2 . [F1,F2] is set
(G1 . F1) . F2 is Element of the carrier' of C
f . F2 is Element of the carrier' of C
f . F2 is Morphism of s . F2,f . F2
G2 . t is Element of the carrier' of C
c₄ . t is Element of the carrier of C
(Obj c₄) . t is Element of the carrier of C
o1 . t is Element of the carrier of C
(Obj o1) . t is Element of the carrier of C
Hom ((c₄ . t),(o1 . t)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . t & cod b₁ = o1 . t ) } is set
t is Element of the carrier of [:A,B:]
c₄ . t is Element of the carrier of C
(Obj c₄) . t is Element of the carrier of C
o1 . t is Element of the carrier of C
(Obj o1) . t is Element of the carrier of C
Hom ((c₄ . t),(o1 . t)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . t & cod b₁ = o1 . t ) } is set
t is Element of the carrier of [:A,B:]
G2 . t is Element of the carrier' of C
c₄ . t is Element of the carrier of C
(Obj c₄) . t is Element of the carrier of C
o1 . t is Element of the carrier of C
(Obj o1) . t is Element of the carrier of C
Hom ((c₄ . t),(o1 . t)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . t & cod b₁ = o1 . t ) } is set
[:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:], the carrier' of C:] is non empty set
s is Element of the carrier of [:A,B:]
f is Element of the carrier of [:A,B:]
Hom (s,f) is Element of bool the carrier' of [:A,B:]
bool the carrier' of [:A,B:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:A,B:] : ( dom b₁ = s & cod b₁ = f ) } is set
o1 . s is Element of the carrier of C
(Obj o1) . s is Element of the carrier of C
o1 . f is Element of the carrier of C
(Obj o1) . f is Element of the carrier of C
Hom ((o1 . s),(o1 . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o1 . s & cod b₁ = o1 . f ) } is set
f is Element of the carrier of A
f2 is Element of the carrier of B
[f,f2] is Element of the carrier of [:A,B:]
{f,f2} is non empty set
{f} is non empty set
{{f,f2},{f}} is non empty set
(A,B,C,c₄) . f is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . f is Element of the carrier of (Functors (B,C))
c₄ ?- f is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id f is Morphism of f,f
(curry c₄) . (id f) is set
(A,B,C,o1) . f is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . f is Element of the carrier of (Functors (B,C))
o1 ?- f is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry o1) . (id f) is set
o2 . f is Morphism of (A,B,C,c₄) . f,(A,B,C,o1) . f
[(c₄ ?- f),(o1 ?- f)] is set
{(c₄ ?- f),(o1 ?- f)} is non empty set
{(c₄ ?- f)} is non empty set
{{(c₄ ?- f),(o1 ?- f)},{(c₄ ?- f)}} is non empty set
G1 . f is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[(c₄ ?- f),(o1 ?- f)],(G1 . f)] is set
{[(c₄ ?- f),(o1 ?- f)],(G1 . f)} is non empty set
{[(c₄ ?- f),(o1 ?- f)]} is non empty Relation-like set
{{[(c₄ ?- f),(o1 ?- f)],(G1 . f)},{[(c₄ ?- f),(o1 ?- f)]}} is non empty set
g1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
f1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[g1,f1] is set
{g1,f1} is non empty set
{g1} is non empty set
{{g1,f1},{g1}} is non empty set
t2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of g1,f1
[[g1,f1],t2] is set
{[g1,f1],t2} is non empty set
{[g1,f1]} is non empty Relation-like set
{{[g1,f1],t2},{[g1,f1]}} is non empty set
a1 is Element of the carrier of A
b1 is Element of the carrier of B
[a1,b1] is Element of the carrier of [:A,B:]
{a1,b1} is non empty set
{a1} is non empty set
{{a1,b1},{a1}} is non empty set
(A,B,C,c₄) . a1 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . a1 is Element of the carrier of (Functors (B,C))
c₄ ?- a1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id a1 is Morphism of a1,a1
(curry c₄) . (id a1) is set
(A,B,C,o1) . a1 is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . a1 is Element of the carrier of (Functors (B,C))
o1 ?- a1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry o1) . (id a1) is set
o2 . a1 is Morphism of (A,B,C,c₄) . a1,(A,B,C,o1) . a1
[(c₄ ?- a1),(o1 ?- a1)] is set
{(c₄ ?- a1),(o1 ?- a1)} is non empty set
{(c₄ ?- a1)} is non empty set
{{(c₄ ?- a1),(o1 ?- a1)},{(c₄ ?- a1)}} is non empty set
G1 . a1 is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[(c₄ ?- a1),(o1 ?- a1)],(G1 . a1)] is set
{[(c₄ ?- a1),(o1 ?- a1)],(G1 . a1)} is non empty set
{[(c₄ ?- a1),(o1 ?- a1)]} is non empty Relation-like set
{{[(c₄ ?- a1),(o1 ?- a1)],(G1 . a1)},{[(c₄ ?- a1),(o1 ?- a1)]}} is non empty set
G1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
H1 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
[G1,H1] is set
{G1,H1} is non empty set
{G1} is non empty set
{{G1,H1},{G1}} is non empty set
t1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,H1
[[G1,H1],t1] is set
{[G1,H1],t1} is non empty set
{[G1,H1]} is non empty Relation-like set
{{[G1,H1],t1},{[G1,H1]}} is non empty set
t is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total transformation of c₄,o1
t . s is Morphism of c₄ . s,o1 . s
c₄ . s is Element of the carrier of C
(Obj c₄) . s is Element of the carrier of C
G2 . (a1,b1) is set
[a1,b1] is set
G2 . [a1,b1] is set
(G1 . a1) . b1 is Element of the carrier' of C
t1 . b1 is Morphism of G1 . b1,H1 . b1
G1 . b1 is Element of the carrier of C
Obj G1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj G1) . b1 is Element of the carrier of C
H1 . b1 is Element of the carrier of C
Obj H1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj H1) . b1 is Element of the carrier of C
G1 . f2 is Element of the carrier of C
(Obj G1) . f2 is Element of the carrier of C
H1 . f2 is Element of the carrier of C
(Obj H1) . f2 is Element of the carrier of C
Hom ((G1 . f2),(H1 . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = G1 . f2 & cod b₁ = H1 . f2 ) } is set
c₄ . f is Element of the carrier of C
(Obj c₄) . f is Element of the carrier of C
Hom ((c₄ . s),(c₄ . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . s & cod b₁ = c₄ . f ) } is set
Hom ((c₄ . f),(o1 . f)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . f & cod b₁ = o1 . f ) } is set
Hom ((G1 . b1),(H1 . b1)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = G1 . b1 & cod b₁ = H1 . b1 ) } is set
Hom (((A,B,C,c₄) . f),((A,B,C,o1) . f)) is Element of bool the carrier' of (Functors (B,C))
bool the carrier' of (Functors (B,C)) is non empty set
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . f & cod b₁ = (A,B,C,o1) . f ) } is set
Hom (((A,B,C,c₄) . a1),((A,B,C,o1) . a1)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . a1 & cod b₁ = (A,B,C,o1) . a1 ) } is set
f is Morphism of s,f
g is Element of the carrier' of A
h is Element of the carrier' of B
[g,h] is Element of the carrier' of [:A,B:]
{g,h} is non empty set
{g} is non empty set
{{g,h},{g}} is non empty set
Hom (a1,f) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = a1 & cod b₁ = f ) } is set
g is Morphism of a1,f
dom g is Element of the carrier of A
the Source of A . g is Element of the carrier of A
cod g is Element of the carrier of A
the Target of A . g is Element of the carrier of A
h is Morphism of b1,f2
id f2 is Morphism of f2,f2
dom (id f2) is Element of the carrier of B
the Source of B . (id f2) is Element of the carrier of B
Hom (a1,a1) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = a1 & cod b₁ = a1 ) } is set
g9 is Element of the carrier' of A
g9 (*) (id a1) is Element of the carrier' of A
g * (id a1) is Morphism of a1,f
Hom (((A,B,C,o1) . a1),((A,B,C,o1) . f)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,o1) . a1 & cod b₁ = (A,B,C,o1) . f ) } is set
(A,B,C,c₄) /. g is Morphism of (A,B,C,c₄) . a1,(A,B,C,c₄) . f
(A,B,C,o1) /. g is Morphism of (A,B,C,o1) . a1,(A,B,C,o1) . f
Hom ((c₄ . s),(o1 . s)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c₄ . s & cod b₁ = o1 . s ) } is set
Hom (b1,f2) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = b1 & cod b₁ = f2 ) } is set
Hom ((G1 . b1),(G1 . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = G1 . b1 & cod b₁ = G1 . f2 ) } is set
H1 /. h is Morphism of H1 . b1,H1 . f2
(o1 ?- a1) /. h is Element of the carrier' of C
(o1 ?- a1) . h is Element of the carrier' of C
o1 . ((id a1),h) is Element of the carrier' of C
[(id a1),h] is set
{(id a1),h} is non empty set
{(id a1)} is non empty set
{{(id a1),h},{(id a1)}} is non empty set
o1 . [(id a1),h] is set
f1 . f2 is Element of the carrier of C
Obj f1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj f1) . f2 is Element of the carrier of C
Hom ((H1 . f2),(f1 . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = H1 . f2 & cod b₁ = f1 . f2 ) } is set
(A,B,C,c₄,g) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄ ?- (dom g),c₄ ?- (cod g)
c₄ ?- (dom g) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (dom g) is Morphism of dom g, dom g
(curry c₄) . (id (dom g)) is set
c₄ ?- (cod g) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
id (cod g) is Morphism of cod g, cod g
(curry c₄) . (id (cod g)) is set
IdMap B is non empty Relation-like the carrier of B -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of B:]
[: the carrier of B, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of B:] is non empty set
(A,B,C,c₄,g) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of B, the carrier' of C:] is non empty set
(curry c₄) . g is set
(A,B,C,c₄,g) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
[: the carrier of B, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of B, the carrier' of C:] is non empty set
Hom (((A,B,C,c₄) . a1),((A,B,C,c₄) . f)) is Element of bool the carrier' of (Functors (B,C))
{ b₁ where b₁ is Element of the carrier' of (Functors (B,C)) : ( dom b₁ = (A,B,C,c₄) . a1 & cod b₁ = (A,B,C,c₄) . f ) } is set
cod (id a1) is Element of the carrier of A
the Target of A . (id a1) is Element of the carrier of A
cod h is Element of the carrier of B
the Target of B . h is Element of the carrier of B
[(id a1),h] is Element of the carrier' of [:A,B:]
cod [(id a1),h] is Element of the carrier of [:A,B:]
the Target of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
[: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty Relation-like set
bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:] is non empty set
the Target of [:A,B:] . [(id a1),h] is Element of the carrier of [:A,B:]
[a1,f2] is Element of the carrier of [:A,B:]
{a1,f2} is non empty set
{{a1,f2},{a1}} is non empty set
[g,(id f2)] is Element of the carrier' of [:A,B:]
{g,(id f2)} is non empty set
{g} is non empty set
{{g,(id f2)},{g}} is non empty set
dom [g,(id f2)] is Element of the carrier of [:A,B:]
the Source of [:A,B:] is non empty Relation-like the carrier' of [:A,B:] -defined the carrier of [:A,B:] -valued Function-like total quasi_total Element of bool [: the carrier' of [:A,B:], the carrier of [:A,B:]:]
the Source of [:A,B:] . [g,(id f2)] is Element of the carrier of [:A,B:]
(A,B,C,o1,g) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o1 ?- (dom g),o1 ?- (cod g)
o1 ?- (dom g) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry o1) . (id (dom g)) is set
o1 ?- (cod g) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
(curry o1) . (id (cod g)) is set
(A,B,C,o1,g) is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier' of C:]
(curry o1) . g is set
(A,B,C,o1,g) * (IdMap B) is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier' of C:]
(A,B,C,o1) . g9 is Element of the carrier' of (Functors (B,C))
[H1,f1] is set
{H1,f1} is non empty set
{H1} is non empty set
{{H1,f1},{H1}} is non empty set
v2 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of H1,f1
[[H1,f1],v2] is set
{[H1,f1],v2} is non empty set
{[H1,f1]} is non empty Relation-like set
{{[H1,f1],v2},{[H1,f1]}} is non empty set
(IdMap B) . f2 is Element of the carrier' of B
v2 . f2 is Morphism of H1 . f2,f1 . f2
((A,B,C,o1,g) * (IdMap B)) . f2 is Element of the carrier' of C
(A,B,C,o1,g) . ((IdMap B) . f2) is Element of the carrier' of C
o1 . (g,(id f2)) is Element of the carrier' of C
[g,(id f2)] is set
o1 . [g,(id f2)] is set
G1 /. h is Morphism of G1 . b1,G1 . f2
(c₄ ?- a1) /. h is Element of the carrier' of C
(c₄ ?- a1) . h is Element of the carrier' of C
c₄ . ((id a1),h) is Element of the carrier' of C
c₄ . [(id a1),h] is set
(A,B,C,c₄) . g9 is Element of the carrier' of (Functors (B,C))
[G1,g1] is set
{G1,g1} is non empty set
{{G1,g1},{G1}} is non empty set
v1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,g1
[[G1,g1],v1] is set
{[G1,g1],v1} is non empty set
{[G1,g1]} is non empty Relation-like set
{{[G1,g1],v1},{[G1,g1]}} is non empty set
[G1,f1] is set
{G1,f1} is non empty set
{{G1,f1},{G1}} is non empty set
t2 `*` v1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,f1
[[G1,f1],(t2 `*` v1)] is set
{[G1,f1],(t2 `*` v1)} is non empty set
{[G1,f1]} is non empty Relation-like set
{{[G1,f1],(t2 `*` v1)},{[G1,f1]}} is non empty set
(o2 . f) (*) ((A,B,C,c₄) . g9) is Element of the carrier' of (Functors (B,C))
e1 is Element of the carrier' of (Functors (B,C))
(o2 . f) (*) e1 is Element of the carrier' of (Functors (B,C))
(o2 . f) * ((A,B,C,c₄) /. g) is Morphism of (A,B,C,c₄) . a1,(A,B,C,o1) . f
((A,B,C,o1) /. g) * (o2 . a1) is Morphism of (A,B,C,c₄) . a1,(A,B,C,o1) . f
e2 is Element of the carrier' of (Functors (B,C))
e2 (*) (o2 . a1) is Element of the carrier' of (Functors (B,C))
((A,B,C,o1) . g9) (*) (o2 . a1) is Element of the carrier' of (Functors (B,C))
v2 `*` t1 is non empty Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,f1
[[G1,f1],(v2 `*` t1)] is set
{[G1,f1],(v2 `*` t1)} is non empty set
{{[G1,f1],(v2 `*` t1)},{[G1,f1]}} is non empty set
v1 . f2 is Morphism of G1 . f2,g1 . f2
g1 . f2 is Element of the carrier of C
Obj g1 is non empty Relation-like the carrier of B -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of B, the carrier of C:]
(Obj g1) . f2 is Element of the carrier of C
((A,B,C,c₄,g) * (IdMap B)) . f2 is Element of the carrier' of C
(A,B,C,c₄,g) . ((IdMap B) . f2) is Element of the carrier' of C
c₄ . (g,(id f2)) is Element of the carrier' of C
c₄ . [g,(id f2)] is set
t . f is Morphism of c₄ . f,o1 . f
G2 . (f,f2) is set
[f,f2] is set
G2 . [f,f2] is set
(G1 . f) . f2 is Element of the carrier' of C
t2 . f2 is Morphism of g1 . f2,f1 . f2
Hom ((g1 . f2),(f1 . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g1 . f2 & cod b₁ = f1 . f2 ) } is set
Hom (f2,f2) is non empty Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = f2 & cod b₁ = f2 ) } is set
h9 is Element of the carrier' of B
(id f2) (*) h9 is Element of the carrier' of B
(id f2) * h is Morphism of b1,f2
[g,(id f2)] (*) [(id a1),h] is Element of the carrier' of [:A,B:]
Hom ((H1 . b1),(H1 . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = H1 . b1 & cod b₁ = H1 . f2 ) } is set
Hom ((H1 . b1),(f1 . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = H1 . b1 & cod b₁ = f1 . f2 ) } is set
o1 /. f is Morphism of o1 . s,o1 . f
f9 is Element of the carrier' of [:A,B:]
o1 /. f9 is Element of the carrier' of C
o1 . f9 is Element of the carrier' of C
(v2 . f2) (*) (H1 /. h) is Element of the carrier' of C
(v2 . f2) * (H1 /. h) is Morphism of H1 . b1,f1 . f2
Hom ((G1 . f2),(g1 . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = G1 . f2 & cod b₁ = g1 . f2 ) } is set
Hom ((G1 . b1),(g1 . f2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = G1 . b1 & cod b₁ = g1 . f2 ) } is set
c₄ /. f is Morphism of c₄ . s,c₄ . f
c₄ /. f9 is Element of the carrier' of C
c₄ . f9 is Element of the carrier' of C
(v1 . f2) (*) (G1 /. h) is Element of the carrier' of C
(v1 . f2) * (G1 /. h) is Morphism of G1 . b1,g1 . f2
(t . f) * (c₄ /. f) is Morphism of c₄ . s,o1 . f
(t2 . f2) (*) ((v1 . f2) * (G1 /. h)) is Element of the carrier' of C
(t2 . f2) * ((v1 . f2) * (G1 /. h)) is Morphism of G1 . b1,f1 . f2
(t2 . f2) * (v1 . f2) is Morphism of G1 . f2,f1 . f2
((t2 . f2) * (v1 . f2)) * (G1 /. h) is Morphism of G1 . b1,f1 . f2
(v2 `*` t1) . f2 is Morphism of G1 . f2,f1 . f2
((v2 `*` t1) . f2) * (G1 /. h) is Morphism of G1 . b1,f1 . f2
t1 . f2 is Morphism of G1 . f2,H1 . f2
(v2 . f2) * (t1 . f2) is Morphism of G1 . f2,f1 . f2
((v2 . f2) * (t1 . f2)) * (G1 /. h) is Morphism of G1 . b1,f1 . f2
(t1 . f2) * (G1 /. h) is Morphism of G1 . b1,H1 . f2
(v2 . f2) * ((t1 . f2) * (G1 /. h)) is Morphism of G1 . b1,f1 . f2
(H1 /. h) * (t1 . b1) is Morphism of G1 . b1,H1 . f2
(v2 . f2) * ((H1 /. h) * (t1 . b1)) is Morphism of G1 . b1,f1 . f2
((v2 . f2) * (H1 /. h)) * (t1 . b1) is Morphism of G1 . b1,f1 . f2
(o1 /. f) (*) (t . s) is Element of the carrier' of C
(o1 /. f) * (t . s) is Morphism of c₄ . s,o1 . f
F1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of c₄,o1
(A,B,C,c₄,o1,F1) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
F2 is non empty Relation-like [: the carrier of A, the carrier of B:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier of A, the carrier of B:], the carrier' of C:]
curry G2 is Relation-like Function-like set
s is Element of the carrier of A
o2 . s is Morphism of (A,B,C,c₄) . s,(A,B,C,o1) . s
(A,B,C,c₄) . s is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,c₄)) . s is Element of the carrier of (Functors (B,C))
(A,B,C,o1) . s is Element of the carrier of (Functors (B,C))
(Obj (A,B,C,o1)) . s is Element of the carrier of (Functors (B,C))
[((A,B,C,c₄) . s),((A,B,C,o1) . s)] is Element of the carrier of [:(Functors (B,C)),(Functors (B,C)):]
[:(Functors (B,C)),(Functors (B,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] is non empty Relation-like set
[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] is non empty Relation-like set
[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:] is non empty set
[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):] is non empty Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):]:]
the Comp of (Functors (B,C)) is Relation-like [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -defined the carrier' of (Functors (B,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):], the carrier' of (Functors (B,C)):] is non empty set
K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) is Relation-like [:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] -defined [: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:]
[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (B,C)), the carrier of (Functors (B,C)):],[: the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)):],[: the Source of (Functors (B,C)), the Source of (Functors (B,C)):],[: the Target of (Functors (B,C)), the Target of (Functors (B,C)):],K209( the carrier' of (Functors (B,C)), the carrier' of (Functors (B,C)), the Comp of (Functors (B,C)), the Comp of (Functors (B,C))) #) is strict CatStr
the carrier of [:(Functors (B,C)),(Functors (B,C)):] is non empty set
{((A,B,C,c₄) . s),((A,B,C,o1) . s)} is non empty set
{((A,B,C,c₄) . s)} is non empty set
{{((A,B,C,c₄) . s),((A,B,C,o1) . s)},{((A,B,C,c₄) . s)}} is non empty set
curry F2 is non empty Relation-like the carrier of A -defined Funcs ( the carrier of B, the carrier' of C) -valued Function-like total quasi_total Element of bool [: the carrier of A,(Funcs ( the carrier of B, the carrier' of C)):]
(curry F2) . s is Relation-like the carrier of B -defined the carrier' of C -valued Function-like total quasi_total Element of Funcs ( the carrier of B, the carrier' of C)
[[((A,B,C,c₄) . s),((A,B,C,o1) . s)],((curry F2) . s)] is set
{[((A,B,C,c₄) . s),((A,B,C,o1) . s)],((curry F2) . s)} is non empty set
{[((A,B,C,c₄) . s),((A,B,C,o1) . s)]} is non empty Relation-like set
{{[((A,B,C,c₄) . s),((A,B,C,o1) . s)],((curry F2) . s)},{[((A,B,C,c₄) . s),((A,B,C,o1) . s)]}} is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Functors ([:A,B:],C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors ([:A,B:],C)) is non empty set
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(Functors (B,C))) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,(Functors (B,C)))) is non empty set
the carrier' of [:A,B:] is non empty set
the carrier' of C is non empty set
the carrier of [:A,B:] is non empty set
c₄ is set
NatTrans ([:A,B:],C) is non empty NatTrans-DOMAIN of [:A,B:],C
o1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
o2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[o1,o2] is set
{o1,o2} is non empty set
{o1} is non empty set
{{o1,o2},{o1}} is non empty set
G1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o1,o2
[[o1,o2],G1] is set
{[o1,o2],G1} is non empty set
{[o1,o2]} is non empty Relation-like set
{{[o1,o2],G1},{[o1,o2]}} is non empty set
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
the carrier' of (Functors (B,C)) is non empty set
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,o1),(A,B,C,o2)] is set
{(A,B,C,o1),(A,B,C,o2)} is non empty set
{(A,B,C,o1)} is non empty set
{{(A,B,C,o1),(A,B,C,o2)},{(A,B,C,o1)}} is non empty set
(A,B,C,o1,o2,G1) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,o1),(A,B,C,o2)
[[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)] is set
{[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)} is non empty set
{[(A,B,C,o1),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)},{[(A,B,C,o1),(A,B,C,o2)]}} is non empty set
G2 is set
NatTrans (A,(Functors (B,C))) is non empty NatTrans-DOMAIN of A, Functors (B,C)
t is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
F1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[t,F1] is set
{t,F1} is non empty set
{t} is non empty set
{{t,F1},{t}} is non empty set
(A,B,C,t) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,F1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,t),(A,B,C,F1)] is set
{(A,B,C,t),(A,B,C,F1)} is non empty set
{(A,B,C,t)} is non empty set
{{(A,B,C,t),(A,B,C,F1)},{(A,B,C,t)}} is non empty set
F2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of t,F1
[[t,F1],F2] is set
{[t,F1],F2} is non empty set
{[t,F1]} is non empty Relation-like set
{{[t,F1],F2},{[t,F1]}} is non empty set
(A,B,C,t,F1,F2) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,t),(A,B,C,F1)
[[(A,B,C,t),(A,B,C,F1)],(A,B,C,t,F1,F2)] is set
{[(A,B,C,t),(A,B,C,F1)],(A,B,C,t,F1,F2)} is non empty set
{[(A,B,C,t),(A,B,C,F1)]} is non empty Relation-like set
{{[(A,B,C,t),(A,B,C,F1)],(A,B,C,t,F1,F2)},{[(A,B,C,t),(A,B,C,F1)]}} is non empty set
[: the carrier' of (Functors ([:A,B:],C)), the carrier' of (Functors (A,(Functors (B,C)))):] is non empty Relation-like set
bool [: the carrier' of (Functors ([:A,B:],C)), the carrier' of (Functors (A,(Functors (B,C)))):] is non empty set
c₄ is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier' of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier' of (Functors (A,(Functors (B,C)))):]
the carrier of (Functors ([:A,B:],C)) is non empty set
the carrier of (Functors (A,(Functors (B,C)))) is non empty set
o1 is Element of the carrier of (Functors ([:A,B:],C))
id o1 is Morphism of o1,o1
c₄ . (id o1) is Element of the carrier' of (Functors (A,(Functors (B,C))))
o2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
G1 is Element of the carrier of (Functors (A,(Functors (B,C))))
id G1 is Morphism of G1,G1
id (A,B,C,o2) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
id o2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,o2
(A,B,C,o2,o2,(id o2)) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
[o2,o2] is set
{o2,o2} is non empty set
{o2} is non empty set
{{o2,o2},{o2}} is non empty set
[[o2,o2],(id o2)] is set
{[o2,o2],(id o2)} is non empty set
{[o2,o2]} is non empty Relation-like set
{{[o2,o2],(id o2)},{[o2,o2]}} is non empty set
[(A,B,C,o2),(A,B,C,o2)] is set
{(A,B,C,o2),(A,B,C,o2)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,o2)},{(A,B,C,o2)}} is non empty set
[[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))] is set
{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))} is non empty set
{[(A,B,C,o2),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))},{[(A,B,C,o2),(A,B,C,o2)]}} is non empty set
o1 is Element of the carrier' of (Functors ([:A,B:],C))
dom o1 is Element of the carrier of (Functors ([:A,B:],C))
the Source of (Functors ([:A,B:],C)) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier of (Functors ([:A,B:],C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):]
[: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):] is non empty Relation-like set
bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):] is non empty set
the Source of (Functors ([:A,B:],C)) . o1 is Element of the carrier of (Functors ([:A,B:],C))
id (dom o1) is Morphism of dom o1, dom o1
c₄ . (id (dom o1)) is Element of the carrier' of (Functors (A,(Functors (B,C))))
c₄ . o1 is Element of the carrier' of (Functors (A,(Functors (B,C))))
dom (c₄ . o1) is Element of the carrier of (Functors (A,(Functors (B,C))))
the Source of (Functors (A,(Functors (B,C)))) is non empty Relation-like the carrier' of (Functors (A,(Functors (B,C)))) -defined the carrier of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,(Functors (B,C)))), the carrier of (Functors (A,(Functors (B,C)))):]
[: the carrier' of (Functors (A,(Functors (B,C)))), the carrier of (Functors (A,(Functors (B,C)))):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,(Functors (B,C)))), the carrier of (Functors (A,(Functors (B,C)))):] is non empty set
the Source of (Functors (A,(Functors (B,C)))) . (c₄ . o1) is Element of the carrier of (Functors (A,(Functors (B,C))))
id (dom (c₄ . o1)) is Morphism of dom (c₄ . o1), dom (c₄ . o1)
cod o1 is Element of the carrier of (Functors ([:A,B:],C))
the Target of (Functors ([:A,B:],C)) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier of (Functors ([:A,B:],C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):]
the Target of (Functors ([:A,B:],C)) . o1 is Element of the carrier of (Functors ([:A,B:],C))
id (cod o1) is Morphism of cod o1, cod o1
c₄ . (id (cod o1)) is Element of the carrier' of (Functors (A,(Functors (B,C))))
cod (c₄ . o1) is Element of the carrier of (Functors (A,(Functors (B,C))))
the Target of (Functors (A,(Functors (B,C)))) is non empty Relation-like the carrier' of (Functors (A,(Functors (B,C)))) -defined the carrier of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,(Functors (B,C)))), the carrier of (Functors (A,(Functors (B,C)))):]
the Target of (Functors (A,(Functors (B,C)))) . (c₄ . o1) is Element of the carrier of (Functors (A,(Functors (B,C))))
id (cod (c₄ . o1)) is Morphism of cod (c₄ . o1), cod (c₄ . o1)
o2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
G1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[o2,G1] is set
{o2,G1} is non empty set
{o2} is non empty set
{{o2,G1},{o2}} is non empty set
G2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1
[[o2,G1],G2] is set
{[o2,G1],G2} is non empty set
{[o2,G1]} is non empty Relation-like set
{{[o2,G1],G2},{[o2,G1]}} is non empty set
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,o2),(A,B,C,G1)] is set
{(A,B,C,o2),(A,B,C,G1)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,G1)},{(A,B,C,o2)}} is non empty set
(A,B,C,o2,G1,G2) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,G1)
[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)] is set
{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)} is non empty set
{[(A,B,C,o2),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)},{[(A,B,C,o2),(A,B,C,G1)]}} is non empty set
[o2,o2] is set
{o2,o2} is non empty set
{{o2,o2},{o2}} is non empty set
id o2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,o2
[[o2,o2],(id o2)] is set
{[o2,o2],(id o2)} is non empty set
{[o2,o2]} is non empty Relation-like set
{{[o2,o2],(id o2)},{[o2,o2]}} is non empty set
[(A,B,C,o2),(A,B,C,o2)] is set
{(A,B,C,o2),(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,o2)},{(A,B,C,o2)}} is non empty set
(A,B,C,o2,o2,(id o2)) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
[[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))] is set
{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))} is non empty set
{[(A,B,C,o2),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))},{[(A,B,C,o2),(A,B,C,o2)]}} is non empty set
id (A,B,C,o2) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
[[(A,B,C,o2),(A,B,C,o2)],(id (A,B,C,o2))] is set
{[(A,B,C,o2),(A,B,C,o2)],(id (A,B,C,o2))} is non empty set
{{[(A,B,C,o2),(A,B,C,o2)],(id (A,B,C,o2))},{[(A,B,C,o2),(A,B,C,o2)]}} is non empty set
[G1,G1] is set
{G1,G1} is non empty set
{G1} is non empty set
{{G1,G1},{G1}} is non empty set
id G1 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,G1
[[G1,G1],(id G1)] is set
{[G1,G1],(id G1)} is non empty set
{[G1,G1]} is non empty Relation-like set
{{[G1,G1],(id G1)},{[G1,G1]}} is non empty set
[(A,B,C,G1),(A,B,C,G1)] is set
{(A,B,C,G1),(A,B,C,G1)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G1)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G1,(id G1)) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G1)
[[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))] is set
{[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))} is non empty set
{[(A,B,C,G1),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))},{[(A,B,C,G1),(A,B,C,G1)]}} is non empty set
id (A,B,C,G1) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G1)
[[(A,B,C,G1),(A,B,C,G1)],(id (A,B,C,G1))] is set
{[(A,B,C,G1),(A,B,C,G1)],(id (A,B,C,G1))} is non empty set
{{[(A,B,C,G1),(A,B,C,G1)],(id (A,B,C,G1))},{[(A,B,C,G1),(A,B,C,G1)]}} is non empty set
o2 is Element of the carrier' of (Functors ([:A,B:],C))
dom o2 is Element of the carrier of (Functors ([:A,B:],C))
the Source of (Functors ([:A,B:],C)) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier of (Functors ([:A,B:],C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):]
[: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):] is non empty Relation-like set
bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):] is non empty set
the Source of (Functors ([:A,B:],C)) . o2 is Element of the carrier of (Functors ([:A,B:],C))
o1 is Element of the carrier' of (Functors ([:A,B:],C))
cod o1 is Element of the carrier of (Functors ([:A,B:],C))
the Target of (Functors ([:A,B:],C)) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier of (Functors ([:A,B:],C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):]
the Target of (Functors ([:A,B:],C)) . o1 is Element of the carrier of (Functors ([:A,B:],C))
o2 (*) o1 is Element of the carrier' of (Functors ([:A,B:],C))
c₄ . (o2 (*) o1) is Element of the carrier' of (Functors (A,(Functors (B,C))))
c₄ . o1 is Element of the carrier' of (Functors (A,(Functors (B,C))))
c₄ . o2 is Element of the carrier' of (Functors (A,(Functors (B,C))))
(c₄ . o2) (*) (c₄ . o1) is Element of the carrier' of (Functors (A,(Functors (B,C))))
dom o1 is Element of the carrier of (Functors ([:A,B:],C))
the Source of (Functors ([:A,B:],C)) . o1 is Element of the carrier of (Functors ([:A,B:],C))
G1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
G2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
cod o2 is Element of the carrier of (Functors ([:A,B:],C))
the Target of (Functors ([:A,B:],C)) . o2 is Element of the carrier of (Functors ([:A,B:],C))
F1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
F2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
s is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of F1,F2
[[F1,F2],s] is set
{[F1,F2],s} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],s},{[F1,F2]}} is non empty set
[G1,F2] is set
{G1,F2} is non empty set
{{G1,F2},{G1}} is non empty set
f is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G2,F2
f `*` t is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,F2
[[G1,F2],(f `*` t)] is set
{[G1,F2],(f `*` t)} is non empty set
{[G1,F2]} is non empty Relation-like set
{{[G1,F2],(f `*` t)},{[G1,F2]}} is non empty set
(A,B,C,F2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,G1),(A,B,C,F2)] is set
{(A,B,C,G1),(A,B,C,F2)} is non empty set
{{(A,B,C,G1),(A,B,C,F2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,F2,(f `*` t)) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,F2)
[[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))] is set
{[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))} is non empty set
{[(A,B,C,G1),(A,B,C,F2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))},{[(A,B,C,G1),(A,B,C,F2)]}} is non empty set
[(A,B,C,G2),(A,B,C,F2)] is set
{(A,B,C,G2),(A,B,C,F2)} is non empty set
{(A,B,C,G2)} is non empty set
{{(A,B,C,G2),(A,B,C,F2)},{(A,B,C,G2)}} is non empty set
(A,B,C,G2,F2,f) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,G2),(A,B,C,F2)
[[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)] is set
{[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)} is non empty set
{[(A,B,C,G2),(A,B,C,F2)]} is non empty Relation-like set
{{[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)},{[(A,B,C,G2),(A,B,C,F2)]}} is non empty set
(A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,F2)
o1 is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier' of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Functor of Functors ([:A,B:],C), Functors (A,(Functors (B,C)))
o2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
G1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[o2,G1] is set
{o2,G1} is non empty set
{o2} is non empty set
{{o2,G1},{o2}} is non empty set
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,o2),(A,B,C,G1)] is set
{(A,B,C,o2),(A,B,C,G1)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,G1)},{(A,B,C,o2)}} is non empty set
G2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1
[[o2,G1],G2] is set
{[o2,G1],G2} is non empty set
{[o2,G1]} is non empty Relation-like set
{{[o2,G1],G2},{[o2,G1]}} is non empty set
o1 . [[o2,G1],G2] is set
(A,B,C,o2,G1,G2) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,G1)
[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)] is set
{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)} is non empty set
{[(A,B,C,o2),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)},{[(A,B,C,o2),(A,B,C,G1)]}} is non empty set
c₄ is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier' of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Functor of Functors ([:A,B:],C), Functors (A,(Functors (B,C)))
o1 is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier' of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Functor of Functors ([:A,B:],C), Functors (A,(Functors (B,C)))
o2 is Element of the carrier' of (Functors ([:A,B:],C))
dom o2 is Element of the carrier of (Functors ([:A,B:],C))
the carrier of (Functors ([:A,B:],C)) is non empty set
the Source of (Functors ([:A,B:],C)) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier of (Functors ([:A,B:],C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):]
[: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):] is non empty Relation-like set
bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):] is non empty set
the Source of (Functors ([:A,B:],C)) . o2 is Element of the carrier of (Functors ([:A,B:],C))
cod o2 is Element of the carrier of (Functors ([:A,B:],C))
the Target of (Functors ([:A,B:],C)) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier of (Functors ([:A,B:],C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):]
the Target of (Functors ([:A,B:],C)) . o2 is Element of the carrier of (Functors ([:A,B:],C))
G1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
G2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
c₄ . o2 is Element of the carrier' of (Functors (A,(Functors (B,C))))
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
the carrier' of (Functors (B,C)) is non empty set
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
o1 . o2 is Element of the carrier' of (Functors (A,(Functors (B,C))))
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Functors ([:A,B:],C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(Functors (B,C))) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
(A,B,C) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier' of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Functor of Functors ([:A,B:],C), Functors (A,(Functors (B,C)))
the carrier' of (Functors ([:A,B:],C)) is non empty set
the carrier' of (Functors (A,(Functors (B,C)))) is non empty set
c₄ is set
dom (A,B,C) is non empty set
o1 is set
(A,B,C) . c₄ is set
(A,B,C) . o1 is set
dom (A,B,C) is non empty Element of bool the carrier' of (Functors ([:A,B:],C))
bool the carrier' of (Functors ([:A,B:],C)) is non empty set
the carrier' of [:A,B:] is non empty set
the carrier' of C is non empty set
the carrier of [:A,B:] is non empty set
o2 is Element of the carrier' of (Functors ([:A,B:],C))
dom o2 is Element of the carrier of (Functors ([:A,B:],C))
the carrier of (Functors ([:A,B:],C)) is non empty set
the Source of (Functors ([:A,B:],C)) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier of (Functors ([:A,B:],C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):]
[: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):] is non empty Relation-like set
bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):] is non empty set
the Source of (Functors ([:A,B:],C)) . o2 is Element of the carrier of (Functors ([:A,B:],C))
cod o2 is Element of the carrier of (Functors ([:A,B:],C))
the Target of (Functors ([:A,B:],C)) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier of (Functors ([:A,B:],C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors ([:A,B:],C)), the carrier of (Functors ([:A,B:],C)):]
the Target of (Functors ([:A,B:],C)) . o2 is Element of the carrier of (Functors ([:A,B:],C))
G1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
G2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
F1 is Element of the carrier' of (Functors ([:A,B:],C))
dom F1 is Element of the carrier of (Functors ([:A,B:],C))
the Source of (Functors ([:A,B:],C)) . F1 is Element of the carrier of (Functors ([:A,B:],C))
cod F1 is Element of the carrier of (Functors ([:A,B:],C))
the Target of (Functors ([:A,B:],C)) . F1 is Element of the carrier of (Functors ([:A,B:],C))
F2 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
s is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
[F2,s] is set
{F2,s} is non empty set
{F2} is non empty set
{{F2,s},{F2}} is non empty set
f is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of F2,s
[[F2,s],f] is set
{[F2,s],f} is non empty set
{[F2,s]} is non empty Relation-like set
{{[F2,s],f},{[F2,s]}} is non empty set
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
the carrier' of (Functors (B,C)) is non empty set
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
(A,B,C) . [[F2,s],f] is set
(A,B,C,F2) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
(A,B,C,s) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[(A,B,C,F2),(A,B,C,s)] is set
{(A,B,C,F2),(A,B,C,s)} is non empty set
{(A,B,C,F2)} is non empty set
{{(A,B,C,F2),(A,B,C,s)},{(A,B,C,F2)}} is non empty set
(A,B,C,F2,s,f) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,F2),(A,B,C,s)
[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)] is set
{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)} is non empty set
{[(A,B,C,F2),(A,B,C,s)]} is non empty Relation-like set
{{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)},{[(A,B,C,F2),(A,B,C,s)]}} is non empty set
rng (A,B,C) is non empty Element of bool the carrier' of (Functors (A,(Functors (B,C))))
bool the carrier' of (Functors (A,(Functors (B,C)))) is non empty set
c₄ is set
the carrier' of (Functors (B,C)) is non empty set
o1 is Element of the carrier' of (Functors (A,(Functors (B,C))))
dom o1 is Element of the carrier of (Functors (A,(Functors (B,C))))
the carrier of (Functors (A,(Functors (B,C)))) is non empty set
the Source of (Functors (A,(Functors (B,C)))) is non empty Relation-like the carrier' of (Functors (A,(Functors (B,C)))) -defined the carrier of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,(Functors (B,C)))), the carrier of (Functors (A,(Functors (B,C)))):]
[: the carrier' of (Functors (A,(Functors (B,C)))), the carrier of (Functors (A,(Functors (B,C)))):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,(Functors (B,C)))), the carrier of (Functors (A,(Functors (B,C)))):] is non empty set
the Source of (Functors (A,(Functors (B,C)))) . o1 is Element of the carrier of (Functors (A,(Functors (B,C))))
cod o1 is Element of the carrier of (Functors (A,(Functors (B,C))))
the Target of (Functors (A,(Functors (B,C)))) is non empty Relation-like the carrier' of (Functors (A,(Functors (B,C)))) -defined the carrier of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,(Functors (B,C)))), the carrier of (Functors (A,(Functors (B,C)))):]
the Target of (Functors (A,(Functors (B,C)))) . o1 is Element of the carrier of (Functors (A,(Functors (B,C))))
o2 is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
G1 is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
[o2,G1] is set
{o2,G1} is non empty set
{o2} is non empty set
{{o2,G1},{o2}} is non empty set
G2 is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of o2,G1
[[o2,G1],G2] is set
{[o2,G1],G2} is non empty set
{[o2,G1]} is non empty Relation-like set
{{[o2,G1],G2},{[o2,G1]}} is non empty set
the carrier' of [:A,B:] is non empty set
the carrier' of C is non empty set
t is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,t) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
F1 is non empty Relation-like the carrier' of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:A,B:],C
(A,B,C,F1) is non empty Relation-like the carrier' of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total Functor of A, Functors (B,C)
the carrier of [:A,B:] is non empty set
F2 is non empty Relation-like the carrier of [:A,B:] -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of t,F1
(A,B,C,t,F1,F2) is non empty Relation-like the carrier of A -defined the carrier' of (Functors (B,C)) -valued Function-like total quasi_total natural_transformation of (A,B,C,t),(A,B,C,F1)
dom (A,B,C) is non empty Element of bool the carrier' of (Functors ([:A,B:],C))
bool the carrier' of (Functors ([:A,B:],C)) is non empty set
[t,F1] is set
{t,F1} is non empty set
{t} is non empty set
{{t,F1},{t}} is non empty set
[[t,F1],F2] is set
{[t,F1],F2} is non empty set
{[t,F1]} is non empty Relation-like set
{{[t,F1],F2},{[t,F1]}} is non empty set
NatTrans ([:A,B:],C) is non empty NatTrans-DOMAIN of [:A,B:],C
(A,B,C) . [[t,F1],F2] is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:A,B:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is non empty Relation-like set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
the Source of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is non empty Relation-like set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is non empty Relation-like the carrier' of A -defined the carrier of A -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is non empty Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is non empty Relation-like set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty Relation-like set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty Relation-like set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],K209( the carrier' of A, the carrier' of B, the Comp of A, the Comp of B) #) is strict CatStr
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Functors ([:A,B:],C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (B,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,(Functors (B,C))) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
(A,B,C) is non empty Relation-like the carrier' of (Functors ([:A,B:],C)) -defined the carrier' of (Functors (A,(Functors (B,C)))) -valued Function-like total quasi_total isomorphic Functor of Functors ([:A,B:],C), Functors (A,(Functors (B,C)))
the carrier' of (Functors ([:A,B:],C)) is non empty set
the carrier' of (Functors (A,(Functors (B,C)))) is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of B -defined the carrier' of C -valued Function-like total quasi_total Functor of B,C
G1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1
o2 * G1 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2 * c₄,o2 * o1
o2 * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
o2 * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
G1 * o2 is Relation-like the carrier of A -defined the carrier' of C -valued set
o2 * G1 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total transformation of o2 * c₄,o2 * o1
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
<:c₄,o1:> is Relation-like Function-like set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
<:c₄,o1:> is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the carrier' of B is non empty set
the carrier' of C is non empty set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
(A,B,C,(A,B,C,c₄,o1)) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * (A,B,C,c₄,o1) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,(A,B,C,c₄,o1)) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * (A,B,C,c₄,o1) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(pr1 ( the carrier' of B, the carrier' of C)) * (A,B,C,c₄,o1) is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like Element of bool [: the carrier' of A, the carrier' of B:]
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
bool [: the carrier' of A, the carrier' of B:] is non empty set
(pr2 ( the carrier' of B, the carrier' of C)) * (A,B,C,c₄,o1) is Relation-like the carrier' of A -defined the carrier' of C -valued Function-like Element of bool [: the carrier' of A, the carrier' of C:]
[: the carrier' of A, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of A, the carrier' of C:] is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the carrier' of C is non empty set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[: the carrier' of A,[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [: the carrier' of A,[: the carrier' of B, the carrier' of C:]:] is non empty set
o2 is non empty Relation-like the carrier' of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier' of A,[: the carrier' of B, the carrier' of C:]:]
(pr1 ( the carrier' of B, the carrier' of C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier' of B:]
[: the carrier' of A, the carrier' of B:] is non empty Relation-like set
bool [: the carrier' of A, the carrier' of B:] is non empty set
G1 is non empty Relation-like the carrier' of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier' of A,[: the carrier' of B, the carrier' of C:]:]
(pr1 ( the carrier' of B, the carrier' of C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier' of B:]
(pr2 ( the carrier' of B, the carrier' of C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier' of C:]
[: the carrier' of A, the carrier' of C:] is non empty Relation-like set
bool [: the carrier' of A, the carrier' of C:] is non empty set
(pr2 ( the carrier' of B, the carrier' of C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier' of A, the carrier' of C:]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the carrier' of B is non empty set
the carrier' of C is non empty set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
the carrier of A is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
o1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
o2 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of c₄,o1
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * o2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * c₄,(pr1 (B,C)) * o1
(pr1 (B,C)) * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(pr1 (B,C)) * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * o2 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * c₄,(pr2 (B,C)) * o1
(pr2 (B,C)) * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(pr2 (B,C)) * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the carrier' of C is non empty set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
o1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
o2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of c₄,o1
(A,B,C,c₄,o1,G2) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(pr1 (B,C)) * G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * c₄,(pr1 (B,C)) * o1
(A,B,C,c₄,o1,G2) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄),(A,B,C,o1)
(A,B,C,c₄) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * c₄ is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(pr2 (B,C)) * G2 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * c₄,(pr2 (B,C)) * o1
t is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of o2,G1
(A,B,C,o2,G1,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,G1)
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(pr1 (B,C)) * t is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * o2,(pr1 (B,C)) * G1
(A,B,C,o2,G1,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,G1)
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(pr2 (B,C)) * t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * o2,(pr2 (B,C)) * G1
[: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty set
F1 is non empty Relation-like the carrier of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:]
(pr2 ( the carrier' of B, the carrier' of C)) * F1 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of C:]
[: the carrier of A, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of C:] is non empty set
(pr2 (B,C)) * F1 is Relation-like the carrier of A -defined the carrier' of C -valued Function-like Element of bool [: the carrier of A, the carrier' of C:]
F2 is non empty Relation-like the carrier of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:]
(pr2 (B,C)) * F2 is Relation-like the carrier of A -defined the carrier' of C -valued Function-like Element of bool [: the carrier of A, the carrier' of C:]
(pr2 ( the carrier' of B, the carrier' of C)) * F2 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of C:]
(pr1 ( the carrier' of B, the carrier' of C)) * F1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of B:]
[: the carrier of A, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of B:] is non empty set
(pr1 (B,C)) * F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like Element of bool [: the carrier of A, the carrier' of B:]
(pr1 (B,C)) * F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like Element of bool [: the carrier of A, the carrier' of B:]
(pr1 ( the carrier' of B, the carrier' of C)) * F2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of B:]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty 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 B, the carrier' of C:] is non empty Relation-like set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total transformation of c₄,o1
t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total transformation of o2,G1
<:G2,t:> is non empty Relation-like the carrier of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:]
[: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty set
F1 is Element of the carrier of A
<:G2,t:> . F1 is Element of [: the carrier' of B, the carrier' of C:]
G2 . F1 is Morphism of c₄ . F1,o1 . F1
c₄ . F1 is Element of the carrier of B
the carrier of B is non empty set
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj c₄) . F1 is Element of the carrier of B
o1 . F1 is Element of the carrier of B
Obj o1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj o1) . F1 is Element of the carrier of B
t . F1 is Morphism of o2 . F1,G1 . F1
o2 . F1 is Element of the carrier of C
the carrier of C is non empty set
Obj o2 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
[: the carrier of A, the carrier of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier of C:] is non empty set
(Obj o2) . F1 is Element of the carrier of C
G1 . F1 is Element of the carrier of C
Obj G1 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
(Obj G1) . F1 is Element of the carrier of C
[(G2 . F1),(t . F1)] is Element of the carrier' of [:B,C:]
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
{(G2 . F1),(t . F1)} is non empty set
{(G2 . F1)} is non empty set
{{(G2 . F1),(t . F1)},{(G2 . F1)}} is non empty set
[: the carrier of A, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of B:] is non empty set
[: the carrier of A, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of C:] is non empty set
F2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of B:]
F2 . F1 is Element of the carrier' of B
s is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of C:]
s . F1 is Element of the carrier' of C
[(F2 . F1),(s . F1)] is Element of the carrier' of [:B,C:]
{(F2 . F1),(s . F1)} is non empty set
{(F2 . F1)} is non empty set
{{(F2 . F1),(s . F1)},{(F2 . F1)}} is non empty set
[(G2 . F1),(s . F1)] is Element of the carrier' of [:B,C:]
{(G2 . F1),(s . F1)} is non empty set
{{(G2 . F1),(s . F1)},{(G2 . F1)}} is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty 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 A is non empty set
o2 is Element of the carrier of A
G1 is Element of the carrier of A
Hom (o2,G1) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = o2 & cod b₁ = G1 ) } is set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is Morphism of o2,G1
(A,B,C,c₄,o1) . G2 is Element of the carrier' of [:B,C:]
c₄ . G2 is Element of the carrier' of B
o1 . G2 is Element of the carrier' of C
[(c₄ . G2),(o1 . G2)] is Element of the carrier' of [:B,C:]
{(c₄ . G2),(o1 . G2)} is non empty set
{(c₄ . G2)} is non empty set
{{(c₄ . G2),(o1 . G2)},{(c₄ . G2)}} is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier' of [:B,C:] is non empty set
o2 is Element of the carrier of A
(A,B,C,c₄,o1) . o2 is Element of the carrier of [:B,C:]
the carrier of [:B,C:] is non empty set
Obj (A,B,C,c₄,o1) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
[: the carrier of A, the carrier of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier of [:B,C:]:] is non empty set
(Obj (A,B,C,c₄,o1)) . o2 is Element of the carrier of [:B,C:]
c₄ . o2 is Element of the carrier of B
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj c₄) . o2 is Element of the carrier of B
o1 . o2 is Element of the carrier of C
Obj o1 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
[: the carrier of A, the carrier of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier of C:] is non empty set
(Obj o1) . o2 is Element of the carrier of C
[(c₄ . o2),(o1 . o2)] is Element of the carrier of [:B,C:]
{(c₄ . o2),(o1 . o2)} is non empty set
{(c₄ . o2)} is non empty set
{{(c₄ . o2),(o1 . o2)},{(c₄ . o2)}} is non empty set
id o2 is Morphism of o2,o2
(A,B,C,c₄,o1) . (id o2) is Element of the carrier' of [:B,C:]
c₄ . (id o2) is Element of the carrier' of B
o1 . (id o2) is Element of the carrier' of C
[(c₄ . (id o2)),(o1 . (id o2))] is Element of the carrier' of [:B,C:]
{(c₄ . (id o2)),(o1 . (id o2))} is non empty set
{(c₄ . (id o2))} is non empty set
{{(c₄ . (id o2)),(o1 . (id o2))},{(c₄ . (id o2))}} is non empty set
id (c₄ . o2) is Morphism of c₄ . o2,c₄ . o2
[(id (c₄ . o2)),(o1 . (id o2))] is Element of the carrier' of [:B,C:]
{(id (c₄ . o2)),(o1 . (id o2))} is non empty set
{(id (c₄ . o2))} is non empty set
{{(id (c₄ . o2)),(o1 . (id o2))},{(id (c₄ . o2))}} is non empty set
id (o1 . o2) is Morphism of o1 . o2,o1 . o2
[(id (c₄ . o2)),(id (o1 . o2))] is Element of the carrier' of [:B,C:]
{(id (c₄ . o2)),(id (o1 . o2))} is non empty set
{{(id (c₄ . o2)),(id (o1 . o2))},{(id (c₄ . o2))}} is non empty set
id [(c₄ . o2),(o1 . o2)] is Morphism of [(c₄ . o2),(o1 . o2)],[(c₄ . o2),(o1 . o2)]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty 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 B, the carrier' of C:] is non empty Relation-like set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier' of [:B,C:] is non empty set
(A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total transformation of c₄,o1
t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total transformation of o2,G1
<:G2,t:> is non empty Relation-like the carrier of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:]
[: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty set
F1 is Element of the carrier of A
<:G2,t:> . F1 is Element of [: the carrier' of B, the carrier' of C:]
(A,B,C,c₄,o2) . F1 is Element of the carrier of [:B,C:]
the carrier of [:B,C:] is non empty set
Obj (A,B,C,c₄,o2) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
[: the carrier of A, the carrier of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier of [:B,C:]:] is non empty set
(Obj (A,B,C,c₄,o2)) . F1 is Element of the carrier of [:B,C:]
(A,B,C,o1,G1) . F1 is Element of the carrier of [:B,C:]
Obj (A,B,C,o1,G1) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
(Obj (A,B,C,o1,G1)) . F1 is Element of the carrier of [:B,C:]
Hom (((A,B,C,c₄,o2) . F1),((A,B,C,o1,G1) . F1)) is Element of bool the carrier' of [:B,C:]
bool the carrier' of [:B,C:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:B,C:] : ( dom b₁ = (A,B,C,c₄,o2) . F1 & cod b₁ = (A,B,C,o1,G1) . F1 ) } is set
G2 . F1 is Morphism of c₄ . F1,o1 . F1
c₄ . F1 is Element of the carrier of B
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj c₄) . F1 is Element of the carrier of B
o1 . F1 is Element of the carrier of B
Obj o1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj o1) . F1 is Element of the carrier of B
Hom ((c₄ . F1),(o1 . F1)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = c₄ . F1 & cod b₁ = o1 . F1 ) } is set
t . F1 is Morphism of o2 . F1,G1 . F1
o2 . F1 is Element of the carrier of C
Obj o2 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
[: the carrier of A, the carrier of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier of C:] is non empty set
(Obj o2) . F1 is Element of the carrier of C
G1 . F1 is Element of the carrier of C
Obj G1 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
(Obj G1) . F1 is Element of the carrier of C
Hom ((o2 . F1),(G1 . F1)) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o2 . F1 & cod b₁ = G1 . F1 ) } is set
[(c₄ . F1),(o2 . F1)] is Element of the carrier of [:B,C:]
{(c₄ . F1),(o2 . F1)} is non empty set
{(c₄ . F1)} is non empty set
{{(c₄ . F1),(o2 . F1)},{(c₄ . F1)}} is non empty set
[(o1 . F1),(G1 . F1)] is Element of the carrier of [:B,C:]
{(o1 . F1),(G1 . F1)} is non empty set
{(o1 . F1)} is non empty set
{{(o1 . F1),(G1 . F1)},{(o1 . F1)}} is non empty set
[(G2 . F1),(t . F1)] is Element of the carrier' of [:B,C:]
{(G2 . F1),(t . F1)} is non empty set
{(G2 . F1)} is non empty set
{{(G2 . F1),(t . F1)},{(G2 . F1)}} is non empty set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier' of [:B,C:] is non empty set
(A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier of A is non empty set
G2 is Element of the carrier of A
(A,B,C,c₄,o2) . G2 is Element of the carrier of [:B,C:]
the carrier of [:B,C:] is non empty set
Obj (A,B,C,c₄,o2) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
[: the carrier of A, the carrier of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier of [:B,C:]:] is non empty set
(Obj (A,B,C,c₄,o2)) . G2 is Element of the carrier of [:B,C:]
(A,B,C,o1,G1) . G2 is Element of the carrier of [:B,C:]
Obj (A,B,C,o1,G1) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
(Obj (A,B,C,o1,G1)) . G2 is Element of the carrier of [:B,C:]
Hom (((A,B,C,c₄,o2) . G2),((A,B,C,o1,G1) . G2)) is Element of bool the carrier' of [:B,C:]
bool the carrier' of [:B,C:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:B,C:] : ( dom b₁ = (A,B,C,c₄,o2) . G2 & cod b₁ = (A,B,C,o1,G1) . G2 ) } is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
the carrier of A is non empty set
G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total transformation of c₄,o1
t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total transformation of o2,G1
<:G2,t:> is non empty Relation-like the carrier of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:]
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
[: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
(A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[: the carrier of A, the carrier' of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of [:B,C:]:] is non empty set
F1 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of [:B,C:]:]
F2 is Element of the carrier of A
F1 . F2 is Element of the carrier' of [:B,C:]
(A,B,C,c₄,o2) . F2 is Element of the carrier of [:B,C:]
the carrier of [:B,C:] is non empty set
Obj (A,B,C,c₄,o2) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
[: the carrier of A, the carrier of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier of [:B,C:]:] is non empty set
(Obj (A,B,C,c₄,o2)) . F2 is Element of the carrier of [:B,C:]
(A,B,C,o1,G1) . F2 is Element of the carrier of [:B,C:]
Obj (A,B,C,o1,G1) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
(Obj (A,B,C,o1,G1)) . F2 is Element of the carrier of [:B,C:]
Hom (((A,B,C,c₄,o2) . F2),((A,B,C,o1,G1) . F2)) is Element of bool the carrier' of [:B,C:]
bool the carrier' of [:B,C:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:B,C:] : ( dom b₁ = (A,B,C,c₄,o2) . F2 & cod b₁ = (A,B,C,o1,G1) . F2 ) } is set
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier' of [:B,C:] is non empty set
(A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total transformation of c₄,o1
t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total transformation of o2,G1
(A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total transformation of (A,B,C,c₄,o2),(A,B,C,o1,G1)
F1 is Element of the carrier of A
(A,B,C,c₄,o1,o2,G1,G2,t) . F1 is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F1
(A,B,C,c₄,o2) . F1 is Element of the carrier of [:B,C:]
the carrier of [:B,C:] is non empty set
Obj (A,B,C,c₄,o2) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
[: the carrier of A, the carrier of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier of [:B,C:]:] is non empty set
(Obj (A,B,C,c₄,o2)) . F1 is Element of the carrier of [:B,C:]
(A,B,C,o1,G1) . F1 is Element of the carrier of [:B,C:]
Obj (A,B,C,o1,G1) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
(Obj (A,B,C,o1,G1)) . F1 is Element of the carrier of [:B,C:]
G2 . F1 is Morphism of c₄ . F1,o1 . F1
c₄ . F1 is Element of the carrier of B
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj c₄) . F1 is Element of the carrier of B
o1 . F1 is Element of the carrier of B
Obj o1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj o1) . F1 is Element of the carrier of B
t . F1 is Morphism of o2 . F1,G1 . F1
o2 . F1 is Element of the carrier of C
Obj o2 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
[: the carrier of A, the carrier of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier of C:] is non empty set
(Obj o2) . F1 is Element of the carrier of C
G1 . F1 is Element of the carrier of C
Obj G1 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
(Obj G1) . F1 is Element of the carrier of C
[(G2 . F1),(t . F1)] is Element of the carrier' of [:B,C:]
{(G2 . F1),(t . F1)} is non empty set
{(G2 . F1)} is non empty set
{{(G2 . F1),(t . F1)},{(G2 . F1)}} is non empty set
[: the carrier of A, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of B:] is non empty set
[: the carrier of A, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of C:] is non empty set
(A,B,C,c₄,o1,o2,G1,G2,t) . F1 is Element of the carrier' of [:B,C:]
F2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of B:]
s is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of C:]
<:F2,s:> is non empty Relation-like the carrier of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:]
[: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty set
<:F2,s:> . F1 is Element of [: the carrier' of B, the carrier' of C:]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier' of [:B,C:] is non empty set
(A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1
t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1
(A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total transformation of (A,B,C,c₄,o2),(A,B,C,o1,G1)
F1 is Element of the carrier of A
F2 is Element of the carrier of A
Hom (F1,F2) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 & cod b₁ = F2 ) } is set
(A,B,C,c₄,o2) . F1 is Element of the carrier of [:B,C:]
the carrier of [:B,C:] is non empty set
Obj (A,B,C,c₄,o2) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
[: the carrier of A, the carrier of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier of [:B,C:]:] is non empty set
(Obj (A,B,C,c₄,o2)) . F1 is Element of the carrier of [:B,C:]
(A,B,C,c₄,o2) . F2 is Element of the carrier of [:B,C:]
(Obj (A,B,C,c₄,o2)) . F2 is Element of the carrier of [:B,C:]
(A,B,C,o1,G1) . F2 is Element of the carrier of [:B,C:]
Obj (A,B,C,o1,G1) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
(Obj (A,B,C,o1,G1)) . F2 is Element of the carrier of [:B,C:]
(A,B,C,c₄,o1,o2,G1,G2,t) . F2 is Morphism of (A,B,C,c₄,o2) . F2,(A,B,C,o1,G1) . F2
(A,B,C,o1,G1) . F1 is Element of the carrier of [:B,C:]
(Obj (A,B,C,o1,G1)) . F1 is Element of the carrier of [:B,C:]
(A,B,C,c₄,o1,o2,G1,G2,t) . F1 is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F1
c₄ . F1 is Element of the carrier of B
Obj c₄ is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj c₄) . F1 is Element of the carrier of B
c₄ . F2 is Element of the carrier of B
(Obj c₄) . F2 is Element of the carrier of B
Hom ((c₄ . F1),(c₄ . F2)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = c₄ . F1 & cod b₁ = c₄ . F2 ) } is set
s is Morphism of F1,F2
(A,B,C,c₄,o2) /. s is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,c₄,o2) . F2
((A,B,C,c₄,o1,o2,G1,G2,t) . F2) * ((A,B,C,c₄,o2) /. s) is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F2
(A,B,C,o1,G1) /. s is Morphism of (A,B,C,o1,G1) . F1,(A,B,C,o1,G1) . F2
((A,B,C,o1,G1) /. s) * ((A,B,C,c₄,o1,o2,G1,G2,t) . F1) is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F2
o1 . F2 is Element of the carrier of B
Obj o1 is non empty Relation-like the carrier of A -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj o1) . F2 is Element of the carrier of B
c₄ /. s is Morphism of c₄ . F1,c₄ . F2
G2 . F2 is Morphism of c₄ . F2,o1 . F2
(G2 . F2) * (c₄ /. s) is Morphism of c₄ . F1,o1 . F2
o1 . F1 is Element of the carrier of B
(Obj o1) . F1 is Element of the carrier of B
G2 . F1 is Morphism of c₄ . F1,o1 . F1
o1 /. s is Morphism of o1 . F1,o1 . F2
(o1 /. s) * (G2 . F1) is Morphism of c₄ . F1,o1 . F2
o2 . F1 is Element of the carrier of C
Obj o2 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
[: the carrier of A, the carrier of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier of C:] is non empty set
(Obj o2) . F1 is Element of the carrier of C
o2 . F2 is Element of the carrier of C
(Obj o2) . F2 is Element of the carrier of C
G1 . F2 is Element of the carrier of C
Obj G1 is non empty Relation-like the carrier of A -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of C:]
(Obj G1) . F2 is Element of the carrier of C
o2 /. s is Morphism of o2 . F1,o2 . F2
t . F2 is Morphism of o2 . F2,G1 . F2
(t . F2) * (o2 /. s) is Morphism of o2 . F1,G1 . F2
G1 . F1 is Element of the carrier of C
(Obj G1) . F1 is Element of the carrier of C
t . F1 is Morphism of o2 . F1,G1 . F1
G1 /. s is Morphism of G1 . F1,G1 . F2
(G1 /. s) * (t . F1) is Morphism of o2 . F1,G1 . F2
o1 . s is Element of the carrier' of B
G1 . s is Element of the carrier' of C
(A,B,C,o1,G1) . s is Element of the carrier' of [:B,C:]
[(o1 /. s),(G1 /. s)] is Element of the carrier' of [:B,C:]
{(o1 /. s),(G1 /. s)} is non empty set
{(o1 /. s)} is non empty set
{{(o1 /. s),(G1 /. s)},{(o1 /. s)}} is non empty set
c₄ . s is Element of the carrier' of B
o2 . s is Element of the carrier' of C
(A,B,C,c₄,o2) . s is Element of the carrier' of [:B,C:]
[(c₄ /. s),(o2 /. s)] is Element of the carrier' of [:B,C:]
{(c₄ /. s),(o2 /. s)} is non empty set
{(c₄ /. s)} is non empty set
{{(c₄ /. s),(o2 /. s)},{(c₄ /. s)}} is non empty set
Hom ((o2 . F2),(G1 . F2)) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o2 . F2 & cod b₁ = G1 . F2 ) } is set
[(G2 . F2),(t . F2)] is Element of the carrier' of [:B,C:]
{(G2 . F2),(t . F2)} is non empty set
{(G2 . F2)} is non empty set
{{(G2 . F2),(t . F2)},{(G2 . F2)}} is non empty set
[(G2 . F1),(t . F1)] is Element of the carrier' of [:B,C:]
{(G2 . F1),(t . F1)} is non empty set
{(G2 . F1)} is non empty set
{{(G2 . F1),(t . F1)},{(G2 . F1)}} is non empty set
Hom ((G1 . F1),(G1 . F2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = G1 . F1 & cod b₁ = G1 . F2 ) } is set
Hom (((A,B,C,c₄,o2) . F1),((A,B,C,o1,G1) . F1)) is Element of bool the carrier' of [:B,C:]
bool the carrier' of [:B,C:] is non empty set
{ b₁ where b₁ is Element of the carrier' of [:B,C:] : ( dom b₁ = (A,B,C,c₄,o2) . F1 & cod b₁ = (A,B,C,o1,G1) . F1 ) } is set
Hom (((A,B,C,o1,G1) . F1),((A,B,C,o1,G1) . F2)) is Element of bool the carrier' of [:B,C:]
{ b₁ where b₁ is Element of the carrier' of [:B,C:] : ( dom b₁ = (A,B,C,o1,G1) . F1 & cod b₁ = (A,B,C,o1,G1) . F2 ) } is set
Hom ((o1 . F1),(o1 . F2)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = o1 . F1 & cod b₁ = o1 . F2 ) } is set
Hom ((o2 . F1),(o2 . F2)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o2 . F1 & cod b₁ = o2 . F2 ) } is set
(t . F2) (*) (o2 /. s) is Element of the carrier' of C
Hom ((o2 . F1),(G1 . F1)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = o2 . F1 & cod b₁ = G1 . F1 ) } is set
(G1 /. s) (*) (t . F1) is Element of the carrier' of C
cod (t . F1) is Element of the carrier of C
the Target of C . (t . F1) is Element of the carrier of C
dom (G1 /. s) is Element of the carrier of C
the Source of C . (G1 /. s) is Element of the carrier of C
Hom ((c₄ . F2),(o1 . F2)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = c₄ . F2 & cod b₁ = o1 . F2 ) } is set
dom (G2 . F2) is Element of the carrier of B
the Source of B . (G2 . F2) is Element of the carrier of B
cod (c₄ /. s) is Element of the carrier of B
the Target of B . (c₄ /. s) is Element of the carrier of B
Hom ((c₄ . F1),(o1 . F1)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = c₄ . F1 & cod b₁ = o1 . F1 ) } is set
(o1 /. s) (*) (G2 . F1) is Element of the carrier' of B
cod (G2 . F1) is Element of the carrier of B
the Target of B . (G2 . F1) is Element of the carrier of B
dom (o1 /. s) is Element of the carrier of B
the Source of B . (o1 /. s) is Element of the carrier of B
dom (t . F2) is Element of the carrier of C
the Source of C . (t . F2) is Element of the carrier of C
cod (o2 /. s) is Element of the carrier of C
the Target of C . (o2 /. s) is Element of the carrier of C
(G2 . F2) (*) (c₄ /. s) is Element of the carrier' of B
Hom (((A,B,C,c₄,o2) . F2),((A,B,C,o1,G1) . F2)) is Element of bool the carrier' of [:B,C:]
{ b₁ where b₁ is Element of the carrier' of [:B,C:] : ( dom b₁ = (A,B,C,c₄,o2) . F2 & cod b₁ = (A,B,C,o1,G1) . F2 ) } is set
Hom (((A,B,C,c₄,o2) . F1),((A,B,C,c₄,o2) . F2)) is Element of bool the carrier' of [:B,C:]
{ b₁ where b₁ is Element of the carrier' of [:B,C:] : ( dom b₁ = (A,B,C,c₄,o2) . F1 & cod b₁ = (A,B,C,c₄,o2) . F2 ) } is set
((A,B,C,c₄,o1,o2,G1,G2,t) . F2) (*) ((A,B,C,c₄,o2) /. s) is Element of the carrier' of [:B,C:]
[((o1 /. s) * (G2 . F1)),((G1 /. s) * (t . F1))] is Element of the carrier' of [:B,C:]
{((o1 /. s) * (G2 . F1)),((G1 /. s) * (t . F1))} is non empty set
{((o1 /. s) * (G2 . F1))} is non empty set
{{((o1 /. s) * (G2 . F1)),((G1 /. s) * (t . F1))},{((o1 /. s) * (G2 . F1))}} is non empty set
((A,B,C,o1,G1) /. s) (*) ((A,B,C,c₄,o1,o2,G1,G2,t) . F1) is Element of the carrier' of [:B,C:]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier' of [:B,C:] is non empty set
(A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier of A is non empty set
the non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1
the non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1
(A,B,C,c₄,o1,o2,G1, the non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1, the non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1) is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total transformation of (A,B,C,c₄,o2),(A,B,C,o1,G1)
F1 is Element of the carrier of A
F2 is Element of the carrier of A
Hom (F1,F2) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 & cod b₁ = F2 ) } is set
(A,B,C,c₄,o2) . F1 is Element of the carrier of [:B,C:]
the carrier of [:B,C:] is non empty set
Obj (A,B,C,c₄,o2) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
[: the carrier of A, the carrier of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier of [:B,C:]:] is non empty set
(Obj (A,B,C,c₄,o2)) . F1 is Element of the carrier of [:B,C:]
(A,B,C,c₄,o2) . F2 is Element of the carrier of [:B,C:]
(Obj (A,B,C,c₄,o2)) . F2 is Element of the carrier of [:B,C:]
(A,B,C,o1,G1) . F2 is Element of the carrier of [:B,C:]
Obj (A,B,C,o1,G1) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
(Obj (A,B,C,o1,G1)) . F2 is Element of the carrier of [:B,C:]
s is Morphism of F1,F2
(A,B,C,c₄,o2) /. s is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,c₄,o2) . F2
(A,B,C,c₄,o1,o2,G1, the non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1, the non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1) . F2 is Morphism of (A,B,C,c₄,o2) . F2,(A,B,C,o1,G1) . F2
((A,B,C,c₄,o1,o2,G1, the non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1, the non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1) . F2) * ((A,B,C,c₄,o2) /. s) is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F2
(A,B,C,o1,G1) . F1 is Element of the carrier of [:B,C:]
(Obj (A,B,C,o1,G1)) . F1 is Element of the carrier of [:B,C:]
(A,B,C,c₄,o1,o2,G1, the non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1, the non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1) . F1 is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F1
(A,B,C,o1,G1) /. s is Morphism of (A,B,C,o1,G1) . F1,(A,B,C,o1,G1) . F2
((A,B,C,o1,G1) /. s) * ((A,B,C,c₄,o1,o2,G1, the non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1, the non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1) . F1) is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F2
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
the carrier of A is non empty set
G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1
t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1
(A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total transformation of (A,B,C,c₄,o2),(A,B,C,o1,G1)
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
(A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
F1 is Element of the carrier of A
F2 is Element of the carrier of A
Hom (F1,F2) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = F1 & cod b₁ = F2 ) } is set
(A,B,C,c₄,o2) . F1 is Element of the carrier of [:B,C:]
the carrier of [:B,C:] is non empty set
Obj (A,B,C,c₄,o2) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
[: the carrier of A, the carrier of [:B,C:]:] is non empty Relation-like set
bool [: the carrier of A, the carrier of [:B,C:]:] is non empty set
(Obj (A,B,C,c₄,o2)) . F1 is Element of the carrier of [:B,C:]
(A,B,C,c₄,o2) . F2 is Element of the carrier of [:B,C:]
(Obj (A,B,C,c₄,o2)) . F2 is Element of the carrier of [:B,C:]
(A,B,C,o1,G1) . F2 is Element of the carrier of [:B,C:]
Obj (A,B,C,o1,G1) is non empty Relation-like the carrier of A -defined the carrier of [:B,C:] -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier of [:B,C:]:]
(Obj (A,B,C,o1,G1)) . F2 is Element of the carrier of [:B,C:]
s is Morphism of F1,F2
(A,B,C,c₄,o2) /. s is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,c₄,o2) . F2
(A,B,C,c₄,o1,o2,G1,G2,t) . F2 is Morphism of (A,B,C,c₄,o2) . F2,(A,B,C,o1,G1) . F2
((A,B,C,c₄,o1,o2,G1,G2,t) . F2) * ((A,B,C,c₄,o2) /. s) is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F2
(A,B,C,o1,G1) . F1 is Element of the carrier of [:B,C:]
(Obj (A,B,C,o1,G1)) . F1 is Element of the carrier of [:B,C:]
(A,B,C,c₄,o1,o2,G1,G2,t) . F1 is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F1
(A,B,C,o1,G1) /. s is Morphism of (A,B,C,o1,G1) . F1,(A,B,C,o1,G1) . F2
((A,B,C,o1,G1) /. s) * ((A,B,C,c₄,o1,o2,G1,G2,t) . F1) is Morphism of (A,B,C,c₄,o2) . F1,(A,B,C,o1,G1) . F2
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of B is non empty set
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier' of C is non empty set
c₄ is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
o2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
the carrier' of [:B,C:] is non empty set
(A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of c₄,o1
t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of o2,G1
(A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of (A,B,C,c₄,o2),(A,B,C,o1,G1)
(A,B,C,(A,B,C,c₄,o2),(A,B,C,o1,G1),(A,B,C,c₄,o1,o2,G1,G2,t)) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,(A,B,C,c₄,o2)),(A,B,C,(A,B,C,o1,G1))
(A,B,C,(A,B,C,c₄,o2)) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * (A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,(A,B,C,o1,G1)) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * (A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(pr1 (B,C)) * (A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * (A,B,C,c₄,o2),(pr1 (B,C)) * (A,B,C,o1,G1)
(A,B,C,(A,B,C,c₄,o2),(A,B,C,o1,G1),(A,B,C,c₄,o1,o2,G1,G2,t)) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,(A,B,C,c₄,o2)),(A,B,C,(A,B,C,o1,G1))
(A,B,C,(A,B,C,c₄,o2)) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * (A,B,C,c₄,o2) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,(A,B,C,o1,G1)) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * (A,B,C,o1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(pr2 (B,C)) * (A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * (A,B,C,c₄,o2),(pr2 (B,C)) * (A,B,C,o1,G1)
[: the carrier of A, the carrier' of B:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of B:] is non empty set
(pr1 (B,C)) * (A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total transformation of (pr1 (B,C)) * (A,B,C,c₄,o2),(pr1 (B,C)) * (A,B,C,o1,G1)
(pr1 (B,C)) * (A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of B:]
(A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total transformation of (A,B,C,c₄,o2),(A,B,C,o1,G1)
(pr1 (B,C)) * (A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of B:]
F1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of B:]
<:F1,t:> is non empty Relation-like the carrier of A -defined [: the carrier' of B, the carrier' of C:] -valued Function-like total quasi_total Element of bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:]
[: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [: the carrier of A,[: the carrier' of B, the carrier' of C:]:] is non empty set
(pr1 (B,C)) * <:F1,t:> is Relation-like the carrier of A -defined the carrier' of B -valued Function-like Element of bool [: the carrier of A, the carrier' of B:]
(pr1 ( the carrier' of B, the carrier' of C)) * <:F1,t:> is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of B:]
(pr2 (B,C)) * (A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total transformation of (pr2 (B,C)) * (A,B,C,c₄,o2),(pr2 (B,C)) * (A,B,C,o1,G1)
(pr2 (B,C)) * (A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of C:]
[: the carrier of A, the carrier' of C:] is non empty Relation-like set
bool [: the carrier of A, the carrier' of C:] is non empty set
(pr2 (B,C)) * (A,B,C,c₄,o1,o2,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of C:]
(pr2 (B,C)) * <:F1,t:> is Relation-like the carrier of A -defined the carrier' of C -valued Function-like Element of bool [: the carrier of A, the carrier' of C:]
(pr2 ( the carrier' of B, the carrier' of C)) * <:F1,t:> is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total Element of bool [: the carrier of A, the carrier' of C:]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the carrier' of B is non empty set
the carrier' of C is non empty set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
Functors (A,[:B,C:]) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
the carrier' of (Functors (A,[:B,C:])) is non empty set
Functors (A,B) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
[:(Functors (A,B)),(Functors (A,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of (Functors (A,B)) is non empty set
the carrier of (Functors (A,C)) is non empty set
[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] is non empty Relation-like set
the carrier' of (Functors (A,B)) is non empty set
the carrier' of (Functors (A,C)) is non empty set
[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] is non empty Relation-like set
the Source of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
[: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty set
the Source of (Functors (A,C)) is non empty Relation-like the carrier' of (Functors (A,C)) -defined the carrier of (Functors (A,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):]
[: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):] is non empty set
[: the Source of (Functors (A,B)), the Source of (Functors (A,C)):] is non empty Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -defined [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:] is non empty set
the Target of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
the Target of (Functors (A,C)) is non empty Relation-like the carrier' of (Functors (A,C)) -defined the carrier of (Functors (A,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):]
[: the Target of (Functors (A,B)), the Target of (Functors (A,C)):] is non empty Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -defined [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:]
the Comp of (Functors (A,B)) is Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] -defined the carrier' of (Functors (A,B)) -valued Function-like Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):]
[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] is non empty Relation-like set
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):] is non empty set
the Comp of (Functors (A,C)) is Relation-like [: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):] -defined the carrier' of (Functors (A,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):]
[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):] is non empty Relation-like set
[:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):] is non empty set
K209( the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)), the Comp of (Functors (A,B)), the Comp of (Functors (A,C))) is Relation-like [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] -defined [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the Source of (Functors (A,B)), the Source of (Functors (A,C)):],[: the Target of (Functors (A,B)), the Target of (Functors (A,C)):],K209( the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)), the Comp of (Functors (A,B)), the Comp of (Functors (A,C))) #) is strict CatStr
the carrier' of [:(Functors (A,B)),(Functors (A,C)):] is non empty set
the carrier' of A is non empty set
the carrier' of [:B,C:] is non empty set
the carrier of A is non empty set
c₄ is Element of the carrier' of (Functors (A,[:B,C:]))
dom c₄ is Element of the carrier of (Functors (A,[:B,C:]))
the carrier of (Functors (A,[:B,C:])) is non empty set
the Source of (Functors (A,[:B,C:])) is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier of (Functors (A,[:B,C:])) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):]
[: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):] is non empty set
the Source of (Functors (A,[:B,C:])) . c₄ is Element of the carrier of (Functors (A,[:B,C:]))
cod c₄ is Element of the carrier of (Functors (A,[:B,C:]))
the Target of (Functors (A,[:B,C:])) is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier of (Functors (A,[:B,C:])) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):]
the Target of (Functors (A,[:B,C:])) . c₄ is Element of the carrier of (Functors (A,[:B,C:]))
o1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
o2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[o1,o2] is set
{o1,o2} is non empty set
{o1} is non empty set
{{o1,o2},{o1}} is non empty set
G1 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of o1,o2
[[o1,o2],G1] is set
{[o1,o2],G1} is non empty set
{[o1,o2]} is non empty Relation-like set
{{[o1,o2],G1},{[o1,o2]}} is non empty set
NatTrans (A,C) is non empty NatTrans-DOMAIN of A,C
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[(A,B,C,o1),(A,B,C,o2)] is set
{(A,B,C,o1),(A,B,C,o2)} is non empty set
{(A,B,C,o1)} is non empty set
{{(A,B,C,o1),(A,B,C,o2)},{(A,B,C,o1)}} is non empty set
(A,B,C,o1,o2,G1) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,o1),(A,B,C,o2)
(pr2 (B,C)) * G1 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * o1,(pr2 (B,C)) * o2
[[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)] is set
{[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)} is non empty set
{[(A,B,C,o1),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)},{[(A,B,C,o1),(A,B,C,o2)]}} is non empty set
NatTrans (A,B) is non empty NatTrans-DOMAIN of A,B
(A,B,C,o1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * o1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
[(A,B,C,o1),(A,B,C,o2)] is set
{(A,B,C,o1),(A,B,C,o2)} is non empty set
{(A,B,C,o1)} is non empty set
{{(A,B,C,o1),(A,B,C,o2)},{(A,B,C,o1)}} is non empty set
(A,B,C,o1,o2,G1) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,o1),(A,B,C,o2)
(pr1 (B,C)) * G1 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * o1,(pr1 (B,C)) * o2
[[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)] is set
{[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)} is non empty set
{[(A,B,C,o1),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o1),(A,B,C,o2)],(A,B,C,o1,o2,G1)},{[(A,B,C,o1),(A,B,C,o2)]}} is non empty set
t is Element of the carrier' of (Functors (A,B))
G2 is Element of the carrier' of (Functors (A,C))
[t,G2] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{t,G2} is non empty set
{t} is non empty set
{{t,G2},{t}} is non empty set
F1 is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
F2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
s is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[F2,s] is set
{F2,s} is non empty set
{F2} is non empty set
{{F2,s},{F2}} is non empty set
(A,B,C,F2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * F2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,s) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * s is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
[(A,B,C,F2),(A,B,C,s)] is set
{(A,B,C,F2),(A,B,C,s)} is non empty set
{(A,B,C,F2)} is non empty set
{{(A,B,C,F2),(A,B,C,s)},{(A,B,C,F2)}} is non empty set
(A,B,C,F2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * F2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,s) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * s is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[(A,B,C,F2),(A,B,C,s)] is set
{(A,B,C,F2),(A,B,C,s)} is non empty set
{(A,B,C,F2)} is non empty set
{{(A,B,C,F2),(A,B,C,s)},{(A,B,C,F2)}} is non empty set
f is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of F2,s
[[F2,s],f] is set
{[F2,s],f} is non empty set
{[F2,s]} is non empty Relation-like set
{{[F2,s],f},{[F2,s]}} is non empty set
(A,B,C,F2,s,f) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,F2),(A,B,C,s)
(pr1 (B,C)) * f is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * F2,(pr1 (B,C)) * s
[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)] is set
{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)} is non empty set
{[(A,B,C,F2),(A,B,C,s)]} is non empty Relation-like set
{{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)},{[(A,B,C,F2),(A,B,C,s)]}} is non empty set
(A,B,C,F2,s,f) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,F2),(A,B,C,s)
(pr2 (B,C)) * f is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * F2,(pr2 (B,C)) * s
[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)] is set
{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)} is non empty set
{[(A,B,C,F2),(A,B,C,s)]} is non empty Relation-like set
{{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)},{[(A,B,C,F2),(A,B,C,s)]}} is non empty set
[[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)],[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]] is set
{[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)],[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]} is non empty Relation-like set
{[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]} is non empty Relation-like set
{{[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)],[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]},{[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]}} is non empty set
[: the carrier' of (Functors (A,[:B,C:])), the carrier' of [:(Functors (A,B)),(Functors (A,C)):]:] is non empty Relation-like set
bool [: the carrier' of (Functors (A,[:B,C:])), the carrier' of [:(Functors (A,B)),(Functors (A,C)):]:] is non empty set
c₄ is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier' of [:(Functors (A,B)),(Functors (A,C)):] -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,[:B,C:])), the carrier' of [:(Functors (A,B)),(Functors (A,C)):]:]
the carrier of [:(Functors (A,B)),(Functors (A,C)):] is non empty set
o1 is Element of the carrier of (Functors (A,[:B,C:]))
id o1 is Morphism of o1,o1
c₄ . (id o1) is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
o2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
G2 is Element of the carrier of (Functors (A,B))
G1 is Element of the carrier of (Functors (A,C))
[G2,G1] is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
{G2,G1} is non empty set
{G2} is non empty set
{{G2,G1},{G2}} is non empty set
id [G2,G1] is Morphism of [G2,G1],[G2,G1]
id o2 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of o2,o2
(A,B,C,o2,o2,(id o2)) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
(pr1 (B,C)) * (id o2) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * o2,(pr1 (B,C)) * o2
id (A,B,C,o2) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
id G2 is Morphism of G2,G2
[(A,B,C,o2),(A,B,C,o2)] is set
{(A,B,C,o2),(A,B,C,o2)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,o2)},{(A,B,C,o2)}} is non empty set
[[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))] is set
{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))} is non empty set
{[(A,B,C,o2),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))},{[(A,B,C,o2),(A,B,C,o2)]}} is non empty set
(A,B,C,o2,o2,(id o2)) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
(pr2 (B,C)) * (id o2) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * o2,(pr2 (B,C)) * o2
id (A,B,C,o2) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
id G1 is Morphism of G1,G1
[(A,B,C,o2),(A,B,C,o2)] is set
{(A,B,C,o2),(A,B,C,o2)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,o2)},{(A,B,C,o2)}} is non empty set
[[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))] is set
{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))} is non empty set
{[(A,B,C,o2),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))},{[(A,B,C,o2),(A,B,C,o2)]}} is non empty set
[o2,o2] is set
{o2,o2} is non empty set
{o2} is non empty set
{{o2,o2},{o2}} is non empty set
[[o2,o2],(id o2)] is set
{[o2,o2],(id o2)} is non empty set
{[o2,o2]} is non empty Relation-like set
{{[o2,o2],(id o2)},{[o2,o2]}} is non empty set
[(id G2),(id G1)] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{(id G2),(id G1)} is non empty set
{(id G2)} is non empty set
{{(id G2),(id G1)},{(id G2)}} is non empty set
o1 is Element of the carrier' of (Functors (A,[:B,C:]))
dom o1 is Element of the carrier of (Functors (A,[:B,C:]))
the Source of (Functors (A,[:B,C:])) . o1 is Element of the carrier of (Functors (A,[:B,C:]))
id (dom o1) is Morphism of dom o1, dom o1
c₄ . (id (dom o1)) is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
c₄ . o1 is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
dom (c₄ . o1) is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
the Source of [:(Functors (A,B)),(Functors (A,C)):] is non empty Relation-like the carrier' of [:(Functors (A,B)),(Functors (A,C)):] -defined the carrier of [:(Functors (A,B)),(Functors (A,C)):] -valued Function-like total quasi_total Element of bool [: the carrier' of [:(Functors (A,B)),(Functors (A,C)):], the carrier of [:(Functors (A,B)),(Functors (A,C)):]:]
[: the carrier' of [:(Functors (A,B)),(Functors (A,C)):], the carrier of [:(Functors (A,B)),(Functors (A,C)):]:] is non empty Relation-like set
bool [: the carrier' of [:(Functors (A,B)),(Functors (A,C)):], the carrier of [:(Functors (A,B)),(Functors (A,C)):]:] is non empty set
the Source of [:(Functors (A,B)),(Functors (A,C)):] . (c₄ . o1) is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
id (dom (c₄ . o1)) is Morphism of dom (c₄ . o1), dom (c₄ . o1)
cod o1 is Element of the carrier of (Functors (A,[:B,C:]))
the Target of (Functors (A,[:B,C:])) . o1 is Element of the carrier of (Functors (A,[:B,C:]))
id (cod o1) is Morphism of cod o1, cod o1
c₄ . (id (cod o1)) is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
cod (c₄ . o1) is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
the Target of [:(Functors (A,B)),(Functors (A,C)):] is non empty Relation-like the carrier' of [:(Functors (A,B)),(Functors (A,C)):] -defined the carrier of [:(Functors (A,B)),(Functors (A,C)):] -valued Function-like total quasi_total Element of bool [: the carrier' of [:(Functors (A,B)),(Functors (A,C)):], the carrier of [:(Functors (A,B)),(Functors (A,C)):]:]
the Target of [:(Functors (A,B)),(Functors (A,C)):] . (c₄ . o1) is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
id (cod (c₄ . o1)) is Morphism of cod (c₄ . o1), cod (c₄ . o1)
o2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[o2,G1] is set
{o2,G1} is non empty set
{o2} is non empty set
{{o2,G1},{o2}} is non empty set
G2 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of o2,G1
[[o2,G1],G2] is set
{[o2,G1],G2} is non empty set
{[o2,G1]} is non empty Relation-like set
{{[o2,G1],G2},{[o2,G1]}} is non empty set
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
[(A,B,C,o2),(A,B,C,G1)] is set
{(A,B,C,o2),(A,B,C,G1)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,G1)},{(A,B,C,o2)}} is non empty set
(A,B,C,o2,G1,G2) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,G1)
(pr1 (B,C)) * G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * o2,(pr1 (B,C)) * G1
[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)] is set
{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)} is non empty set
{[(A,B,C,o2),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)},{[(A,B,C,o2),(A,B,C,G1)]}} is non empty set
t is Element of the carrier' of (Functors (A,B))
dom t is Element of the carrier of (Functors (A,B))
the Source of (Functors (A,B)) . t is Element of the carrier of (Functors (A,B))
id o2 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of o2,o2
(A,B,C,o2,o2,(id o2)) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
(pr1 (B,C)) * (id o2) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * o2,(pr1 (B,C)) * o2
id (A,B,C,o2) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
id (dom t) is Morphism of dom t, dom t
[(A,B,C,o2),(A,B,C,o2)] is set
{(A,B,C,o2),(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,o2)},{(A,B,C,o2)}} is non empty set
[[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))] is set
{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))} is non empty set
{[(A,B,C,o2),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))},{[(A,B,C,o2),(A,B,C,o2)]}} is non empty set
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[(A,B,C,o2),(A,B,C,G1)] is set
{(A,B,C,o2),(A,B,C,G1)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,G1)},{(A,B,C,o2)}} is non empty set
(A,B,C,o2,G1,G2) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,G1)
(pr2 (B,C)) * G2 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * o2,(pr2 (B,C)) * G1
[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)] is set
{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)} is non empty set
{[(A,B,C,o2),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)},{[(A,B,C,o2),(A,B,C,G1)]}} is non empty set
F1 is Element of the carrier' of (Functors (A,C))
dom F1 is Element of the carrier of (Functors (A,C))
the Source of (Functors (A,C)) . F1 is Element of the carrier of (Functors (A,C))
(A,B,C,o2,o2,(id o2)) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
(pr2 (B,C)) * (id o2) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * o2,(pr2 (B,C)) * o2
id (A,B,C,o2) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,o2)
id (dom F1) is Morphism of dom F1, dom F1
[(A,B,C,o2),(A,B,C,o2)] is set
{(A,B,C,o2),(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,o2)},{(A,B,C,o2)}} is non empty set
[[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))] is set
{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))} is non empty set
{[(A,B,C,o2),(A,B,C,o2)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,o2)],(A,B,C,o2,o2,(id o2))},{[(A,B,C,o2),(A,B,C,o2)]}} is non empty set
[o2,o2] is set
{o2,o2} is non empty set
{{o2,o2},{o2}} is non empty set
[[o2,o2],(id o2)] is set
{[o2,o2],(id o2)} is non empty set
{[o2,o2]} is non empty Relation-like set
{{[o2,o2],(id o2)},{[o2,o2]}} is non empty set
[(id (dom t)),(id (dom F1))] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{(id (dom t)),(id (dom F1))} is non empty set
{(id (dom t))} is non empty set
{{(id (dom t)),(id (dom F1))},{(id (dom t))}} is non empty set
[(dom t),(dom F1)] is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
{(dom t),(dom F1)} is non empty set
{(dom t)} is non empty set
{{(dom t),(dom F1)},{(dom t)}} is non empty set
id [(dom t),(dom F1)] is Morphism of [(dom t),(dom F1)],[(dom t),(dom F1)]
[t,F1] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{t,F1} is non empty set
{t} is non empty set
{{t,F1},{t}} is non empty set
dom [t,F1] is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
the Source of [:(Functors (A,B)),(Functors (A,C)):] . [t,F1] is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
id (dom [t,F1]) is Morphism of dom [t,F1], dom [t,F1]
cod t is Element of the carrier of (Functors (A,B))
the Target of (Functors (A,B)) . t is Element of the carrier of (Functors (A,B))
id G1 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of G1,G1
(A,B,C,G1,G1,(id G1)) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G1)
(pr1 (B,C)) * (id G1) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * G1,(pr1 (B,C)) * G1
id (A,B,C,G1) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G1)
id (cod t) is Morphism of cod t, cod t
[(A,B,C,G1),(A,B,C,G1)] is set
{(A,B,C,G1),(A,B,C,G1)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G1)},{(A,B,C,G1)}} is non empty set
[[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))] is set
{[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))} is non empty set
{[(A,B,C,G1),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))},{[(A,B,C,G1),(A,B,C,G1)]}} is non empty set
cod F1 is Element of the carrier of (Functors (A,C))
the Target of (Functors (A,C)) . F1 is Element of the carrier of (Functors (A,C))
(A,B,C,G1,G1,(id G1)) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G1)
(pr2 (B,C)) * (id G1) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * G1,(pr2 (B,C)) * G1
id (A,B,C,G1) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G1)
id (cod F1) is Morphism of cod F1, cod F1
[(A,B,C,G1),(A,B,C,G1)] is set
{(A,B,C,G1),(A,B,C,G1)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G1)},{(A,B,C,G1)}} is non empty set
[[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))] is set
{[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))} is non empty set
{[(A,B,C,G1),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G1)],(A,B,C,G1,G1,(id G1))},{[(A,B,C,G1),(A,B,C,G1)]}} is non empty set
[G1,G1] is set
{G1,G1} is non empty set
{G1} is non empty set
{{G1,G1},{G1}} is non empty set
[[G1,G1],(id G1)] is set
{[G1,G1],(id G1)} is non empty set
{[G1,G1]} is non empty Relation-like set
{{[G1,G1],(id G1)},{[G1,G1]}} is non empty set
[(id (cod t)),(id (cod F1))] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{(id (cod t)),(id (cod F1))} is non empty set
{(id (cod t))} is non empty set
{{(id (cod t)),(id (cod F1))},{(id (cod t))}} is non empty set
[(cod t),(cod F1)] is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
{(cod t),(cod F1)} is non empty set
{(cod t)} is non empty set
{{(cod t),(cod F1)},{(cod t)}} is non empty set
id [(cod t),(cod F1)] is Morphism of [(cod t),(cod F1)],[(cod t),(cod F1)]
cod [t,F1] is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
the Target of [:(Functors (A,B)),(Functors (A,C)):] . [t,F1] is Element of the carrier of [:(Functors (A,B)),(Functors (A,C)):]
id (cod [t,F1]) is Morphism of cod [t,F1], cod [t,F1]
o2 is Element of the carrier' of (Functors (A,[:B,C:]))
dom o2 is Element of the carrier of (Functors (A,[:B,C:]))
the Source of (Functors (A,[:B,C:])) . o2 is Element of the carrier of (Functors (A,[:B,C:]))
o1 is Element of the carrier' of (Functors (A,[:B,C:]))
cod o1 is Element of the carrier of (Functors (A,[:B,C:]))
the Target of (Functors (A,[:B,C:])) . o1 is Element of the carrier of (Functors (A,[:B,C:]))
o2 (*) o1 is Element of the carrier' of (Functors (A,[:B,C:]))
c₄ . (o2 (*) o1) is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
c₄ . o1 is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
c₄ . o2 is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
(c₄ . o2) (*) (c₄ . o1) is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
dom o1 is Element of the carrier of (Functors (A,[:B,C:]))
the Source of (Functors (A,[:B,C:])) . o1 is Element of the carrier of (Functors (A,[:B,C:]))
G1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
cod o2 is Element of the carrier of (Functors (A,[:B,C:]))
the Target of (Functors (A,[:B,C:])) . o2 is Element of the carrier of (Functors (A,[:B,C:]))
F1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
F2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
s is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of F1,F2
[[F1,F2],s] is set
{[F1,F2],s} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],s},{[F1,F2]}} is non empty set
[G1,F2] is set
{G1,F2} is non empty set
{{G1,F2},{G1}} is non empty set
f is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of G2,F2
f `*` t is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of G1,F2
[[G1,F2],(f `*` t)] is set
{[G1,F2],(f `*` t)} is non empty set
{[G1,F2]} is non empty Relation-like set
{{[G1,F2],(f `*` t)},{[G1,F2]}} is non empty set
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * G2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,F2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * F2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[(A,B,C,G2),(A,B,C,F2)] is set
{(A,B,C,G2),(A,B,C,F2)} is non empty set
{(A,B,C,G2)} is non empty set
{{(A,B,C,G2),(A,B,C,F2)},{(A,B,C,G2)}} is non empty set
(A,B,C,G2,F2,f) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,G2),(A,B,C,F2)
(pr2 (B,C)) * f is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * G2,(pr2 (B,C)) * F2
[[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)] is set
{[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)} is non empty set
{[(A,B,C,G2),(A,B,C,F2)]} is non empty Relation-like set
{{[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)},{[(A,B,C,G2),(A,B,C,F2)]}} is non empty set
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
(pr2 (B,C)) * t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * G1,(pr2 (B,C)) * G2
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
f2 is Element of the carrier' of (Functors (A,C))
f is Element of the carrier' of (Functors (A,C))
f (*) f2 is Element of the carrier' of (Functors (A,C))
[(A,B,C,G1),(A,B,C,F2)] is set
{(A,B,C,G1),(A,B,C,F2)} is non empty set
{{(A,B,C,G1),(A,B,C,F2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,F2)
[[(A,B,C,G1),(A,B,C,F2)],((A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t))] is set
{[(A,B,C,G1),(A,B,C,F2)],((A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t))} is non empty set
{[(A,B,C,G1),(A,B,C,F2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,F2)],((A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t))},{[(A,B,C,G1),(A,B,C,F2)]}} is non empty set
(A,B,C,G1,F2,(f `*` t)) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,F2)
(pr2 (B,C)) * (f `*` t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * G1,(pr2 (B,C)) * F2
[[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))] is set
{[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))} is non empty set
{{[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))},{[(A,B,C,G1),(A,B,C,F2)]}} is non empty set
dom f is Element of the carrier of (Functors (A,C))
the Source of (Functors (A,C)) . f is Element of the carrier of (Functors (A,C))
cod f2 is Element of the carrier of (Functors (A,C))
the Target of (Functors (A,C)) . f2 is Element of the carrier of (Functors (A,C))
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * G2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,F2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * F2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
[(A,B,C,G2),(A,B,C,F2)] is set
{(A,B,C,G2),(A,B,C,F2)} is non empty set
{(A,B,C,G2)} is non empty set
{{(A,B,C,G2),(A,B,C,F2)},{(A,B,C,G2)}} is non empty set
(A,B,C,G2,F2,f) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,G2),(A,B,C,F2)
(pr1 (B,C)) * f is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * G2,(pr1 (B,C)) * F2
[[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)] is set
{[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)} is non empty set
{[(A,B,C,G2),(A,B,C,F2)]} is non empty Relation-like set
{{[(A,B,C,G2),(A,B,C,F2)],(A,B,C,G2,F2,f)},{[(A,B,C,G2),(A,B,C,F2)]}} is non empty set
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
(pr1 (B,C)) * t is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * G1,(pr1 (B,C)) * G2
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
g1 is Element of the carrier' of (Functors (A,B))
dom g1 is Element of the carrier of (Functors (A,B))
the Source of (Functors (A,B)) . g1 is Element of the carrier of (Functors (A,B))
f1 is Element of the carrier' of (Functors (A,B))
cod f1 is Element of the carrier of (Functors (A,B))
the Target of (Functors (A,B)) . f1 is Element of the carrier of (Functors (A,B))
[[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]] is set
{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]} is non empty Relation-like set
{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]} is non empty Relation-like set
{{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]},{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]}} is non empty set
g1 (*) f1 is Element of the carrier' of (Functors (A,B))
[(A,B,C,G1),(A,B,C,F2)] is set
{(A,B,C,G1),(A,B,C,F2)} is non empty set
{{(A,B,C,G1),(A,B,C,F2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,F2)
[[(A,B,C,G1),(A,B,C,F2)],((A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t))] is set
{[(A,B,C,G1),(A,B,C,F2)],((A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t))} is non empty set
{[(A,B,C,G1),(A,B,C,F2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,F2)],((A,B,C,G2,F2,f) `*` (A,B,C,G1,G2,t))},{[(A,B,C,G1),(A,B,C,F2)]}} is non empty set
(A,B,C,G1,F2,(f `*` t)) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,F2)
(pr1 (B,C)) * (f `*` t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * G1,(pr1 (B,C)) * F2
[[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))] is set
{[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))} is non empty set
{{[(A,B,C,G1),(A,B,C,F2)],(A,B,C,G1,F2,(f `*` t))},{[(A,B,C,G1),(A,B,C,F2)]}} is non empty set
[(g1 (*) f1),(f (*) f2)] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{(g1 (*) f1),(f (*) f2)} is non empty set
{(g1 (*) f1)} is non empty set
{{(g1 (*) f1),(f (*) f2)},{(g1 (*) f1)}} is non empty set
[f1,f2] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{f1,f2} is non empty set
{f1} is non empty set
{{f1,f2},{f1}} is non empty set
[g1,f] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{g1,f} is non empty set
{g1} is non empty set
{{g1,f},{g1}} is non empty set
[g1,f] (*) [f1,f2] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
o1 is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier' of [:(Functors (A,B)),(Functors (A,C)):] -valued Function-like total quasi_total Functor of Functors (A,[:B,C:]),[:(Functors (A,B)),(Functors (A,C)):]
o2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[o2,G1] is set
{o2,G1} is non empty set
{o2} is non empty set
{{o2,G1},{o2}} is non empty set
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
[(A,B,C,o2),(A,B,C,G1)] is set
{(A,B,C,o2),(A,B,C,G1)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,G1)},{(A,B,C,o2)}} is non empty set
(A,B,C,o2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * o2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[(A,B,C,o2),(A,B,C,G1)] is set
{(A,B,C,o2),(A,B,C,G1)} is non empty set
{(A,B,C,o2)} is non empty set
{{(A,B,C,o2),(A,B,C,G1)},{(A,B,C,o2)}} is non empty set
G2 is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of o2,G1
[[o2,G1],G2] is set
{[o2,G1],G2} is non empty set
{[o2,G1]} is non empty Relation-like set
{{[o2,G1],G2},{[o2,G1]}} is non empty set
o1 . [[o2,G1],G2] is set
(A,B,C,o2,G1,G2) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,G1)
(pr1 (B,C)) * G2 is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * o2,(pr1 (B,C)) * G1
[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)] is set
{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)} is non empty set
{[(A,B,C,o2),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)},{[(A,B,C,o2),(A,B,C,G1)]}} is non empty set
(A,B,C,o2,G1,G2) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,o2),(A,B,C,G1)
(pr2 (B,C)) * G2 is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * o2,(pr2 (B,C)) * G1
[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)] is set
{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)} is non empty set
{[(A,B,C,o2),(A,B,C,G1)]} is non empty Relation-like set
{{[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)},{[(A,B,C,o2),(A,B,C,G1)]}} is non empty set
[[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)],[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)]] is set
{[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)],[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)]} is non empty Relation-like set
{[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)]} is non empty Relation-like set
{{[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)],[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)]},{[[(A,B,C,o2),(A,B,C,G1)],(A,B,C,o2,G1,G2)]}} is non empty set
NatTrans (A,[:B,C:]) is non empty NatTrans-DOMAIN of A,[:B,C:]
F1 is Element of the carrier' of (Functors (A,[:B,C:]))
o1 . F1 is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
c₄ is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier' of [:(Functors (A,B)),(Functors (A,C)):] -valued Function-like total quasi_total Functor of Functors (A,[:B,C:]),[:(Functors (A,B)),(Functors (A,C)):]
o1 is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier' of [:(Functors (A,B)),(Functors (A,C)):] -valued Function-like total quasi_total Functor of Functors (A,[:B,C:]),[:(Functors (A,B)),(Functors (A,C)):]
o2 is Element of the carrier' of (Functors (A,[:B,C:]))
dom o2 is Element of the carrier of (Functors (A,[:B,C:]))
the carrier of (Functors (A,[:B,C:])) is non empty set
the Source of (Functors (A,[:B,C:])) is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier of (Functors (A,[:B,C:])) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):]
[: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):] is non empty set
the Source of (Functors (A,[:B,C:])) . o2 is Element of the carrier of (Functors (A,[:B,C:]))
cod o2 is Element of the carrier of (Functors (A,[:B,C:]))
the Target of (Functors (A,[:B,C:])) is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier of (Functors (A,[:B,C:])) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):]
the Target of (Functors (A,[:B,C:])) . o2 is Element of the carrier of (Functors (A,[:B,C:]))
G1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
c₄ . o2 is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * G2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
(pr1 (B,C)) * t is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * G1,(pr1 (B,C)) * G2
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * G2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
(pr2 (B,C)) * t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * G1,(pr2 (B,C)) * G2
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
[[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]] is set
{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]} is non empty Relation-like set
{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]} is non empty Relation-like set
{{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]},{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]}} is non empty set
o1 . o2 is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the carrier' of B is non empty set
the carrier' of C is non empty set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
Functors (A,[:B,C:]) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,B) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
[:(Functors (A,B)),(Functors (A,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of (Functors (A,B)) is non empty set
the carrier of (Functors (A,C)) is non empty set
[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] is non empty Relation-like set
the carrier' of (Functors (A,B)) is non empty set
the carrier' of (Functors (A,C)) is non empty set
[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] is non empty Relation-like set
the Source of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
[: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty set
the Source of (Functors (A,C)) is non empty Relation-like the carrier' of (Functors (A,C)) -defined the carrier of (Functors (A,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):]
[: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):] is non empty set
[: the Source of (Functors (A,B)), the Source of (Functors (A,C)):] is non empty Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -defined [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:] is non empty set
the Target of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
the Target of (Functors (A,C)) is non empty Relation-like the carrier' of (Functors (A,C)) -defined the carrier of (Functors (A,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):]
[: the Target of (Functors (A,B)), the Target of (Functors (A,C)):] is non empty Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -defined [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:]
the Comp of (Functors (A,B)) is Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] -defined the carrier' of (Functors (A,B)) -valued Function-like Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):]
[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] is non empty Relation-like set
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):] is non empty set
the Comp of (Functors (A,C)) is Relation-like [: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):] -defined the carrier' of (Functors (A,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):]
[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):] is non empty Relation-like set
[:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):] is non empty set
K209( the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)), the Comp of (Functors (A,B)), the Comp of (Functors (A,C))) is Relation-like [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] -defined [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the Source of (Functors (A,B)), the Source of (Functors (A,C)):],[: the Target of (Functors (A,B)), the Target of (Functors (A,C)):],K209( the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)), the Comp of (Functors (A,B)), the Comp of (Functors (A,C))) #) is strict CatStr
(A,B,C) is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier' of [:(Functors (A,B)),(Functors (A,C)):] -valued Function-like total quasi_total Functor of Functors (A,[:B,C:]),[:(Functors (A,B)),(Functors (A,C)):]
the carrier' of (Functors (A,[:B,C:])) is non empty set
the carrier' of [:(Functors (A,B)),(Functors (A,C)):] is non empty set
c₄ is set
dom (A,B,C) is non empty set
o1 is set
(A,B,C) . c₄ is set
(A,B,C) . o1 is set
dom (A,B,C) is non empty Element of bool the carrier' of (Functors (A,[:B,C:]))
bool the carrier' of (Functors (A,[:B,C:])) is non empty set
the carrier' of A is non empty set
the carrier' of [:B,C:] is non empty set
the carrier of A is non empty set
o2 is Element of the carrier' of (Functors (A,[:B,C:]))
dom o2 is Element of the carrier of (Functors (A,[:B,C:]))
the carrier of (Functors (A,[:B,C:])) is non empty set
the Source of (Functors (A,[:B,C:])) is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier of (Functors (A,[:B,C:])) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):]
[: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):] is non empty set
the Source of (Functors (A,[:B,C:])) . o2 is Element of the carrier of (Functors (A,[:B,C:]))
cod o2 is Element of the carrier of (Functors (A,[:B,C:]))
the Target of (Functors (A,[:B,C:])) is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier of (Functors (A,[:B,C:])) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,[:B,C:])), the carrier of (Functors (A,[:B,C:])):]
the Target of (Functors (A,[:B,C:])) . o2 is Element of the carrier of (Functors (A,[:B,C:]))
G1 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
G2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
F1 is Element of the carrier' of (Functors (A,[:B,C:]))
dom F1 is Element of the carrier of (Functors (A,[:B,C:]))
the Source of (Functors (A,[:B,C:])) . F1 is Element of the carrier of (Functors (A,[:B,C:]))
cod F1 is Element of the carrier of (Functors (A,[:B,C:]))
the Target of (Functors (A,[:B,C:])) . F1 is Element of the carrier of (Functors (A,[:B,C:]))
F2 is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
s is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[F2,s] is set
{F2,s} is non empty set
{F2} is non empty set
{{F2,s},{F2}} is non empty set
f is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of F2,s
[[F2,s],f] is set
{[F2,s],f} is non empty set
{[F2,s]} is non empty Relation-like set
{{[F2,s],f},{[F2,s]}} is non empty set
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * G2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
(pr1 (B,C)) * t is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * G1,(pr1 (B,C)) * G2
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
(A,B,C,G1) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * G1 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,G2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * G2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[(A,B,C,G1),(A,B,C,G2)] is set
{(A,B,C,G1),(A,B,C,G2)} is non empty set
{(A,B,C,G1)} is non empty set
{{(A,B,C,G1),(A,B,C,G2)},{(A,B,C,G1)}} is non empty set
(A,B,C,G1,G2,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,G1),(A,B,C,G2)
(pr2 (B,C)) * t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * G1,(pr2 (B,C)) * G2
[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)] is set
{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)} is non empty set
{[(A,B,C,G1),(A,B,C,G2)]} is non empty Relation-like set
{{[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)},{[(A,B,C,G1),(A,B,C,G2)]}} is non empty set
[[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]] is set
{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]} is non empty Relation-like set
{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]} is non empty Relation-like set
{{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)],[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]},{[[(A,B,C,G1),(A,B,C,G2)],(A,B,C,G1,G2,t)]}} is non empty set
(A,B,C) . [[F2,s],f] is set
(A,B,C,F2) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * F2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,s) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * s is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
[(A,B,C,F2),(A,B,C,s)] is set
{(A,B,C,F2),(A,B,C,s)} is non empty set
{(A,B,C,F2)} is non empty set
{{(A,B,C,F2),(A,B,C,s)},{(A,B,C,F2)}} is non empty set
(A,B,C,F2,s,f) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,F2),(A,B,C,s)
(pr1 (B,C)) * f is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * F2,(pr1 (B,C)) * s
[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)] is set
{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)} is non empty set
{[(A,B,C,F2),(A,B,C,s)]} is non empty Relation-like set
{{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)},{[(A,B,C,F2),(A,B,C,s)]}} is non empty set
(A,B,C,F2) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * F2 is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,s) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * s is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
[(A,B,C,F2),(A,B,C,s)] is set
{(A,B,C,F2),(A,B,C,s)} is non empty set
{(A,B,C,F2)} is non empty set
{{(A,B,C,F2),(A,B,C,s)},{(A,B,C,F2)}} is non empty set
(A,B,C,F2,s,f) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,F2),(A,B,C,s)
(pr2 (B,C)) * f is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * F2,(pr2 (B,C)) * s
[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)] is set
{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)} is non empty set
{[(A,B,C,F2),(A,B,C,s)]} is non empty Relation-like set
{{[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)},{[(A,B,C,F2),(A,B,C,s)]}} is non empty set
[[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)],[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]] is set
{[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)],[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]} is non empty Relation-like set
{[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]} is non empty Relation-like set
{{[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)],[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]},{[[(A,B,C,F2),(A,B,C,s)],(A,B,C,F2,s,f)]}} is non empty set
rng (A,B,C) is non empty Element of bool the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
bool the carrier' of [:(Functors (A,B)),(Functors (A,C)):] is non empty set
c₄ is set
o1 is Element of the carrier' of (Functors (A,B))
o2 is Element of the carrier' of (Functors (A,C))
[o1,o2] is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
{o1,o2} is non empty set
{o1} is non empty set
{{o1,o2},{o1}} is non empty set
the carrier' of A is non empty set
the carrier of A is non empty set
dom o2 is Element of the carrier of (Functors (A,C))
the Source of (Functors (A,C)) . o2 is Element of the carrier of (Functors (A,C))
cod o2 is Element of the carrier of (Functors (A,C))
the Target of (Functors (A,C)) . o2 is Element of the carrier of (Functors (A,C))
G1 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
G2 is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
[G1,G2] is set
{G1,G2} is non empty set
{G1} is non empty set
{{G1,G2},{G1}} is non empty set
t is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of G1,G2
[[G1,G2],t] is set
{[G1,G2],t} is non empty set
{[G1,G2]} is non empty Relation-like set
{{[G1,G2],t},{[G1,G2]}} is non empty set
dom o1 is Element of the carrier of (Functors (A,B))
the Source of (Functors (A,B)) . o1 is Element of the carrier of (Functors (A,B))
cod o1 is Element of the carrier of (Functors (A,B))
the Target of (Functors (A,B)) . o1 is Element of the carrier of (Functors (A,B))
F1 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
F2 is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
[F1,F2] is set
{F1,F2} is non empty set
{F1} is non empty set
{{F1,F2},{F1}} is non empty set
s is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of F1,F2
[[F1,F2],s] is set
{[F1,F2],s} is non empty set
{[F1,F2]} is non empty Relation-like set
{{[F1,F2],s},{[F1,F2]}} is non empty set
(A,B,C,F1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
the carrier' of [:B,C:] is non empty set
(A,B,C,F2,G2) is non empty Relation-like the carrier' of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total Functor of A,[:B,C:]
[(A,B,C,F1,G1),(A,B,C,F2,G2)] is set
{(A,B,C,F1,G1),(A,B,C,F2,G2)} is non empty set
{(A,B,C,F1,G1)} is non empty set
{{(A,B,C,F1,G1),(A,B,C,F2,G2)},{(A,B,C,F1,G1)}} is non empty set
(A,B,C,F1,F2,G1,G2,s,t) is non empty Relation-like the carrier of A -defined the carrier' of [:B,C:] -valued Function-like total quasi_total natural_transformation of (A,B,C,F1,G1),(A,B,C,F2,G2)
[[(A,B,C,F1,G1),(A,B,C,F2,G2)],(A,B,C,F1,F2,G1,G2,s,t)] is set
{[(A,B,C,F1,G1),(A,B,C,F2,G2)],(A,B,C,F1,F2,G1,G2,s,t)} is non empty set
{[(A,B,C,F1,G1),(A,B,C,F2,G2)]} is non empty Relation-like set
{{[(A,B,C,F1,G1),(A,B,C,F2,G2)],(A,B,C,F1,F2,G1,G2,s,t)},{[(A,B,C,F1,G1),(A,B,C,F2,G2)]}} is non empty set
NatTrans (A,[:B,C:]) is non empty NatTrans-DOMAIN of A,[:B,C:]
(A,B,C,(A,B,C,F1,G1)) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
pr1 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of B -valued Function-like total quasi_total Functor of [:B,C:],B
pr1 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of B -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of B:] is non empty set
(pr1 (B,C)) * (A,B,C,F1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,(A,B,C,F2,G2)) is non empty Relation-like the carrier' of A -defined the carrier' of B -valued Function-like total quasi_total Functor of A,B
(pr1 (B,C)) * (A,B,C,F2,G2) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of B -valued the carrier' of B -valued Function-like total quasi_total quasi_total Functor of A,B
(A,B,C,(A,B,C,F1,G1)) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
pr2 (B,C) is non empty Relation-like the carrier' of [:B,C:] -defined the carrier' of C -valued Function-like total quasi_total Functor of [:B,C:],C
pr2 ( the carrier' of B, the carrier' of C) is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined the carrier' of C -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:]
[:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:], the carrier' of C:] is non empty set
(pr2 (B,C)) * (A,B,C,F1,G1) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,(A,B,C,F2,G2)) is non empty Relation-like the carrier' of A -defined the carrier' of C -valued Function-like total quasi_total Functor of A,C
(pr2 (B,C)) * (A,B,C,F2,G2) is non empty Relation-like the carrier' of A -defined the carrier' of A -defined the carrier' of C -valued the carrier' of C -valued Function-like total quasi_total quasi_total Functor of A,C
(A,B,C,(A,B,C,F1,G1),(A,B,C,F2,G2),(A,B,C,F1,F2,G1,G2,s,t)) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (A,B,C,(A,B,C,F1,G1)),(A,B,C,(A,B,C,F2,G2))
(pr1 (B,C)) * (A,B,C,F1,F2,G1,G2,s,t) is non empty Relation-like the carrier of A -defined the carrier' of B -valued Function-like total quasi_total natural_transformation of (pr1 (B,C)) * (A,B,C,F1,G1),(pr1 (B,C)) * (A,B,C,F2,G2)
(A,B,C,(A,B,C,F1,G1),(A,B,C,F2,G2),(A,B,C,F1,F2,G1,G2,s,t)) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (A,B,C,(A,B,C,F1,G1)),(A,B,C,(A,B,C,F2,G2))
(pr2 (B,C)) * (A,B,C,F1,F2,G1,G2,s,t) is non empty Relation-like the carrier of A -defined the carrier' of C -valued Function-like total quasi_total natural_transformation of (pr2 (B,C)) * (A,B,C,F1,G1),(pr2 (B,C)) * (A,B,C,F2,G2)
f is Element of the carrier' of (Functors (A,[:B,C:]))
(A,B,C) . f is Element of the carrier' of [:(Functors (A,B)),(Functors (A,C)):]
A is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
B is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
Functors (A,B) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
C is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
[:B,C:] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of B is non empty set
the carrier of C is non empty set
[: the carrier of B, the carrier of C:] is non empty Relation-like set
the carrier' of B is non empty set
the carrier' of C is non empty set
[: the carrier' of B, the carrier' of C:] is non empty Relation-like set
the Source of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is non empty Relation-like set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is non empty Relation-like set
bool [: the carrier' of C, the carrier of C:] is non empty set
[: the Source of B, the Source of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:] is non empty set
the Target of B is non empty Relation-like the carrier' of B -defined the carrier of B -valued Function-like total quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of C is non empty Relation-like the carrier' of C -defined the carrier of C -valued Function-like total quasi_total Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of B, the Target of C:] is non empty Relation-like [: the carrier' of B, the carrier' of C:] -defined [: the carrier of B, the carrier of C:] -valued Function-like total quasi_total Element of bool [:[: the carrier' of B, the carrier' of C:],[: the carrier of B, the carrier of C:]:]
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is non empty Relation-like set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty Relation-like set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of C is Relation-like [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like Element of bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:]
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty Relation-like set
bool [:[: the carrier' of C, the carrier' of C:], the carrier' of C:] is non empty set
K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) is Relation-like [:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] -defined [: the carrier' of B, the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:]
[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of B, the carrier' of C:],[: the carrier' of B, the carrier' of C:]:],[: the carrier' of B, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of B, the carrier of C:],[: the carrier' of B, the carrier' of C:],[: the Source of B, the Source of C:],[: the Target of B, the Target of C:],K209( the carrier' of B, the carrier' of C, the Comp of B, the Comp of C) #) is strict CatStr
Functors (A,[:B,C:]) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
Functors (A,C) is non empty non void V55() strict Category-like V68() V69() V70() with_identities CatStr
[:(Functors (A,B)),(Functors (A,C)):] is non empty non void V55() Category-like V68() V69() V70() with_identities CatStr
the carrier of (Functors (A,B)) is non empty set
the carrier of (Functors (A,C)) is non empty set
[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] is non empty Relation-like set
the carrier' of (Functors (A,B)) is non empty set
the carrier' of (Functors (A,C)) is non empty set
[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] is non empty Relation-like set
the Source of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
[: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):] is non empty set
the Source of (Functors (A,C)) is non empty Relation-like the carrier' of (Functors (A,C)) -defined the carrier of (Functors (A,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):]
[: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):] is non empty Relation-like set
bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):] is non empty set
[: the Source of (Functors (A,B)), the Source of (Functors (A,C)):] is non empty Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -defined [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:] is non empty set
the Target of (Functors (A,B)) is non empty Relation-like the carrier' of (Functors (A,B)) -defined the carrier of (Functors (A,B)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,B)), the carrier of (Functors (A,B)):]
the Target of (Functors (A,C)) is non empty Relation-like the carrier' of (Functors (A,C)) -defined the carrier of (Functors (A,C)) -valued Function-like total quasi_total Element of bool [: the carrier' of (Functors (A,C)), the carrier of (Functors (A,C)):]
[: the Target of (Functors (A,B)), the Target of (Functors (A,C)):] is non empty Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -defined [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):] -valued Function-like total quasi_total Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):]:]
the Comp of (Functors (A,B)) is Relation-like [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] -defined the carrier' of (Functors (A,B)) -valued Function-like Element of bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):]
[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):] is non empty Relation-like set
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,B)):], the carrier' of (Functors (A,B)):] is non empty set
the Comp of (Functors (A,C)) is Relation-like [: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):] -defined the carrier' of (Functors (A,C)) -valued Function-like Element of bool [:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):]
[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):] is non empty Relation-like set
[:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):] is non empty Relation-like set
bool [:[: the carrier' of (Functors (A,C)), the carrier' of (Functors (A,C)):], the carrier' of (Functors (A,C)):] is non empty set
K209( the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)), the Comp of (Functors (A,B)), the Comp of (Functors (A,C))) is Relation-like [:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] -defined [: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):] -valued Function-like Element of bool [:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:]
[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty Relation-like set
[:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):]:] is non empty set
CatStr(# [: the carrier of (Functors (A,B)), the carrier of (Functors (A,C)):],[: the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)):],[: the Source of (Functors (A,B)), the Source of (Functors (A,C)):],[: the Target of (Functors (A,B)), the Target of (Functors (A,C)):],K209( the carrier' of (Functors (A,B)), the carrier' of (Functors (A,C)), the Comp of (Functors (A,B)), the Comp of (Functors (A,C))) #) is strict CatStr
(A,B,C) is non empty Relation-like the carrier' of (Functors (A,[:B,C:])) -defined the carrier' of [:(Functors (A,B)),(Functors (A,C)):] -valued Function-like total quasi_total isomorphic Functor of Functors (A,[:B,C:]),[:(Functors (A,B)),(Functors (A,C)):]
the carrier' of (Functors (A,[:B,C:])) is non empty set
the carrier' of [:(Functors (A,B)),(Functors (A,C)):] is non empty set