:: CAT_5 semantic presentation

K158() is Element of bool K154()
K154() is set
bool K154() is non empty set
{} is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional set
the empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional set is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional set
1 is non empty set
{{},1} is non empty set
K153() is set
bool K153() is non empty set
bool K158() is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
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
CatStr(# the carrier of C, the carrier' of C, the Source of C, the Target of C, the Comp of C #) is non empty non void V58() strict CatStr
f is non empty non void V58() CatStr
the carrier of f is non empty set
the carrier' of f is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
CatStr(# the carrier of f, the carrier' of f, the Source of f, the Target of f, the Comp of f #) is non empty non void V58() strict CatStr
dom the Comp of f is Relation-like the carrier' of f -defined the carrier' of f -valued Element of bool [: the carrier' of f, the carrier' of f:]
bool [: the carrier' of f, the carrier' of f:] is non empty set
A1 is Element of the carrier' of f
g is Element of the carrier' of f
[A1,g] is V18() Element of [: the carrier' of f, the carrier' of f:]
{A1,g} is non empty set
{A1} is non empty set
{{A1,g},{A1}} is non empty set
dom A1 is Element of the carrier of f
the Source of f . A1 is Element of the carrier of f
cod g is Element of the carrier of f
the Target of f . g is Element of the carrier of f
A3 is Element of the carrier' of C
A2 is Element of the carrier' of C
[A3,A2] is V18() Element of the carrier' of [:C,C:]
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:C,C:] is non empty set
{A3,A2} is non empty set
{A3} is non empty set
{{A3,A2},{A3}} is non empty set
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
A1 is Element of the carrier' of f
dom A1 is Element of the carrier of f
the Source of f . A1 is Element of the carrier of f
g is Element of the carrier' of f
cod g is Element of the carrier of f
the Target of f . g is Element of the carrier of f
A1 (*) g is Element of the carrier' of f
dom (A1 (*) g) is Element of the carrier of f
the Source of f . (A1 (*) g) is Element of the carrier of f
dom g is Element of the carrier of f
the Source of f . g is Element of the carrier of f
cod (A1 (*) g) is Element of the carrier of f
the Target of f . (A1 (*) g) is Element of the carrier of f
cod A1 is Element of the carrier of f
the Target of f . A1 is Element of the carrier of f
A3 is Element of the carrier' of C
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
A2 is Element of the carrier' of C
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
[A3,A2] is V18() Element of the carrier' of [:C,C:]
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:C,C:] is non empty set
{A3,A2} is non empty set
{A3} is non empty set
{{A3,A2},{A3}} is non empty set
dom the Comp of C is Relation-like the carrier' of C -defined the carrier' of C -valued Element of bool [: the carrier' of C, the carrier' of C:]
bool [: the carrier' of C, the carrier' of C:] is non empty set
the Comp of C . (A3,A2) is set
[A3,A2] is V18() set
the Comp of C . [A3,A2] is set
A3 (*) A2 is Element of the carrier' of C
dom (A3 (*) A2) is Element of the carrier of C
the Source of C . (A3 (*) A2) is Element of the carrier of C
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod (A3 (*) A2) is Element of the carrier of C
the Target of C . (A3 (*) A2) is Element of the carrier of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
A1 is Element of the carrier' of f
cod A1 is Element of the carrier of f
the Target of f . A1 is Element of the carrier of f
g is Element of the carrier' of f
dom g is Element of the carrier of f
the Source of f . g is Element of the carrier of f
g (*) A1 is Element of the carrier' of f
A2 is Element of the carrier' of C
A3 is Element of the carrier' of C
A2 (*) A3 is Element of the carrier' of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
the Comp of f . (g,A1) is set
[g,A1] is V18() set
{g,A1} is non empty set
{g} is non empty set
{{g,A1},{g}} is non empty set
the Comp of f . [g,A1] is set
the Comp of C . (A2,A3) is set
[A2,A3] is V18() set
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
the Comp of C . [A2,A3] is set
A2 is Element of the carrier' of f
dom A2 is Element of the carrier of f
the Source of f . A2 is Element of the carrier of f
A1 is Element of the carrier' of f
cod A1 is Element of the carrier of f
the Target of f . A1 is Element of the carrier of f
dom A1 is Element of the carrier of f
the Source of f . A1 is Element of the carrier of f
g is Element of the carrier' of f
cod g is Element of the carrier of f
the Target of f . g is Element of the carrier of f
A1 (*) g is Element of the carrier' of f
A2 (*) (A1 (*) g) is Element of the carrier' of f
A2 (*) A1 is Element of the carrier' of f
(A2 (*) A1) (*) g is Element of the carrier' of f
G is Element of the carrier' of C
dom G is Element of the carrier of C
the Source of C . G is Element of the carrier of C
F is Element of the carrier' of C
cod F is Element of the carrier of C
the Target of C . F is Element of the carrier of C
dom F is Element of the carrier of C
the Source of C . F is Element of the carrier of C
A3 is Element of the carrier' of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
F (*) A3 is Element of the carrier' of C
G (*) F is Element of the carrier' of C
dom (A2 (*) A1) is Element of the carrier of f
the Source of f . (A2 (*) A1) is Element of the carrier of f
cod (A1 (*) g) is Element of the carrier of f
the Target of f . (A1 (*) g) is Element of the carrier of f
G (*) (F (*) A3) is Element of the carrier' of C
(G (*) F) (*) A3 is Element of the carrier' of C
g is Element of the carrier of f
Hom (g,g) is Element of bool the carrier' of f
bool the carrier' of f is non empty set
{ b₁ where b₁ is Element of the carrier' of f : ( dom b₁ = g & cod b₁ = g ) } is set
A1 is Element of the carrier of C
id A1 is Morphism of A1,A1
A2 is Element of the carrier' of f
cod A2 is Element of the carrier of f
the Target of f . A2 is Element of the carrier of f
cod (id A1) is Element of the carrier of C
the Target of C . (id A1) is Element of the carrier of C
dom A2 is Element of the carrier of f
the Source of f . A2 is Element of the carrier of f
dom (id A1) is Element of the carrier of C
the Source of C . (id A1) is Element of the carrier of C
g is Element of the carrier of f
A1 is Element of the carrier of C
id A1 is Morphism of A1,A1
A2 is Element of the carrier' of f
cod A2 is Element of the carrier of f
the Target of f . A2 is Element of the carrier of f
cod (id A1) is Element of the carrier of C
the Target of C . (id A1) is Element of the carrier of C
dom A2 is Element of the carrier of f
the Source of f . A2 is Element of the carrier of f
dom (id A1) is Element of the carrier of C
the Source of C . (id A1) is Element of the carrier of C
A3 is Morphism of g,g
F is Element of the carrier of f
Hom (g,F) is Element of bool the carrier' of f
bool the carrier' of f is non empty set
{ b₁ where b₁ is Element of the carrier' of f : ( dom b₁ = g & cod b₁ = F ) } is set
Hom (F,g) is Element of bool the carrier' of f
{ b₁ where b₁ is Element of the carrier' of f : ( dom b₁ = F & cod b₁ = g ) } is set
FG is Morphism of g,F
FG (*) A3 is Element of the carrier' of f
m is Element of the carrier' of C
cod m is Element of the carrier of C
the Target of C . m is Element of the carrier of C
cod FG is Element of the carrier of f
the Target of f . FG is Element of the carrier of f
G is Element of the carrier of C
dom m is Element of the carrier of C
the Source of C . m is Element of the carrier of C
dom FG is Element of the carrier of f
the Source of f . FG is Element of the carrier of f
Hom (A1,G) 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 = A1 & cod b₁ = G ) } is set
g1 is Morphism of A1,G
dom g1 is Element of the carrier of C
the Source of C . g1 is Element of the carrier of C
cod A3 is Element of the carrier of f
the Target of f . A3 is Element of the carrier of f
the Comp of f . (FG,A3) is set
[FG,A3] is V18() set
{FG,A3} is non empty set
{FG} is non empty set
{{FG,A3},{FG}} is non empty set
the Comp of f . [FG,A3] is set
the Comp of C . (g1,(id A1)) is set
[g1,(id A1)] is V18() set
{g1,(id A1)} is non empty set
{g1} is non empty set
{{g1,(id A1)},{g1}} is non empty set
the Comp of C . [g1,(id A1)] is set
g1 (*) (id A1) is Element of the carrier' of C
FG is Morphism of F,g
A3 (*) FG is Element of the carrier' of f
m is Element of the carrier' of C
dom m is Element of the carrier of C
the Source of C . m is Element of the carrier of C
dom FG is Element of the carrier of f
the Source of f . FG is Element of the carrier of f
G is Element of the carrier of C
cod m is Element of the carrier of C
the Target of C . m is Element of the carrier of C
cod FG is Element of the carrier of f
the Target of f . FG is Element of the carrier of f
Hom (G,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 = G & cod b₁ = A1 ) } is set
g1 is Morphism of G,A1
cod g1 is Element of the carrier of C
the Target of C . g1 is Element of the carrier of C
dom A3 is Element of the carrier of f
the Source of f . A3 is Element of the carrier of f
the Comp of f . (A3,FG) is set
[A3,FG] is V18() set
{A3,FG} is non empty set
{A3} is non empty set
{{A3,FG},{A3}} is non empty set
the Comp of f . [A3,FG] is set
the Comp of C . ((id A1),g1) is set
[(id A1),g1] is V18() set
{(id A1),g1} is non empty set
{(id A1)} is non empty set
{{(id A1),g1},{(id A1)}} is non empty set
the Comp of C . [(id A1),g1] is set
(id A1) (*) g1 is Element of the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
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
CatStr(# the carrier of C, the carrier' of C, the Source of C, the Target of C, the Comp of C #) is non empty non void V58() strict CatStr
f is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of f is non empty set
the carrier' of f is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
CatStr(# the carrier of f, the carrier' of f, the Source of f, the Target of f, the Comp of f #) is non empty non void V58() strict CatStr
g is Element of the carrier of C
id g is Morphism of g,g
A1 is Element of the carrier of f
id A1 is Morphism of A1,A1
A2 is Element of the carrier' of f
cod A2 is Element of the carrier of f
the Target of f . A2 is Element of the carrier of f
cod (id g) is Element of the carrier of C
the Target of C . (id g) is Element of the carrier of C
dom A2 is Element of the carrier of f
the Source of f . A2 is Element of the carrier of f
dom (id g) is Element of the carrier of C
the Source of C . (id g) is Element of the carrier of C
A3 is Morphism of A1,A1
F is Element of the carrier of f
Hom (A1,F) is Element of bool the carrier' of f
bool the carrier' of f is non empty set
{ b₁ where b₁ is Element of the carrier' of f : ( dom b₁ = A1 & cod b₁ = F ) } is set
Hom (F,A1) is Element of bool the carrier' of f
{ b₁ where b₁ is Element of the carrier' of f : ( dom b₁ = F & cod b₁ = A1 ) } is set
FG is Morphism of A1,F
FG (*) A3 is Element of the carrier' of f
m is Element of the carrier' of C
dom m is Element of the carrier of C
the Source of C . m is Element of the carrier of C
dom FG is Element of the carrier of f
the Source of f . FG is Element of the carrier of f
cod A3 is Element of the carrier of f
the Target of f . A3 is Element of the carrier of f
the Comp of f . (FG,A3) is set
[FG,A3] is V18() set
{FG,A3} is non empty set
{FG} is non empty set
{{FG,A3},{FG}} is non empty set
the Comp of f . [FG,A3] is set
the Comp of C . (m,(id g)) is set
[m,(id g)] is V18() set
{m,(id g)} is non empty set
{m} is non empty set
{{m,(id g)},{m}} is non empty set
the Comp of C . [m,(id g)] is set
m (*) (id g) is Element of the carrier' of C
FG is Morphism of F,A1
A3 (*) FG is Element of the carrier' of f
m is Element of the carrier' of C
cod m is Element of the carrier of C
the Target of C . m is Element of the carrier of C
cod FG is Element of the carrier of f
the Target of f . FG is Element of the carrier of f
dom A3 is Element of the carrier of f
the Source of f . A3 is Element of the carrier of f
the Comp of f . (A3,FG) is set
[A3,FG] is V18() set
{A3,FG} is non empty set
{A3} is non empty set
{{A3,FG},{A3}} is non empty set
the Comp of f . [A3,FG] is set
the Comp of C . ((id g),m) is set
[(id g),m] is V18() set
{(id g),m} is non empty set
{(id g)} is non empty set
{{(id g),m},{(id g)}} is non empty set
the Comp of C . [(id g),m] is set
(id g) (*) m is Element of the carrier' of C
0 is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional Element of K158()
[0,0] is V18() set
{0,0} is non empty functional set
{0} is non empty functional set
{{0,0},{0}} is non empty set
[[0,0],1] is V18() set
{[0,0],1} is non empty set
{[0,0]} is non empty Relation-like Function-like set
{{[0,0],1},{[0,0]}} is non empty set
1Cat (0,[[0,0],1]) is non empty trivial V52() non void 1 -element V58() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{[[0,0],1]} is non empty Relation-like Function-like set
K262([[0,0],1],0) is Relation-like {[[0,0],1]} -defined {0} -valued Function-like V21({[[0,0],1]},{0}) Element of bool [:{[[0,0],1]},{0}:]
[:{[[0,0],1]},{0}:] is non empty Relation-like set
bool [:{[[0,0],1]},{0}:] is non empty set
K261([[0,0],1],[[0,0],1],[[0,0],1]) is Relation-like [:{[[0,0],1]},{[[0,0],1]}:] -defined {[[0,0],1]} -valued Function-like V21([:{[[0,0],1]},{[[0,0],1]}:],{[[0,0],1]}) Element of bool [:[:{[[0,0],1]},{[[0,0],1]}:],{[[0,0],1]}:]
[:{[[0,0],1]},{[[0,0],1]}:] is non empty Relation-like set
[:[:{[[0,0],1]},{[[0,0],1]}:],{[[0,0],1]}:] is non empty Relation-like set
bool [:[:{[[0,0],1]},{[[0,0],1]}:],{[[0,0],1]}:] is non empty set
CatStr(# {0},{[[0,0],1]},K262([[0,0],1],0),K262([[0,0],1],0),K261([[0,0],1],[[0,0],1],[[0,0],1]) #) is non empty non void V58() strict CatStr
C is non empty trivial V52() non void 1 -element V58() trivial' strict Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty trivial set
f is Element of the carrier' of C
the carrier of C is non empty trivial V34() set
dom f is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . f is Element of the carrier of C
[(dom f),(cod f)] is V18() Element of [: the carrier of C, the carrier of C:]
[: the carrier of C, the carrier of C:] is non empty Relation-like set
{(dom f),(cod f)} is non empty set
{(dom f)} is non empty set
{{(dom f),(cod f)},{(dom f)}} is non empty set
[[(dom f),(cod f)],1] is V18() set
{[(dom f),(cod f)],1} is non empty set
{[(dom f),(cod f)]} is non empty Relation-like Function-like set
{{[(dom f),(cod f)],1},{[(dom f),(cod f)]}} is non empty set
C is non empty non void V58() () CatStr
the carrier' of C is non empty set
the carrier of C is non empty set
f is Element of the carrier' of C
dom f is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
f `11 is set
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . f is Element of the carrier of C
f `12 is set
[(dom f),(cod f)] is V18() Element of [: the carrier of C, the carrier of C:]
[: the carrier of C, the carrier of C:] is non empty Relation-like set
{(dom f),(cod f)} is non empty set
{(dom f)} is non empty set
{{(dom f),(cod f)},{(dom f)}} is non empty set
f `2 is set
[[(dom f),(cod f)],(f `2)] is V18() set
{[(dom f),(cod f)],(f `2)} is non empty set
{[(dom f),(cod f)]} is non empty Relation-like Function-like set
{{[(dom f),(cod f)],(f `2)},{[(dom f),(cod f)]}} is non empty set
g is set
[[(dom f),(cod f)],g] is V18() set
{[(dom f),(cod f)],g} is non empty set
{{[(dom f),(cod f)],g},{[(dom f),(cod f)]}} is non empty set
C is non empty non void V58() () CatStr
the carrier' of C is non empty set
f is Element of the carrier' of C
f `11 is set
the carrier of C is non empty set
dom f is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
f `12 is set
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C . f is Element of the carrier of C
F₁() is non empty set
F₂() is non empty set
[:F₁(),F₁():] is non empty Relation-like set
{ [[b₁,b₂],b₃] where b₁, b₂ is Element of F₁(), b₃ is Element of F₂() : P₁[b₁,b₂,b₃] } is set
the Element of F₁() is Element of F₁()
g is Element of F₂()
[ the Element of F₁(), the Element of F₁()] is V18() Element of [:F₁(),F₁():]
{ the Element of F₁(), the Element of F₁()} is non empty set
{ the Element of F₁()} is non empty set
{{ the Element of F₁(), the Element of F₁()},{ the Element of F₁()}} is non empty set
[[ the Element of F₁(), the Element of F₁()],g] is V18() Element of [:[:F₁(),F₁():],F₂():]
[:[:F₁(),F₁():],F₂():] is non empty Relation-like set
{[ the Element of F₁(), the Element of F₁()],g} is non empty set
{[ the Element of F₁(), the Element of F₁()]} is non empty Relation-like Function-like set
{{[ the Element of F₁(), the Element of F₁()],g},{[ the Element of F₁(), the Element of F₁()]}} is non empty set
A1 is set
A2 is Element of F₁()
A3 is Element of F₁()
[A2,A3] is V18() Element of [:F₁(),F₁():]
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
F is Element of F₂()
[[A2,A3],F] is V18() Element of [:[:F₁(),F₁():],F₂():]
{[A2,A3],F} is non empty set
{[A2,A3]} is non empty Relation-like Function-like set
{{[A2,A3],F},{[A2,A3]}} is non empty set
bool [:[:F₁(),F₁():],F₂():] is non empty set
A1 is non empty Relation-like [:F₁(),F₁():] -defined F₂() -valued Element of bool [:[:F₁(),F₁():],F₂():]
A2 is Element of A1
A3 is Element of F₁()
F is Element of F₁()
[A3,F] is V18() Element of [:F₁(),F₁():]
{A3,F} is non empty set
{A3} is non empty set
{{A3,F},{A3}} is non empty set
G is Element of F₂()
[[A3,F],G] is V18() Element of [:[:F₁(),F₁():],F₂():]
{[A3,F],G} is non empty set
{[A3,F]} is non empty Relation-like Function-like set
{{[A3,F],G},{[A3,F]}} is non empty set
A2 `11 is Element of F<sub>1</sub>()
A2 `12 is Element of F₁()
[(A2 `11),(A2 `12)] is V18() Element of [:F₁(),F₁():]
{(A2 `11),(A2 `12)} is non empty set
{(A2 `11)} is non empty set
{{(A2 `11),(A2 `12)},{(A2 `11)}} is non empty set
A2 `2 is Element of F<sub>2</sub>()
[[(A2 `11),(A2 `12)],(A2 `2)] is V18() Element of [:[:F₁(),F₁():],F₂():]
{[(A2 `11),(A2 `12)],(A2 `2)} is non empty set
{[(A2 `11),(A2 `12)]} is non empty Relation-like Function-like set
{{[(A2 `11),(A2 `12)],(A2 `2)},{[(A2 `11),(A2 `12)]}} is non empty set
[:A1,F₁():] is non empty Relation-like set
bool [:A1,F₁():] is non empty set
A2 is Relation-like A1 -defined F₁() -valued Function-like V21(A1,F₁()) Element of bool [:A1,F₁():]
A3 is Relation-like A1 -defined F₁() -valued Function-like V21(A1,F₁()) Element of bool [:A1,F₁():]
F is set
G is set
F `11 is set
G `12 is set
FG is Element of F₁()
m is Element of F₁()
[FG,m] is V18() Element of [:F₁(),F₁():]
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
g1 is Element of F₂()
[[FG,m],g1] is V18() Element of [:[:F₁(),F₁():],F₂():]
{[FG,m],g1} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],g1},{[FG,m]}} is non empty set
a2 is Element of F₁()
b2 is Element of F₁()
[a2,b2] is V18() Element of [:F₁(),F₁():]
{a2,b2} is non empty set
{a2} is non empty set
{{a2,b2},{a2}} is non empty set
g2 is Element of F₂()
[[a2,b2],g2] is V18() Element of [:[:F₁(),F₁():],F₂():]
{[a2,b2],g2} is non empty set
{[a2,b2]} is non empty Relation-like Function-like set
{{[a2,b2],g2},{[a2,b2]}} is non empty set
F `12 is set
G `11 is set
F `2 is set
G `2 is set
F₃(g1,g2) is set
[(G `11),(F `12)] is V18() set
{(G `11),(F `12)} is non empty set
{(G `11)} is non empty set
{{(G `11),(F `12)},{(G `11)}} is non empty set
F₃((F `2),(G `2)) is set
[[(G `11),(F `12)],F₃((F `2),(G `2))] is V18() set
{[(G `11),(F `12)],F₃((F `2),(G `2))} is non empty set
{[(G `11),(F `12)]} is non empty Relation-like Function-like set
{{[(G `11),(F `12)],F₃((F `2),(G `2))},{[(G `11),(F `12)]}} is non empty set
[:A1,A1:] is non empty Relation-like [:[:F₁(),F₁():],F₂():] -defined [:[:F₁(),F₁():],F₂():] -valued Element of bool [:[:[:F₁(),F₁():],F₂():],[:[:F₁(),F₁():],F₂():]:]
[:[:[:F₁(),F₁():],F₂():],[:[:F₁(),F₁():],F₂():]:] is non empty Relation-like set
bool [:[:[:F₁(),F₁():],F₂():],[:[:F₁(),F₁():],F₂():]:] is non empty set
[:[:A1,A1:],A1:] is non empty Relation-like set
bool [:[:A1,A1:],A1:] is non empty set
F is Relation-like [:A1,A1:] -defined A1 -valued Function-like Element of bool [:[:A1,A1:],A1:]
dom F is Relation-like [:[:F₁(),F₁():],F₂():] -defined [:[:F₁(),F₁():],F₂():] -valued Element of bool [:A1,A1:]
bool [:A1,A1:] is non empty set
G is Element of F₁()
FG is Element of F₂()
[G,G] is V18() Element of [:F₁(),F₁():]
{G,G} is non empty set
{G} is non empty set
{{G,G},{G}} is non empty set
[[G,G],FG] is V18() Element of [:[:F₁(),F₁():],F₂():]
{[G,G],FG} is non empty set
{[G,G]} is non empty Relation-like Function-like set
{{[G,G],FG},{[G,G]}} is non empty set
m is Element of A1
g1 is Element of A1
[:F₁(),A1:] is non empty Relation-like set
bool [:F₁(),A1:] is non empty set
G is Relation-like F₁() -defined A1 -valued Function-like V21(F₁(),A1) Element of bool [:F₁(),A1:]
CatStr(# F₁(),A1,A2,A3,F #) is non empty non void V58() strict CatStr
the carrier' of CatStr(# F₁(),A1,A2,A3,F #) is non empty set
g1 is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
m is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
[g1,m] is V18() Element of [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] is non empty Relation-like set
{g1,m} is non empty set
{g1} is non empty set
{{g1,m},{g1}} is non empty set
g1 `11 is set
m `12 is set
A2 . g1 is set
the Comp of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] -defined the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):], the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
[:[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):], the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] is non empty Relation-like set
bool [:[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):], the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] is non empty set
dom the Comp of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -valued Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] is non empty set
dom g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the carrier of CatStr(# F₁(),A1,A2,A3,F #) is non empty set
the Source of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):] is non empty set
the Source of CatStr(# F₁(),A1,A2,A3,F #) . g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
cod m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
the Target of CatStr(# F₁(),A1,A2,A3,F #) . m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the carrier' of CatStr(# F₁(),A1,A2,A3,F #) is non empty set
[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] is non empty Relation-like set
the Comp of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] -defined the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):], the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
[:[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):], the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] is non empty Relation-like set
bool [:[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):], the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] is non empty set
dom the Comp of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -valued Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):] is non empty set
g1 is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
m is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
[g1,m] is V18() Element of [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
{g1,m} is non empty set
{g1} is non empty set
{{g1,m},{g1}} is non empty set
dom g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the carrier of CatStr(# F₁(),A1,A2,A3,F #) is non empty set
the Source of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):] is non empty set
the Source of CatStr(# F₁(),A1,A2,A3,F #) . g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
cod m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
the Target of CatStr(# F₁(),A1,A2,A3,F #) . m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
b2 is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
dom b2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Source of CatStr(# F₁(),A1,A2,A3,F #) . b2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
a2 is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
cod a2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) . a2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
[b2,a2] is V18() Element of [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
{b2,a2} is non empty set
{b2} is non empty set
{{b2,a2},{b2}} is non empty set
g1 is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
dom g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the carrier of CatStr(# F₁(),A1,A2,A3,F #) is non empty set
the Source of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):] is non empty set
the Source of CatStr(# F₁(),A1,A2,A3,F #) . g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
m is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
cod m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
the Target of CatStr(# F₁(),A1,A2,A3,F #) . m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
g1 (*) m is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
dom (g1 (*) m) is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Source of CatStr(# F₁(),A1,A2,A3,F #) . (g1 (*) m) is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
dom m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Source of CatStr(# F₁(),A1,A2,A3,F #) . m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
cod (g1 (*) m) is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) . (g1 (*) m) is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
cod g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) . g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
m `11 is set
g1 `11 is set
m `12 is set
g1 `12 is set
F . (g1,m) is set
[g1,m] is V18() set
{g1,m} is non empty set
{g1} is non empty set
{{g1,m},{g1}} is non empty set
F . [g1,m] is set
[(m `11),(g1 `12)] is V18() set
{(m `11),(g1 `12)} is non empty set
{(m `11)} is non empty set
{{(m `11),(g1 `12)},{(m `11)}} is non empty set
g1 `2 is set
m `2 is set
F₃((g1 `2),(m `2)) is set
[[(m `11),(g1 `12)],F₃((g1 `2),(m `2))] is V18() set
{[(m `11),(g1 `12)],F₃((g1 `2),(m `2))} is non empty set
{[(m `11),(g1 `12)]} is non empty Relation-like Function-like set
{{[(m `11),(g1 `12)],F₃((g1 `2),(m `2))},{[(m `11),(g1 `12)]}} is non empty set
[g1,m] is V18() Element of [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
F . [g1,m] is set
(F . [g1,m]) `11 is set
the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (g1,m) is set
the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . [g1,m] is set
(F . [g1,m]) `12 is set
a2 is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
dom a2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the carrier of CatStr(# F₁(),A1,A2,A3,F #) is non empty set
the Source of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
[: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):] is non empty set
the Source of CatStr(# F₁(),A1,A2,A3,F #) . a2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
g1 is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
cod g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
the Target of CatStr(# F₁(),A1,A2,A3,F #) . g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
dom g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Source of CatStr(# F₁(),A1,A2,A3,F #) . g1 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
m is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
cod m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) . m is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
g1 (*) m is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
a2 (*) (g1 (*) m) is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
a2 (*) g1 is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
(a2 (*) g1) (*) m is Element of the carrier' of CatStr(# F₁(),A1,A2,A3,F #)
g1 `11 is set
a2 `11 is set
m `12 is set
g1 `12 is set
[g1,m] is V18() Element of [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
{g1,m} is non empty set
{g1} is non empty set
{{g1,m},{g1}} is non empty set
[a2,g1] is V18() Element of [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier' of CatStr(# F₁(),A1,A2,A3,F #):]
{a2,g1} is non empty set
{a2} is non empty set
{{a2,g1},{a2}} is non empty set
F . [g1,m] is set
rng F is Relation-like [:F₁(),F₁():] -defined F₂() -valued Element of bool A1
bool A1 is non empty set
F . [a2,g1] is set
F . (g1,m) is set
[g1,m] is V18() set
F . [g1,m] is set
F . (a2,g1) is set
[a2,g1] is V18() set
F . [a2,g1] is set
b2 is Element of A1
m `11 is set
[(m `11),(g1 `12)] is V18() set
{(m `11),(g1 `12)} is non empty set
{(m `11)} is non empty set
{{(m `11),(g1 `12)},{(m `11)}} is non empty set
g1 `2 is set
m `2 is set
F<sub>3</sub>((g1 `2),(m `2)) is set
[[(m `11),(g1 `12)],F<sub>3</sub>((g1 `2),(m `2))] is V18() set
{[(m `11),(g1 `12)],F<sub>3</sub>((g1 `2),(m `2))} is non empty set
{[(m `11),(g1 `12)]} is non empty Relation-like Function-like set
{{[(m `11),(g1 `12)],F<sub>3</sub>((g1 `2),(m `2))},{[(m `11),(g1 `12)]}} is non empty set
g2 is Element of A1
a2 `12 is set
[(g1 `11),(a2 `12)] is V18() set
{(g1 `11),(a2 `12)} is non empty set
{(g1 `11)} is non empty set
{{(g1 `11),(a2 `12)},{(g1 `11)}} is non empty set
a2 `2 is set
F<sub>3</sub>((a2 `2),(g1 `2)) is set
[[(g1 `11),(a2 `12)],F<sub>3</sub>((a2 `2),(g1 `2))] is V18() set
{[(g1 `11),(a2 `12)],F<sub>3</sub>((a2 `2),(g1 `2))} is non empty set
{[(g1 `11),(a2 `12)]} is non empty Relation-like Function-like set
{{[(g1 `11),(a2 `12)],F<sub>3</sub>((a2 `2),(g1 `2))},{[(g1 `11),(a2 `12)]}} is non empty set
A2 . b2 is Element of F<sub>1</sub>()
b2 `11 is Element of F₁()
A2 . g2 is Element of F₁()
g2 `11 is Element of F<sub>1</sub>()
A3 . b2 is Element of F<sub>1</sub>()
b2 `12 is Element of F₁()
A3 . g2 is Element of F₁()
g2 `12 is Element of F<sub>1</sub>()
[a2,b2] is V18() Element of [: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #),A1:]
[: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #),A1:] is non empty Relation-like set
{a2,b2} is non empty set
{{a2,b2},{a2}} is non empty set
[g2,m] is V18() Element of [:A1, the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):]
[:A1, the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):] is non empty Relation-like set
{g2,m} is non empty set
{g2} is non empty set
{{g2,m},{g2}} is non empty set
ha1 is Element of A1
ha1 `11 is Element of F₁()
ha1 `12 is Element of F<sub>1</sub>()
ha1 `2 is Element of F₂()
ha2 is Element of A1
ha2 `11 is Element of F<sub>1</sub>()
ha2 `12 is Element of F₁()
ha2 `2 is Element of F<sub>2</sub>()
hb1 is Element of A1
hb1 `11 is Element of F₁()
hb1 `12 is Element of F<sub>1</sub>()
hb1 `2 is Element of F₂()
the Comp of CatStr(# F₁(),A1,A2,A3,F #) . (a2,g1) is set
the Comp of CatStr(# F₁(),A1,A2,A3,F #) . [a2,g1] is set
dom (a2 (*) g1) is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Source of CatStr(# F₁(),A1,A2,A3,F #) . (a2 (*) g1) is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Comp of CatStr(# F₁(),A1,A2,A3,F #) . (g1,m) is set
the Comp of CatStr(# F₁(),A1,A2,A3,F #) . [g1,m] is set
cod (g1 (*) m) is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Target of CatStr(# F₁(),A1,A2,A3,F #) . (g1 (*) m) is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Comp of CatStr(# F₁(),A1,A2,A3,F #) . (a2,( the Comp of CatStr(# F₁(),A1,A2,A3,F #) . (g1,m))) is set
[a2,( the Comp of CatStr(# F₁(),A1,A2,A3,F #) . (g1,m))] is V18() set
{a2,( the Comp of CatStr(# F₁(),A1,A2,A3,F #) . (g1,m))} is non empty set
{{a2,( the Comp of CatStr(# F₁(),A1,A2,A3,F #) . (g1,m))},{a2}} is non empty set
the Comp of CatStr(# F₁(),A1,A2,A3,F #) . [a2,( the Comp of CatStr(# F₁(),A1,A2,A3,F #) . (g1,m))] is set
[(m `11),(a2 `12)] is V18() set
{(m `11),(a2 `12)} is non empty set
{{(m `11),(a2 `12)},{(m `11)}} is non empty set
b2 `2 is Element of F₂()
F₃((a2 `2),(b2 `2)) is set
[[(m `11),(a2 `12)],F₃((a2 `2),(b2 `2))] is V18() set
{[(m `11),(a2 `12)],F₃((a2 `2),(b2 `2))} is non empty set
{[(m `11),(a2 `12)]} is non empty Relation-like Function-like set
{{[(m `11),(a2 `12)],F₃((a2 `2),(b2 `2))},{[(m `11),(a2 `12)]}} is non empty set
F₃((ha2 `2),(ha1 `2)) is set
F₃((hb1 `2),F<sub>3</sub>((ha2 `2),(ha1 `2))) is set
[[(m `11),(a2 `12)],F<sub>3</sub>((hb1 `2),F₃((ha2 `2),(ha1 `2)))] is V18() set
{[(m `11),(a2 `12)],F₃((hb1 `2),F<sub>3</sub>((ha2 `2),(ha1 `2)))} is non empty set
{{[(m `11),(a2 `12)],F<sub>3</sub>((hb1 `2),F₃((ha2 `2),(ha1 `2)))},{[(m `11),(a2 `12)]}} is non empty set
F₃((hb1 `2),(ha2 `2)) is set
F₃(F₃((hb1 `2),(ha2 `2)),(ha1 `2)) is set
[[(m `11),(a2 `12)],F<sub>3</sub>(F<sub>3</sub>((hb1 `2),(ha2 `2)),(ha1 `2))] is V18() set
{[(m `11),(a2 `12)],F₃(F₃((hb1 `2),(ha2 `2)),(ha1 `2))} is non empty set
{{[(m `11),(a2 `12)],F<sub>3</sub>(F<sub>3</sub>((hb1 `2),(ha2 `2)),(ha1 `2))},{[(m `11),(a2 `12)]}} is non empty set
g2 `2 is Element of F<sub>2</sub>()
F<sub>3</sub>((g2 `2),(m `2)) is set
[[(m `11),(a2 `12)],F<sub>3</sub>((g2 `2),(m `2))] is V18() set
{[(m `11),(a2 `12)],F<sub>3</sub>((g2 `2),(m `2))} is non empty set
{{[(m `11),(a2 `12)],F<sub>3</sub>((g2 `2),(m `2))},{[(m `11),(a2 `12)]}} is non empty set
the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (( the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (a2,g1)),m) is set
[( the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (a2,g1)),m] is V18() set
{( the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (a2,g1)),m} is non empty set
{( the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (a2,g1))} is non empty set
{{( the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (a2,g1)),m},{( the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (a2,g1))}} is non empty set
the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . [( the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (a2,g1)),m] is set
the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) is non empty set
m is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
Hom (m,m) is Element of bool the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
bool the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) : ( dom b<sub>1</sub> = m & cod b<sub>1</sub> = m ) } is set
G . m is set
[: the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):] is non empty Relation-like set
[m,m] is V18() Element of [: the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):]
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
g1 is Element of F<sub>2</sub>()
[[m,m],g1] is V18() Element of [:[: the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):],F<sub>2</sub>():]
[:[: the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):],F<sub>2</sub>():] is non empty Relation-like set
{[m,m],g1} is non empty set
{[m,m]} is non empty Relation-like Function-like set
{{[m,m],g1},{[m,m]}} is non empty set
a2 is Element of F<sub>1</sub>()
G . a2 is Element of A1
g2 is Element of the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
cod g2 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
the Target of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) -defined the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):]
[: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):] is non empty set
the Target of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . g2 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
(G . m) `12 is set
dom g2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Source of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
the Source of CatStr(# F₁(),A1,A2,A3,F #) . g2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
(G . m) `11 is set
the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) is non empty set
m is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
G . m is set
[: the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):] is non empty Relation-like set
[m,m] is V18() Element of [: the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):]
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
g1 is Element of F<sub>2</sub>()
[[m,m],g1] is V18() Element of [:[: the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):],F<sub>2</sub>():]
[:[: the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):],F<sub>2</sub>():] is non empty Relation-like set
{[m,m],g1} is non empty set
{[m,m]} is non empty Relation-like Function-like set
{{[m,m],g1},{[m,m]}} is non empty set
a2 is Element of F<sub>1</sub>()
G . a2 is Element of A1
g2 is Element of the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
cod g2 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
the Target of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) -defined the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):]
[: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):] is non empty set
the Target of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . g2 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
(G . m) `12 is set
dom g2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
the Source of CatStr(# F₁(),A1,A2,A3,F #) is Relation-like the carrier' of CatStr(# F₁(),A1,A2,A3,F #) -defined the carrier of CatStr(# F₁(),A1,A2,A3,F #) -valued Function-like V21( the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #)) Element of bool [: the carrier' of CatStr(# F₁(),A1,A2,A3,F #), the carrier of CatStr(# F₁(),A1,A2,A3,F #):]
the Source of CatStr(# F₁(),A1,A2,A3,F #) . g2 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
(G . m) `11 is set
ha1 is Morphism of m,m
ha2 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
Hom (m,ha2) is Element of bool the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
bool the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) : ( dom b<sub>1</sub> = m & cod b<sub>1</sub> = ha2 ) } is set
Hom (ha2,m) is Element of bool the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) : ( dom b<sub>1</sub> = ha2 & cod b<sub>1</sub> = m ) } is set
hb1 is Morphism of m,ha2
hb1 (*) ha1 is Element of the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
C is Element of F<sub>1</sub>()
F is Element of F<sub>1</sub>()
[C,F] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{C,F} is non empty set
{C} is non empty set
{{C,F},{C}} is non empty set
G is Element of F<sub>2</sub>()
[[C,F],G] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
{[C,F],G} is non empty set
{[C,F]} is non empty Relation-like Function-like set
{{[C,F],G},{[C,F]}} is non empty set
dom hb1 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
the Source of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . hb1 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
A2 . hb1 is set
[[C,F],G] `11 is Element of F₁()
F₃(G,g1) is set
[[m,m],g1] `11 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
[[m,m],g1] `2 is Element of F₂()
[[C,F],G] `12 is Element of F<sub>1</sub>()
[[C,F],G] `2 is Element of F₂()
hb1 `11 is set
[[m,m],g1] `12 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
ha1 `12 is set
[hb1,ha1] is V18() Element of [: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):]
{hb1,ha1} is non empty set
{hb1} is non empty set
{{hb1,ha1},{hb1}} is non empty set
the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (hb1,ha1) is set
[hb1,ha1] is V18() set
the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . [hb1,ha1] is set
F . (hb1,ha1) is set
F . [hb1,ha1] is set
ha1 `11 is set
hb1 `12 is set
[(ha1 `11),(hb1 `12)] is V18() set
{(ha1 `11),(hb1 `12)} is non empty set
{(ha1 `11)} is non empty set
{{(ha1 `11),(hb1 `12)},{(ha1 `11)}} is non empty set
hb1 `2 is set
ha1 `2 is set
F<sub>3</sub>((hb1 `2),(ha1 `2)) is set
[[(ha1 `11),(hb1 `12)],F<sub>3</sub>((hb1 `2),(ha1 `2))] is V18() set
{[(ha1 `11),(hb1 `12)],F<sub>3</sub>((hb1 `2),(ha1 `2))} is non empty set
{[(ha1 `11),(hb1 `12)]} is non empty Relation-like Function-like set
{{[(ha1 `11),(hb1 `12)],F<sub>3</sub>((hb1 `2),(ha1 `2))},{[(ha1 `11),(hb1 `12)]}} is non empty set
hb1 is Morphism of ha2,m
ha1 (*) hb1 is Element of the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
C is Element of F<sub>1</sub>()
F is Element of F<sub>1</sub>()
[C,F] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{C,F} is non empty set
{C} is non empty set
{{C,F},{C}} is non empty set
G is Element of F<sub>2</sub>()
[[C,F],G] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
{[C,F],G} is non empty set
{[C,F]} is non empty Relation-like Function-like set
{{[C,F],G},{[C,F]}} is non empty set
cod hb1 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
the Target of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . hb1 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
A3 . hb1 is set
[[C,F],G] `12 is Element of F₁()
F₃(g1,G) is set
[[m,m],g1] `12 is Element of the carrier of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #)
[[m,m],g1] `2 is Element of F₂()
[[C,F],G] `11 is Element of F<sub>1</sub>()
[[C,F],G] `2 is Element of F₂()
hb1 `12 is set
[[m,m],g1] `11 is Element of the carrier of CatStr(# F₁(),A1,A2,A3,F #)
ha1 `11 is set
[ha1,hb1] is V18() Element of [: the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #), the carrier' of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #):]
{ha1,hb1} is non empty set
{ha1} is non empty set
{{ha1,hb1},{ha1}} is non empty set
the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . (ha1,hb1) is set
[ha1,hb1] is V18() set
the Comp of CatStr(# F<sub>1</sub>(),A1,A2,A3,F #) . [ha1,hb1] is set
F . (ha1,hb1) is set
F . [ha1,hb1] is set
hb1 `11 is set
ha1 `12 is set
[(hb1 `11),(ha1 `12)] is V18() set
{(hb1 `11),(ha1 `12)} is non empty set
{(hb1 `11)} is non empty set
{{(hb1 `11),(ha1 `12)},{(hb1 `11)}} is non empty set
ha1 `2 is set
hb1 `2 is set
F<sub>3</sub>((ha1 `2),(hb1 `2)) is set
[[(hb1 `11),(ha1 `12)],F<sub>3</sub>((ha1 `2),(hb1 `2))] is V18() set
{[(hb1 `11),(ha1 `12)],F<sub>3</sub>((ha1 `2),(hb1 `2))} is non empty set
{[(hb1 `11),(ha1 `12)]} is non empty Relation-like Function-like set
{{[(hb1 `11),(ha1 `12)],F<sub>3</sub>((ha1 `2),(hb1 `2))},{[(hb1 `11),(ha1 `12)]}} is non empty set
m is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
the carrier' of m is non empty set
g1 is Element of the carrier' of m
the carrier of m is non empty set
dom g1 is Element of the carrier of m
the Source of m is Relation-like the carrier' of m -defined the carrier of m -valued Function-like V21( the carrier' of m, the carrier of m) Element of bool [: the carrier' of m, the carrier of m:]
[: the carrier' of m, the carrier of m:] is non empty Relation-like set
bool [: the carrier' of m, the carrier of m:] is non empty set
the Source of m . g1 is Element of the carrier of m
cod g1 is Element of the carrier of m
the Target of m is Relation-like the carrier' of m -defined the carrier of m -valued Function-like V21( the carrier' of m, the carrier of m) Element of bool [: the carrier' of m, the carrier of m:]
the Target of m . g1 is Element of the carrier of m
[(dom g1),(cod g1)] is V18() Element of [: the carrier of m, the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty Relation-like set
{(dom g1),(cod g1)} is non empty set
{(dom g1)} is non empty set
{{(dom g1),(cod g1)},{(dom g1)}} is non empty set
a2 is Element of F<sub>1</sub>()
b2 is Element of F<sub>1</sub>()
[a2,b2] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{a2,b2} is non empty set
{a2} is non empty set
{{a2,b2},{a2}} is non empty set
g2 is Element of F<sub>2</sub>()
[[a2,b2],g2] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
{[a2,b2],g2} is non empty set
{[a2,b2]} is non empty Relation-like Function-like set
{{[a2,b2],g2},{[a2,b2]}} is non empty set
[[(dom g1),(cod g1)],g2] is V18() set
{[(dom g1),(cod g1)],g2} is non empty set
{[(dom g1),(cod g1)]} is non empty Relation-like Function-like set
{{[(dom g1),(cod g1)],g2},{[(dom g1),(cod g1)]}} is non empty set
g1 `11 is set
g1 `12 is set
g1 is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier of g1 is non empty set
the carrier' of g1 is non empty set
a2 is Element of F<sub>1</sub>()
b2 is Element of F<sub>1</sub>()
g2 is Element of F<sub>2</sub>()
[a2,b2] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{a2,b2} is non empty set
{a2} is non empty set
{{a2,b2},{a2}} is non empty set
[[a2,b2],g2] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
{[a2,b2],g2} is non empty set
{[a2,b2]} is non empty Relation-like Function-like set
{{[a2,b2],g2},{[a2,b2]}} is non empty set
a2 is Element of the carrier' of g1
a2 is Element of the carrier' of g1
b2 is Element of the carrier' of g1
b2 (*) a2 is Element of the carrier' of g1
g2 is Element of F<sub>1</sub>()
ha1 is Element of F<sub>1</sub>()
[g2,ha1] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{g2,ha1} is non empty set
{g2} is non empty set
{{g2,ha1},{g2}} is non empty set
ha2 is Element of F<sub>1</sub>()
[ha1,ha2] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{ha1,ha2} is non empty set
{ha1} is non empty set
{{ha1,ha2},{ha1}} is non empty set
[g2,ha2] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{g2,ha2} is non empty set
{{g2,ha2},{g2}} is non empty set
hb1 is Element of F<sub>2</sub>()
[[g2,ha1],hb1] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
{[g2,ha1],hb1} is non empty set
{[g2,ha1]} is non empty Relation-like Function-like set
{{[g2,ha1],hb1},{[g2,ha1]}} is non empty set
hb2 is Element of F<sub>2</sub>()
[[ha1,ha2],hb2] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
{[ha1,ha2],hb2} is non empty set
{[ha1,ha2]} is non empty Relation-like Function-like set
{{[ha1,ha2],hb2},{[ha1,ha2]}} is non empty set
F<sub>3</sub>(hb2,hb1) is set
[[g2,ha2],F<sub>3</sub>(hb2,hb1)] is V18() set
{[g2,ha2],F<sub>3</sub>(hb2,hb1)} is non empty set
{[g2,ha2]} is non empty Relation-like Function-like set
{{[g2,ha2],F<sub>3</sub>(hb2,hb1)},{[g2,ha2]}} is non empty set
(g1,a2) is Element of the carrier of g1
(g1,a2) is Element of the carrier of g1
(g1,b2) is Element of the carrier of g1
(g1,b2) is Element of the carrier of g1
F . (b2,a2) is set
[b2,a2] is V18() set
{b2,a2} is non empty set
{b2} is non empty set
{{b2,a2},{b2}} is non empty set
F . [b2,a2] is set
b2 `2 is set
a2 `2 is set
F<sub>3</sub>((b2 `2),(a2 `2)) is set
[[g2,ha2],F<sub>3</sub>((b2 `2),(a2 `2))] is V18() set
{[g2,ha2],F<sub>3</sub>((b2 `2),(a2 `2))} is non empty set
{{[g2,ha2],F<sub>3</sub>((b2 `2),(a2 `2))},{[g2,ha2]}} is non empty set
F<sub>3</sub>(hb2,(a2 `2)) is set
[[g2,ha2],F₃(hb2,(a2 `2))] is V18() set
{[g2,ha2],F<sub>3</sub>(hb2,(a2 `2))} is non empty set
{{[g2,ha2],F₃(hb2,(a2 `2))},{[g2,ha2]}} is non empty set
F<sub>1</sub>() is non empty set
F<sub>2</sub>() is non empty set
[:F<sub>1</sub>(),F<sub>1</sub>():] is non empty Relation-like set
C is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
f is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier of f is non empty set
the carrier' of f is non empty set
g is set
A1 is Element of F<sub>1</sub>()
A2 is Element of F<sub>1</sub>()
[A1,A2] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of F<sub>2</sub>()
[[A1,A2],A3] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
[:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():] is non empty Relation-like set
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
g is set
A1 is Element of F<sub>1</sub>()
A2 is Element of F<sub>1</sub>()
[A1,A2] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of F<sub>2</sub>()
[[A1,A2],A3] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
[:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():] is non empty Relation-like set
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
dom the Source of C is Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
dom the Source of f is Element of bool the carrier' of f
bool the carrier' of f is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
dom the Target of C is Element of bool the carrier' of C
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
dom the Target of f is Element of bool the carrier' of f
g is set
A1 is Element of the carrier' of C
the Source of C . g is set
dom A1 is Element of the carrier of C
the Source of C . A1 is Element of the carrier of C
(C,A1) is Element of the carrier of C
A2 is Element of the carrier' of f
dom A2 is Element of the carrier of f
the Source of f . A2 is Element of the carrier of f
the Source of f . g is set
g is set
A1 is Element of the carrier' of C
the Target of C . g is set
cod A1 is Element of the carrier of C
the Target of C . A1 is Element of the carrier of C
(C,A1) is Element of the carrier of C
A2 is Element of the carrier' of f
cod A2 is Element of the carrier of f
the Target of f . A2 is Element of the carrier of f
the Target of f . g is set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like 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:], 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
dom the Comp of C is Relation-like the carrier' of C -defined the carrier' of C -valued Element of bool [: the carrier' of C, the carrier' of C:]
bool [: the carrier' of C, the carrier' of C:] is non empty set
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
dom the Comp of f is Relation-like the carrier' of f -defined the carrier' of f -valued Element of bool [: the carrier' of f, the carrier' of f:]
bool [: the carrier' of f, the carrier' of f:] is non empty set
g is set
A1 is Element of [: the carrier' of C, the carrier' of C:]
A2 is Element of [: the carrier' of f, the carrier' of f:]
A1 `1 is Element of the carrier' of C
A1 `2 is Element of the carrier' of C
[(A1 `1),(A1 `2)] is V18() Element of the carrier' of [:C,C:]
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:C,C:] is non empty set
{(A1 `1),(A1 `2)} is non empty set
{(A1 `1)} is non empty set
{{(A1 `1),(A1 `2)},{(A1 `1)}} is non empty set
dom (A1 `1) is Element of the carrier of C
the Source of C . (A1 `1) is Element of the carrier of C
cod (A1 `2) is Element of the carrier of C
the Target of C . (A1 `2) is Element of the carrier of C
A2 `1 is Element of the carrier' of f
dom (A2 `1) is Element of the carrier of f
the Source of f . (A2 `1) is Element of the carrier of f
A2 `2 is Element of the carrier' of f
cod (A2 `2) is Element of the carrier of f
the Target of f . (A2 `2) is Element of the carrier of f
g is set
A1 is Element of [: the carrier' of C, the carrier' of C:]
A2 is Element of [: the carrier' of f, the carrier' of f:]
A2 `1 is Element of the carrier' of f
A2 `2 is Element of the carrier' of f
[(A2 `1),(A2 `2)] is V18() Element of the carrier' of [:f,f:]
[:f,f:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of f, the carrier of f:] is non empty Relation-like set
[: the Source of f, the Source of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier of f, the carrier of f:] -valued Function-like V21([: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]) Element of bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:]
[:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:] is non empty set
[: the Target of f, the Target of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier of f, the carrier of f:] -valued Function-like V21([: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]) Element of bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:]
K222( the carrier' of f, the carrier' of f, the Comp of f, the Comp of f) is Relation-like [:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:] -defined [: the carrier' of f, the carrier' of f:] -valued Function-like Element of bool [:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:]
[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:] is non empty Relation-like set
[:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:] is non empty Relation-like set
bool [:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:] is non empty set
CatStr(# [: the carrier of f, the carrier of f:],[: the carrier' of f, the carrier' of f:],[: the Source of f, the Source of f:],[: the Target of f, the Target of f:],K222( the carrier' of f, the carrier' of f, the Comp of f, the Comp of f) #) is non empty non void V58() strict CatStr
the carrier' of [:f,f:] is non empty set
{(A2 `1),(A2 `2)} is non empty set
{(A2 `1)} is non empty set
{{(A2 `1),(A2 `2)},{(A2 `1)}} is non empty set
dom (A2 `1) is Element of the carrier of f
the Source of f . (A2 `1) is Element of the carrier of f
cod (A2 `2) is Element of the carrier of f
the Target of f . (A2 `2) is Element of the carrier of f
A1 `1 is Element of the carrier' of C
dom (A1 `1) is Element of the carrier of C
the Source of C . (A1 `1) is Element of the carrier of C
A1 `2 is Element of the carrier' of C
cod (A1 `2) is Element of the carrier of C
the Target of C . (A1 `2) is Element of the carrier of C
g is set
A1 is set
[g,A1] is V18() set
{g,A1} is non empty set
{g} is non empty set
{{g,A1},{g}} is non empty set
A2 is Element of the carrier' of C
A3 is Element of the carrier' of C
FG is Element of F<sub>1</sub>()
m is Element of F<sub>1</sub>()
[FG,m] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
g1 is Element of F<sub>2</sub>()
[[FG,m],g1] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
[:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():] is non empty Relation-like set
{[FG,m],g1} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],g1},{[FG,m]}} is non empty set
a2 is Element of F<sub>1</sub>()
b2 is Element of F<sub>1</sub>()
[a2,b2] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{a2,b2} is non empty set
{a2} is non empty set
{{a2,b2},{a2}} is non empty set
g2 is Element of F<sub>2</sub>()
[[a2,b2],g2] is V18() Element of [:[:F<sub>1</sub>(),F<sub>1</sub>():],F<sub>2</sub>():]
{[a2,b2],g2} is non empty set
{[a2,b2]} is non empty Relation-like Function-like set
{{[a2,b2],g2},{[a2,b2]}} is non empty set
(C,A2) is Element of the carrier of C
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
(C,A3) is Element of the carrier of C
the Comp of C . (g,A1) is set
the Comp of C . [g,A1] is set
A2 (*) A3 is Element of the carrier' of C
[a2,m] is V18() Element of [:F<sub>1</sub>(),F<sub>1</sub>():]
{a2,m} is non empty set
{{a2,m},{a2}} is non empty set
F<sub>3</sub>(g1,g2) is set
[[a2,m],F<sub>3</sub>(g1,g2)] is V18() set
{[a2,m],F<sub>3</sub>(g1,g2)} is non empty set
{[a2,m]} is non empty Relation-like Function-like set
{{[a2,m],F<sub>3</sub>(g1,g2)},{[a2,m]}} is non empty set
G is Element of the carrier' of f
F is Element of the carrier' of f
F (*) G is Element of the carrier' of f
the Comp of f . (g,A1) is set
the Comp of f . [g,A1] is set
F<sub>2</sub>() is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of F<sub>2</sub>() is non empty set
F<sub>1</sub>() is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of F<sub>1</sub>() is non empty set
the carrier' of F<sub>2</sub>() is non empty set
the carrier of F<sub>1</sub>() is non empty set
C is Relation-like Function-like set
proj1 C is set
proj2 C is set
f is set
g is set
C . g is set
F<sub>4</sub>(g) is set
[: the carrier' of F<sub>1</sub>(), the carrier' of F<sub>2</sub>():] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(), the carrier' of F<sub>2</sub>():] is non empty set
g is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>(g) is Element of the carrier of F<sub>2</sub>()
f is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier' of F<sub>2</sub>() -valued Function-like V21( the carrier' of F<sub>1</sub>(), the carrier' of F<sub>2</sub>()) Element of bool [: the carrier' of F<sub>1</sub>(), the carrier' of F<sub>2</sub>():]
id g is Morphism of g,g
f . (id g) is Element of the carrier' of F<sub>2</sub>()
F<sub>4</sub>((id g)) is set
A1 is Element of the carrier of F<sub>2</sub>()
id A1 is Morphism of A1,A1
g is Element of the carrier' of F<sub>1</sub>()
F<sub>4</sub>(g) is set
dom g is Element of the carrier of F<sub>1</sub>()
the Source of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() -valued Function-like V21( the carrier' of F<sub>1</sub>(), the carrier of F<sub>1</sub>()) Element of bool [: the carrier' of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
[: the carrier' of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is non empty Relation-like set
bool [: the carrier' of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is non empty set
the Source of F<sub>1</sub>() . g is Element of the carrier of F<sub>1</sub>()
id (dom g) is Morphism of dom g, dom g
f . (id (dom g)) is Element of the carrier' of F<sub>2</sub>()
F<sub>4</sub>((id (dom g))) is set
F<sub>3</sub>((dom g)) is Element of the carrier of F<sub>2</sub>()
id F<sub>3</sub>((dom g)) is Morphism of F<sub>3</sub>((dom g)),F<sub>3</sub>((dom g))
A1 is Element of the carrier' of F<sub>2</sub>()
dom A1 is Element of the carrier of F<sub>2</sub>()
the Source of F<sub>2</sub>() is Relation-like the carrier' of F<sub>2</sub>() -defined the carrier of F<sub>2</sub>() -valued Function-like V21( the carrier' of F<sub>2</sub>(), the carrier of F<sub>2</sub>()) Element of bool [: the carrier' of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[: the carrier' of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is non empty Relation-like set
bool [: the carrier' of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is non empty set
the Source of F<sub>2</sub>() . A1 is Element of the carrier of F<sub>2</sub>()
id (dom A1) is Morphism of dom A1, dom A1
f . g is Element of the carrier' of F<sub>2</sub>()
dom (f . g) is Element of the carrier of F<sub>2</sub>()
the Source of F<sub>2</sub>() . (f . g) is Element of the carrier of F<sub>2</sub>()
id (dom (f . g)) is Morphism of dom (f . g), dom (f . g)
cod g is Element of the carrier of F<sub>1</sub>()
the Target of F<sub>1</sub>() is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() -valued Function-like V21( the carrier' of F<sub>1</sub>(), the carrier of F<sub>1</sub>()) Element of bool [: the carrier' of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
the Target of F<sub>1</sub>() . g is Element of the carrier of F<sub>1</sub>()
id (cod g) is Morphism of cod g, cod g
f . (id (cod g)) is Element of the carrier' of F<sub>2</sub>()
F<sub>4</sub>((id (cod g))) is set
F<sub>3</sub>((cod g)) is Element of the carrier of F<sub>2</sub>()
id F<sub>3</sub>((cod g)) is Morphism of F<sub>3</sub>((cod g)),F<sub>3</sub>((cod g))
cod A1 is Element of the carrier of F<sub>2</sub>()
the Target of F<sub>2</sub>() is Relation-like the carrier' of F<sub>2</sub>() -defined the carrier of F<sub>2</sub>() -valued Function-like V21( the carrier' of F<sub>2</sub>(), the carrier of F<sub>2</sub>()) Element of bool [: the carrier' of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
the Target of F<sub>2</sub>() . A1 is Element of the carrier of F<sub>2</sub>()
id (cod A1) is Morphism of cod A1, cod A1
cod (f . g) is Element of the carrier of F<sub>2</sub>()
the Target of F<sub>2</sub>() . (f . g) is Element of the carrier of F<sub>2</sub>()
id (cod (f . g)) is Morphism of cod (f . g), cod (f . g)
A1 is Element of the carrier' of F<sub>1</sub>()
dom A1 is Element of the carrier of F<sub>1</sub>()
the Source of F<sub>1</sub>() . A1 is Element of the carrier of F<sub>1</sub>()
g is Element of the carrier' of F<sub>1</sub>()
cod g is Element of the carrier of F<sub>1</sub>()
the Target of F<sub>1</sub>() . g is Element of the carrier of F<sub>1</sub>()
f . A1 is Element of the carrier' of F<sub>2</sub>()
F<sub>4</sub>(A1) is set
f . g is Element of the carrier' of F<sub>2</sub>()
F<sub>4</sub>(g) is set
A1 (*) g is Element of the carrier' of F<sub>1</sub>()
f . (A1 (*) g) is Element of the carrier' of F<sub>2</sub>()
F<sub>4</sub>((A1 (*) g)) is set
(f . A1) (*) (f . g) is Element of the carrier' of F<sub>2</sub>()
g is Relation-like the carrier' of F<sub>1</sub>() -defined the carrier' of F<sub>2</sub>() -valued Function-like V21( the carrier' of F<sub>1</sub>(), the carrier' of F<sub>2</sub>()) Functor of F<sub>1</sub>(),F<sub>2</sub>()
A1 is Element of the carrier' of F<sub>1</sub>()
g . A1 is Element of the carrier' of F<sub>2</sub>()
F<sub>4</sub>(A1) is set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
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
CatStr(# the carrier of C, the carrier' of C, the Source of C, the Target of C, the Comp of C #) is non empty non void V58() strict CatStr
f is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
the carrier of f is non empty set
the carrier' of f is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
CatStr(# the carrier of f, the carrier' of f, the Source of f, the Target of f, the Comp of f #) is non empty non void V58() strict CatStr
g is Element of the carrier' of C
the Source of C . g is Element of the carrier of C
dom g is Element of the carrier of C
A1 is Element of the carrier' of f
dom A1 is Element of the carrier of f
the Source of f . A1 is Element of the carrier of f
the Source of f . g is set
g is Element of the carrier' of C
the Target of C . g is Element of the carrier of C
cod g is Element of the carrier of C
A1 is Element of the carrier' of f
cod A1 is Element of the carrier of f
the Target of f . A1 is Element of the carrier of f
the Target of f . g is set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
f is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
g is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of f is non empty set
the carrier of C is non empty set
the carrier' of f is non empty set
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] 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 is non empty set
[: 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
the carrier of g is non empty set
the carrier' of g is non empty set
[: the carrier' of g, the carrier' of g:] is non empty Relation-like set
the Comp of g is Relation-like [: the carrier' of g, the carrier' of g:] -defined the carrier' of g -valued Function-like Element of bool [:[: the carrier' of g, the carrier' of g:], the carrier' of g:]
[:[: the carrier' of g, the carrier' of g:], the carrier' of g:] is non empty Relation-like set
bool [:[: the carrier' of g, the carrier' of g:], the carrier' of g:] is non empty set
A1 is Element of the carrier of g
A2 is Element of the carrier of g
A3 is Element of the carrier of C
F is Element of the carrier of C
Hom (A1,A2) is Element of bool the carrier' of g
bool the carrier' of g is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of g : ( dom b<sub>1</sub> = A1 & cod b<sub>1</sub> = A2 ) } is set
G is Element of the carrier of f
FG is Element of the carrier of f
Hom (G,FG) is Element of bool the carrier' of f
bool the carrier' of f is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of f : ( dom b<sub>1</sub> = G & cod b<sub>1</sub> = FG ) } is set
Hom (A3,F) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C : ( dom b<sub>1</sub> = A3 & cod b<sub>1</sub> = F ) } is set
A1 is Element of the carrier of g
id A1 is Morphism of A1,A1
A2 is Element of the carrier of C
id A2 is Morphism of A2,A2
A3 is Element of the carrier of f
id A3 is Morphism of A3,A3
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
f is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
g is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier of f is non empty set
A1 is Element of the carrier of C
the carrier of C /\ the carrier of f is set
the carrier' of C is non empty set
the carrier' of f is non empty set
the carrier' of C /\ the carrier' of f is set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 | the carrier' of f is Relation-like the carrier' of C -defined the carrier' of f -defined the carrier' of C -defined the carrier of C -valued Function-like Element of bool [: the carrier' of C, the carrier of C:]
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C | the carrier' of f is Relation-like the carrier' of C -defined the carrier' of f -defined the carrier' of C -defined the carrier of C -valued Function-like Element of bool [: the carrier' of C, the carrier of C:]
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
the Comp of C || the carrier' of f is Relation-like Function-like set
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
the Comp of C | [: the carrier' of f, the carrier' of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like set
the carrier of g is non empty set
id A1 is Morphism of A1,A1
m is Element of the carrier of g
id m is Morphism of m,m
FG is Element of the carrier of f
id FG is Morphism of FG,FG
dom the Source of C is Element of bool the carrier' of C
bool the carrier' of C is non empty set
dom the Target of C is Element of bool the carrier' of C
dom ( the Source of C | the carrier' of f) is Element of bool the carrier' of C
g1 is non empty set
dom ( the Target of C | the carrier' of f) is Element of bool the carrier' of C
rng ( the Source of C | the carrier' of f) is Element of bool the carrier of C
bool the carrier of C is non empty set
G is non empty set
a2 is set
b2 is set
( the Source of C | the carrier' of f) . b2 is set
the carrier' of g is non empty set
g2 is Element of the carrier' of C
dom g2 is Element of the carrier of C
the Source of C . g2 is Element of the carrier of C
ha2 is Element of the carrier' of g
dom ha2 is Element of the carrier of g
the Source of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
[: the carrier' of g, the carrier of g:] is non empty Relation-like set
bool [: the carrier' of g, the carrier of g:] is non empty set
the Source of g . ha2 is Element of the carrier of g
ha1 is Element of the carrier' of f
dom ha1 is Element of the carrier of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f . ha1 is Element of the carrier of f
[:g1,G:] is non empty Relation-like set
bool [:g1,G:] is non empty set
rng ( the Target of C | the carrier' of f) is Element of bool the carrier of C
b2 is set
g2 is set
( the Target of C | the carrier' of f) . g2 is set
the carrier' of g is non empty set
ha1 is Element of the carrier' of C
cod ha1 is Element of the carrier of C
the Target of C . ha1 is Element of the carrier of C
hb1 is Element of the carrier' of g
cod hb1 is Element of the carrier of g
the Target of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
[: the carrier' of g, the carrier of g:] is non empty Relation-like set
bool [: the carrier' of g, the carrier of g:] is non empty set
the Target of g . hb1 is Element of the carrier of g
ha2 is Element of the carrier' of f
cod ha2 is Element of the carrier of f
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Target of f . ha2 is Element of the carrier of f
proj1 ( the Comp of C || the carrier' of f) is set
dom the Comp of C is Relation-like the carrier' of C -defined the carrier' of C -valued Element of bool [: the carrier' of C, the carrier' of C:]
bool [: the carrier' of C, the carrier' of C:] is non empty set
(dom the Comp of C) /\ [: the carrier' of f, the carrier' of f:] is Relation-like the carrier' of C -defined the carrier' of C -valued Element of bool [: the carrier' of C, the carrier' of C:]
[: the carrier' of C, the carrier' of C:] /\ [: the carrier' of f, the carrier' of f:] is Relation-like set
[:g1,g1:] is non empty Relation-like set
proj2 ( the Comp of C || the carrier' of f) is set
g2 is set
ha1 is set
( the Comp of C || the carrier' of f) . ha1 is set
ha1 `1 is set
ha1 `2 is set
[(ha1 `1),(ha1 `2)] is V18() set
{(ha1 `1),(ha1 `2)} is non empty set
{(ha1 `1)} is non empty set
{{(ha1 `1),(ha1 `2)},{(ha1 `1)}} is non empty set
the carrier' of g is non empty set
ha2 is Element of the carrier' of C
hb1 is Element of the carrier' of C
dom ha2 is Element of the carrier of C
the Source of C . ha2 is Element of the carrier of C
cod hb1 is Element of the carrier of C
the Target of C . hb1 is Element of the carrier of C
the Comp of C . (ha2,hb1) is set
[ha2,hb1] is V18() set
{ha2,hb1} is non empty set
{ha2} is non empty set
{{ha2,hb1},{ha2}} is non empty set
the Comp of C . [ha2,hb1] is set
F is Element of the carrier' of g
dom F is Element of the carrier of g
the Source of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
[: the carrier' of g, the carrier of g:] is non empty Relation-like set
bool [: the carrier' of g, the carrier of g:] is non empty set
the Source of g . F is Element of the carrier of g
hb2 is Element of the carrier' of f
dom hb2 is Element of the carrier of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f . hb2 is Element of the carrier of f
G is Element of the carrier' of g
cod G is Element of the carrier of g
the Target of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
the Target of g . G is Element of the carrier of g
C is Element of the carrier' of f
cod C is Element of the carrier of f
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f . C is Element of the carrier of f
ha2 (*) hb1 is Element of the carrier' of C
F (*) G is Element of the carrier' of g
hb2 (*) C is Element of the carrier' of f
[:[:g1,g1:],g1:] is non empty Relation-like set
bool [:[:g1,g1:],g1:] is non empty set
a2 is Relation-like g1 -defined G -valued Function-like V21(g1,G) Element of bool [:g1,G:]
b2 is Relation-like g1 -defined G -valued Function-like V21(g1,G) Element of bool [:g1,G:]
g2 is Relation-like [:g1,g1:] -defined g1 -valued Function-like Element of bool [:[:g1,g1:],g1:]
CatStr(# G,g1,a2,b2,g2 #) is non empty non void V58() strict CatStr
the carrier' of CatStr(# G,g1,a2,b2,g2 #) is non empty set
hb1 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
[hb1,ha2] is V18() set
{hb1,ha2} is non empty set
{hb1} is non empty set
{{hb1,ha2},{hb1}} is non empty set
the Comp of CatStr(# G,g1,a2,b2,g2 #) is Relation-like [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):] -defined the carrier' of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):], the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
[:[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):], the carrier' of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [:[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):], the carrier' of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
proj1 the Comp of CatStr(# G,g1,a2,b2,g2 #) is Relation-like set
dom hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the carrier of CatStr(# G,g1,a2,b2,g2 #) is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) . hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
the Target of CatStr(# G,g1,a2,b2,g2 #) . ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
[hb1,ha2] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
dom the Comp of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier' of CatStr(# G,g1,a2,b2,g2 #) -valued Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
hb2 is Element of the carrier' of C
dom hb2 is Element of the carrier of C
the Source of C . hb2 is Element of the carrier of C
C is Element of the carrier' of C
cod C is Element of the carrier of C
the Target of C . C is Element of the carrier of C
the carrier' of CatStr(# G,g1,a2,b2,g2 #) is non empty set
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
the Comp of CatStr(# G,g1,a2,b2,g2 #) is Relation-like [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):] -defined the carrier' of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):], the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
[:[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):], the carrier' of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [:[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):], the carrier' of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
dom the Comp of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier' of CatStr(# G,g1,a2,b2,g2 #) -valued Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
hb1 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
[hb1,ha2] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{hb1,ha2} is non empty set
{hb1} is non empty set
{{hb1,ha2},{hb1}} is non empty set
dom hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the carrier of CatStr(# G,g1,a2,b2,g2 #) is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) . hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
the Target of CatStr(# G,g1,a2,b2,g2 #) . ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
C is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom C is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . C is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
hb2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
cod hb2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . hb2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
[C,hb2] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{C,hb2} is non empty set
{C} is non empty set
{{C,hb2},{C}} is non empty set
hb1 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the carrier of CatStr(# G,g1,a2,b2,g2 #) is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) . hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
cod ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
the Target of CatStr(# G,g1,a2,b2,g2 #) . ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
hb1 (*) ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
dom ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
[hb1,ha2] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{hb1,ha2} is non empty set
{hb1} is non empty set
{{hb1,ha2},{hb1}} is non empty set
F is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb1,ha2) is set
[hb1,ha2] is V18() set
the Comp of CatStr(# G,g1,a2,b2,g2 #) . [hb1,ha2] is set
hb2 is Element of the carrier' of C
C is Element of the carrier' of C
the Comp of C . (hb2,C) is set
[hb2,C] is V18() set
{hb2,C} is non empty set
{hb2} is non empty set
{{hb2,C},{hb2}} is non empty set
the Comp of C . [hb2,C] is set
hb2 (*) C is Element of the carrier' of C
dom C is Element of the carrier of C
the Source of C . C is Element of the carrier of C
dom hb2 is Element of the carrier of C
the Source of C . hb2 is Element of the carrier of C
dom F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
G is Element of the carrier' of C
dom G is Element of the carrier of C
the Source of C . G is Element of the carrier of C
cod C is Element of the carrier of C
the Target of C . C is Element of the carrier of C
cod hb2 is Element of the carrier of C
the Target of C . hb2 is Element of the carrier of C
cod F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
hb1 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the carrier of CatStr(# G,g1,a2,b2,g2 #) is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) . hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
cod ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
the Target of CatStr(# G,g1,a2,b2,g2 #) . ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
hb1 (*) ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
dom ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
hb2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom hb2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the carrier of CatStr(# G,g1,a2,b2,g2 #) is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) . hb2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
hb1 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
cod hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
the Target of CatStr(# G,g1,a2,b2,g2 #) . hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
dom hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . hb1 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
cod ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
hb1 (*) ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
hb2 (*) (hb1 (*) ha2) is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
hb2 (*) hb1 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
(hb2 (*) hb1) (*) ha2 is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
[hb2,hb1] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{hb2,hb1} is non empty set
{hb2} is non empty set
{{hb2,hb1},{hb2}} is non empty set
[hb1,ha2] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{hb1,ha2} is non empty set
{hb1} is non empty set
{{hb1,ha2},{hb1}} is non empty set
the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,hb1) is set
[hb2,hb1] is V18() set
the Comp of CatStr(# G,g1,a2,b2,g2 #) . [hb2,hb1] is set
the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb1,ha2) is set
[hb1,ha2] is V18() set
the Comp of CatStr(# G,g1,a2,b2,g2 #) . [hb1,ha2] is set
COMP is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
T is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom COMP is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . COMP is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
dom (hb2 (*) hb1) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . (hb2 (*) hb1) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod T is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . T is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . (hb1 (*) ha2) is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
[COMP,ha2] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{COMP,ha2} is non empty set
{COMP} is non empty set
{{COMP,ha2},{COMP}} is non empty set
[hb2,T] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{hb2,T} is non empty set
{{hb2,T},{hb2}} is non empty set
C is Element of the carrier' of C
dom C is Element of the carrier of C
the Source of C . C is Element of the carrier of C
F is Element of the carrier' of C
cod F is Element of the carrier of C
the Target of C . F is Element of the carrier of C
C (*) F is Element of the carrier' of C
the Comp of C . (C,F) is set
[C,F] is V18() set
{C,F} is non empty set
{C} is non empty set
{{C,F},{C}} is non empty set
the Comp of C . [C,F] is set
dom F is Element of the carrier of C
the Source of C . F is Element of the carrier of C
G is Element of the carrier' of C
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
F (*) G is Element of the carrier' of C
the Comp of C . (F,G) is set
[F,G] is V18() set
{F,G} is non empty set
{F} is non empty set
{{F,G},{F}} is non empty set
the Comp of C . [F,G] is set
cod (F (*) G) is Element of the carrier of C
the Target of C . (F (*) G) is Element of the carrier of C
dom (C (*) F) is Element of the carrier of C
the Source of C . (C (*) F) is Element of the carrier of C
the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb1,ha2))) is set
[hb2,( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb1,ha2))] is V18() set
{hb2,( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb1,ha2))} is non empty set
{{hb2,( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb1,ha2))},{hb2}} is non empty set
the Comp of CatStr(# G,g1,a2,b2,g2 #) . [hb2,( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb1,ha2))] is set
a is Element of the carrier' of C
[C,a] is V18() Element of the carrier' of [:C,C:]
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:C,C:] is non empty set
{C,a} is non empty set
{{C,a},{C}} is non empty set
the Comp of C . [C,a] is set
the Comp of C . (C,( the Comp of C . (F,G))) is set
[C,( the Comp of C . (F,G))] is V18() set
{C,( the Comp of C . (F,G))} is non empty set
{{C,( the Comp of C . (F,G))},{C}} is non empty set
the Comp of C . [C,( the Comp of C . (F,G))] is set
C (*) (F (*) G) is Element of the carrier' of C
(C (*) F) (*) G is Element of the carrier' of C
the Comp of C . (( the Comp of C . (C,F)),G) is set
[( the Comp of C . (C,F)),G] is V18() set
{( the Comp of C . (C,F)),G} is non empty set
{( the Comp of C . (C,F))} is non empty set
{{( the Comp of C . (C,F)),G},{( the Comp of C . (C,F))}} is non empty set
the Comp of C . [( the Comp of C . (C,F)),G] is set
E is Element of the carrier' of C
[E,G] is V18() Element of the carrier' of [:C,C:]
{E,G} is non empty set
{E} is non empty set
{{E,G},{E}} is non empty set
the Comp of C . [E,G] is set
the Comp of CatStr(# G,g1,a2,b2,g2 #) . (( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,hb1)),ha2) is set
[( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,hb1)),ha2] is V18() set
{( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,hb1)),ha2} is non empty set
{( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,hb1))} is non empty set
{{( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,hb1)),ha2},{( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,hb1))}} is non empty set
the Comp of CatStr(# G,g1,a2,b2,g2 #) . [( the Comp of CatStr(# G,g1,a2,b2,g2 #) . (hb2,hb1)),ha2] is set
the carrier of CatStr(# G,g1,a2,b2,g2 #) is non empty set
ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
Hom (ha2,ha2) is Element of bool the carrier' of CatStr(# G,g1,a2,b2,g2 #)
bool the carrier' of CatStr(# G,g1,a2,b2,g2 #) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #) : ( dom b<sub>1</sub> = ha2 & cod b<sub>1</sub> = ha2 ) } is set
hb1 is Element of the carrier of C
id hb1 is Morphism of hb1,hb1
C is Element of the carrier of g
id C is Morphism of C,C
hb2 is Element of the carrier of f
id hb2 is Morphism of hb2,hb2
F is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) . F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
dom (id hb1) is Element of the carrier of C
the Source of C . (id hb1) is Element of the carrier of C
cod F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
the Target of CatStr(# G,g1,a2,b2,g2 #) . F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod (id hb1) is Element of the carrier of C
the Target of C . (id hb1) is Element of the carrier of C
the carrier of CatStr(# G,g1,a2,b2,g2 #) is non empty set
ha2 is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
hb1 is Element of the carrier of C
id hb1 is Morphism of hb1,hb1
C is Element of the carrier of g
id C is Morphism of C,C
hb2 is Element of the carrier of f
id hb2 is Morphism of hb2,hb2
F is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
dom F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
[: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty Relation-like set
bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):] is non empty set
the Source of CatStr(# G,g1,a2,b2,g2 #) . F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
dom (id hb1) is Element of the carrier of C
the Source of C . (id hb1) is Element of the carrier of C
cod F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) is Relation-like the carrier' of CatStr(# G,g1,a2,b2,g2 #) -defined the carrier of CatStr(# G,g1,a2,b2,g2 #) -valued Function-like V21( the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #)) Element of bool [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier of CatStr(# G,g1,a2,b2,g2 #):]
the Target of CatStr(# G,g1,a2,b2,g2 #) . F is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod (id hb1) is Element of the carrier of C
the Target of C . (id hb1) is Element of the carrier of C
Hom (ha2,ha2) is Element of bool the carrier' of CatStr(# G,g1,a2,b2,g2 #)
bool the carrier' of CatStr(# G,g1,a2,b2,g2 #) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #) : ( dom b<sub>1</sub> = ha2 & cod b<sub>1</sub> = ha2 ) } is set
G is Morphism of ha2,ha2
COMP is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
Hom (ha2,COMP) is Element of bool the carrier' of CatStr(# G,g1,a2,b2,g2 #)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #) : ( dom b<sub>1</sub> = ha2 & cod b<sub>1</sub> = COMP ) } is set
Hom (COMP,ha2) is Element of bool the carrier' of CatStr(# G,g1,a2,b2,g2 #)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #) : ( dom b<sub>1</sub> = COMP & cod b<sub>1</sub> = ha2 ) } is set
T is Morphism of ha2,COMP
T (*) G is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
E is Element of the carrier' of C
dom E is Element of the carrier of C
the Source of C . E is Element of the carrier of C
the Source of C . T is set
( the Source of C | the carrier' of f) . T is set
dom T is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . T is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
cod G is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . G is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
[T,G] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{T,G} is non empty set
{T} is non empty set
{{T,G},{T}} is non empty set
g2 . (T,G) is set
[T,G] is V18() set
g2 . [T,G] is set
( the Comp of C || the carrier' of f) . (T,G) is set
( the Comp of C || the carrier' of f) . [T,G] is set
the Comp of C . (E,(id hb1)) is set
[E,(id hb1)] is V18() set
{E,(id hb1)} is non empty set
{E} is non empty set
{{E,(id hb1)},{E}} is non empty set
the Comp of C . [E,(id hb1)] is set
E (*) (id hb1) is Element of the carrier' of C
T is Morphism of COMP,ha2
G (*) T is Element of the carrier' of CatStr(# G,g1,a2,b2,g2 #)
E is Element of the carrier' of C
cod E is Element of the carrier of C
the Target of C . E is Element of the carrier of C
the Target of C . T is set
( the Target of C | the carrier' of f) . T is set
cod T is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Target of CatStr(# G,g1,a2,b2,g2 #) . T is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
dom G is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
the Source of CatStr(# G,g1,a2,b2,g2 #) . G is Element of the carrier of CatStr(# G,g1,a2,b2,g2 #)
[G,T] is V18() Element of [: the carrier' of CatStr(# G,g1,a2,b2,g2 #), the carrier' of CatStr(# G,g1,a2,b2,g2 #):]
{G,T} is non empty set
{G} is non empty set
{{G,T},{G}} is non empty set
g2 . (G,T) is set
[G,T] is V18() set
g2 . [G,T] is set
( the Comp of C || the carrier' of f) . (G,T) is set
( the Comp of C || the carrier' of f) . [G,T] is set
the Comp of C . ((id hb1),E) is set
[(id hb1),E] is V18() set
{(id hb1),E} is non empty set
{(id hb1)} is non empty set
{{(id hb1),E},{(id hb1)}} is non empty set
the Comp of C . [(id hb1),E] is set
(id hb1) (*) E is Element of the carrier' of C
A2 is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of A2 is non empty set
the carrier' of A2 is non empty set
the Source of A2 is Relation-like the carrier' of A2 -defined the carrier of A2 -valued Function-like V21( the carrier' of A2, the carrier of A2) Element of bool [: the carrier' of A2, the carrier of A2:]
[: the carrier' of A2, the carrier of A2:] is non empty Relation-like set
bool [: the carrier' of A2, the carrier of A2:] is non empty set
the Target of A2 is Relation-like the carrier' of A2 -defined the carrier of A2 -valued Function-like V21( the carrier' of A2, the carrier of A2) Element of bool [: the carrier' of A2, the carrier of A2:]
the Comp of A2 is Relation-like [: the carrier' of A2, the carrier' of A2:] -defined the carrier' of A2 -valued Function-like Element of bool [:[: the carrier' of A2, the carrier' of A2:], the carrier' of A2:]
[: the carrier' of A2, the carrier' of A2:] is non empty Relation-like set
[:[: the carrier' of A2, the carrier' of A2:], the carrier' of A2:] is non empty Relation-like set
bool [:[: the carrier' of A2, the carrier' of A2:], the carrier' of A2:] is non empty set
A3 is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of A3 is non empty set
the carrier' of A3 is non empty set
the Source of A3 is Relation-like the carrier' of A3 -defined the carrier of A3 -valued Function-like V21( the carrier' of A3, the carrier of A3) Element of bool [: the carrier' of A3, the carrier of A3:]
[: the carrier' of A3, the carrier of A3:] is non empty Relation-like set
bool [: the carrier' of A3, the carrier of A3:] is non empty set
the Target of A3 is Relation-like the carrier' of A3 -defined the carrier of A3 -valued Function-like V21( the carrier' of A3, the carrier of A3) Element of bool [: the carrier' of A3, the carrier of A3:]
the Comp of A3 is Relation-like [: the carrier' of A3, the carrier' of A3:] -defined the carrier' of A3 -valued Function-like Element of bool [:[: the carrier' of A3, the carrier' of A3:], the carrier' of A3:]
[: the carrier' of A3, the carrier' of A3:] is non empty Relation-like set
[:[: the carrier' of A3, the carrier' of A3:], the carrier' of A3:] is non empty Relation-like set
bool [:[: the carrier' of A3, the carrier' of A3:], the carrier' of A3:] is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
f is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
the carrier of f is non empty set
g is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
the carrier of g is non empty set
(f,g) is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
(g,f) is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of f /\ the carrier of g is set
A1 is non empty set
the Element of A1 is Element of A1
the carrier' of f is non empty set
the carrier' of g is non empty set
the carrier of (f,g) is non empty set
the carrier of (g,f) is non empty set
the carrier' of (f,g) is non empty set
the carrier' of f /\ the carrier' of g is set
the Source of (g,f) is Relation-like the carrier' of (g,f) -defined the carrier of (g,f) -valued Function-like V21( the carrier' of (g,f), the carrier of (g,f)) Element of bool [: the carrier' of (g,f), the carrier of (g,f):]
the carrier' of (g,f) is non empty set
[: the carrier' of (g,f), the carrier of (g,f):] is non empty Relation-like set
bool [: the carrier' of (g,f), the carrier of (g,f):] is non empty set
the Source of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
[: the carrier' of g, the carrier of g:] is non empty Relation-like set
bool [: the carrier' of g, the carrier of g:] is non empty set
the Source of g | the carrier' of f is Relation-like the carrier' of f -defined the carrier' of g -defined the carrier of g -valued Function-like Element of bool [: the carrier' of g, the carrier of g:]
the Source of (f,g) is Relation-like the carrier' of (f,g) -defined the carrier of (f,g) -valued Function-like V21( the carrier' of (f,g), the carrier of (f,g)) Element of bool [: the carrier' of (f,g), the carrier of (f,g):]
[: the carrier' of (f,g), the carrier of (f,g):] is non empty Relation-like set
bool [: the carrier' of (f,g), the carrier of (f,g):] is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f | the carrier' of g is Relation-like the carrier' of f -defined the carrier' of g -defined the carrier' of f -defined the carrier of f -valued Function-like Element of bool [: the carrier' of f, the carrier of f:]
the Target of (g,f) is Relation-like the carrier' of (g,f) -defined the carrier of (g,f) -valued Function-like V21( the carrier' of (g,f), the carrier of (g,f)) Element of bool [: the carrier' of (g,f), the carrier of (g,f):]
the Target of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
the Target of g | the carrier' of f is Relation-like the carrier' of f -defined the carrier' of g -defined the carrier of g -valued Function-like Element of bool [: the carrier' of g, the carrier of g:]
the Target of (f,g) is Relation-like the carrier' of (f,g) -defined the carrier of (f,g) -valued Function-like V21( the carrier' of (f,g), the carrier of (f,g)) Element of bool [: the carrier' of (f,g), the carrier of (f,g):]
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f | the carrier' of g is Relation-like the carrier' of f -defined the carrier' of g -defined the carrier' of f -defined the carrier of f -valued Function-like Element of bool [: the carrier' of f, the carrier of f:]
the Comp of (g,f) is Relation-like [: the carrier' of (g,f), the carrier' of (g,f):] -defined the carrier' of (g,f) -valued Function-like Element of bool [:[: the carrier' of (g,f), the carrier' of (g,f):], the carrier' of (g,f):]
[: the carrier' of (g,f), the carrier' of (g,f):] is non empty Relation-like set
[:[: the carrier' of (g,f), the carrier' of (g,f):], the carrier' of (g,f):] is non empty Relation-like set
bool [:[: the carrier' of (g,f), the carrier' of (g,f):], the carrier' of (g,f):] is non empty set
the Comp of g is Relation-like [: the carrier' of g, the carrier' of g:] -defined the carrier' of g -valued Function-like Element of bool [:[: the carrier' of g, the carrier' of g:], the carrier' of g:]
[: the carrier' of g, the carrier' of g:] is non empty Relation-like set
[:[: the carrier' of g, the carrier' of g:], the carrier' of g:] is non empty Relation-like set
bool [:[: the carrier' of g, the carrier' of g:], the carrier' of g:] is non empty set
the Comp of g || the carrier' of f is Relation-like Function-like set
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
the Comp of g | [: the carrier' of f, the carrier' of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier' of g, the carrier' of g:] -defined the carrier' of g -valued Function-like set
the Comp of (f,g) is Relation-like [: the carrier' of (f,g), the carrier' of (f,g):] -defined the carrier' of (f,g) -valued Function-like Element of bool [:[: the carrier' of (f,g), the carrier' of (f,g):], the carrier' of (f,g):]
[: the carrier' of (f,g), the carrier' of (f,g):] is non empty Relation-like set
[:[: the carrier' of (f,g), the carrier' of (f,g):], the carrier' of (f,g):] is non empty Relation-like set
bool [:[: the carrier' of (f,g), the carrier' of (f,g):], the carrier' of (f,g):] is non empty set
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
the Comp of f || the carrier' of g is Relation-like Function-like set
the Comp of f | [: the carrier' of g, the carrier' of g:] is Relation-like [: the carrier' of g, the carrier' of g:] -defined [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like set
the carrier' of C is non empty set
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 | the carrier' of f is Relation-like the carrier' of f -defined the carrier' of C -defined the carrier of C -valued Function-like Element of bool [: the carrier' of C, the carrier of C:]
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C | the carrier' of f is Relation-like the carrier' of f -defined the carrier' of C -defined the carrier of C -valued Function-like Element of bool [: the carrier' of C, the carrier of C:]
the Source of C | the carrier' of g is Relation-like the carrier' of g -defined the carrier' of C -defined the carrier of C -valued Function-like Element of bool [: the carrier' of C, the carrier of C:]
the Target of C | the carrier' of g is Relation-like the carrier' of g -defined the carrier' of C -defined the carrier of C -valued Function-like Element of bool [: the carrier' of C, the carrier of C:]
the Source of C | ( the carrier' of f /\ the carrier' of g) is Relation-like the carrier' of f /\ the carrier' of g -defined the carrier' of C -defined the carrier of C -valued Function-like Element of bool [: the carrier' of C, the carrier of C:]
the Target of C | ( the carrier' of f /\ the carrier' of g) is Relation-like the carrier' of f /\ the carrier' of g -defined the carrier' of C -defined the carrier of C -valued Function-like Element of bool [: the carrier' of C, the carrier of C:]
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
the Comp of C || the carrier' of f is Relation-like Function-like set
the Comp of C | [: the carrier' of f, the carrier' of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like set
( the Comp of C || the carrier' of f) || the carrier' of g is Relation-like Function-like set
( the Comp of C || the carrier' of f) | [: the carrier' of g, the carrier' of g:] is Relation-like Function-like set
[: the carrier' of f, the carrier' of f:] /\ [: the carrier' of g, the carrier' of g:] is Relation-like set
the Comp of C | ([: the carrier' of f, the carrier' of f:] /\ [: the carrier' of g, the carrier' of g:]) is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier' of f, the carrier' of f:] /\ [: the carrier' of g, the carrier' of g:] -defined [: 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 Comp of C || the carrier' of g is Relation-like Function-like set
the Comp of C | [: the carrier' of g, the carrier' of g:] is Relation-like [: the carrier' of g, the carrier' of g:] -defined [: the carrier' of C, the carrier' of C:] -defined the carrier' of C -valued Function-like set
( the Comp of C || the carrier' of g) || the carrier' of f is Relation-like Function-like set
( the Comp of C || the carrier' of g) | [: the carrier' of f, the carrier' of f:] is Relation-like Function-like set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
f is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
the carrier of f is non empty set
g is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
the carrier of g is non empty set
(f,g) is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of f /\ the carrier of g is set
(g,f) is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
A1 is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
the carrier of A1 is non empty set
A2 is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
the carrier of A2 is non empty set
the carrier of A1 /\ the carrier of A2 is set
the carrier' of A1 is non empty set
the carrier' of A2 is non empty set
the carrier' of A1 /\ the carrier' of A2 is set
A3 is non empty set
the Element of A3 is Element of A3
(A1,A2) is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of (A1,A2) is non empty set
the carrier' of (A1,A2) is non empty set
the Source of (A1,A2) is Relation-like the carrier' of (A1,A2) -defined the carrier of (A1,A2) -valued Function-like V21( the carrier' of (A1,A2), the carrier of (A1,A2)) Element of bool [: the carrier' of (A1,A2), the carrier of (A1,A2):]
[: the carrier' of (A1,A2), the carrier of (A1,A2):] is non empty Relation-like set
bool [: the carrier' of (A1,A2), the carrier of (A1,A2):] is non empty set
the Source of A1 is Relation-like the carrier' of A1 -defined the carrier of A1 -valued Function-like V21( the carrier' of A1, the carrier of A1) Element of bool [: the carrier' of A1, the carrier of A1:]
[: the carrier' of A1, the carrier of A1:] is non empty Relation-like set
bool [: the carrier' of A1, the carrier of A1:] is non empty set
the Source of A1 | the carrier' of A2 is Relation-like the carrier' of A1 -defined the carrier' of A2 -defined the carrier' of A1 -defined the carrier of A1 -valued Function-like Element of bool [: the carrier' of A1, the carrier of A1:]
the Target of (A1,A2) is Relation-like the carrier' of (A1,A2) -defined the carrier of (A1,A2) -valued Function-like V21( the carrier' of (A1,A2), the carrier of (A1,A2)) Element of bool [: the carrier' of (A1,A2), the carrier of (A1,A2):]
the Target of A1 is Relation-like the carrier' of A1 -defined the carrier of A1 -valued Function-like V21( the carrier' of A1, the carrier of A1) Element of bool [: the carrier' of A1, the carrier of A1:]
the Target of A1 | the carrier' of A2 is Relation-like the carrier' of A1 -defined the carrier' of A2 -defined the carrier' of A1 -defined the carrier of A1 -valued Function-like Element of bool [: the carrier' of A1, the carrier of A1:]
the Comp of (A1,A2) is Relation-like [: the carrier' of (A1,A2), the carrier' of (A1,A2):] -defined the carrier' of (A1,A2) -valued Function-like Element of bool [:[: the carrier' of (A1,A2), the carrier' of (A1,A2):], the carrier' of (A1,A2):]
[: the carrier' of (A1,A2), the carrier' of (A1,A2):] is non empty Relation-like set
[:[: the carrier' of (A1,A2), the carrier' of (A1,A2):], the carrier' of (A1,A2):] is non empty Relation-like set
bool [:[: the carrier' of (A1,A2), the carrier' of (A1,A2):], the carrier' of (A1,A2):] is non empty set
the Comp of A1 is Relation-like [: the carrier' of A1, the carrier' of A1:] -defined the carrier' of A1 -valued Function-like Element of bool [:[: the carrier' of A1, the carrier' of A1:], the carrier' of A1:]
[: the carrier' of A1, the carrier' of A1:] is non empty Relation-like set
[:[: the carrier' of A1, the carrier' of A1:], the carrier' of A1:] is non empty Relation-like set
bool [:[: the carrier' of A1, the carrier' of A1:], the carrier' of A1:] is non empty set
the Comp of A1 || the carrier' of A2 is Relation-like Function-like set
[: the carrier' of A2, the carrier' of A2:] is non empty Relation-like set
the Comp of A1 | [: the carrier' of A2, the carrier' of A2:] is Relation-like [: the carrier' of A2, the carrier' of A2:] -defined [: the carrier' of A1, the carrier' of A1:] -defined the carrier' of A1 -valued Function-like set
dom the Source of A1 is Element of bool the carrier' of A1
bool the carrier' of A1 is non empty set
the Source of A1 | (dom the Source of A1) is Relation-like the carrier' of A1 -defined dom the Source of A1 -defined the carrier' of A1 -defined the carrier of A1 -valued Function-like Element of bool [: the carrier' of A1, the carrier of A1:]
the Source of A1 | the carrier' of (A1,A2) is Relation-like the carrier' of A1 -defined the carrier' of (A1,A2) -defined the carrier' of A1 -defined the carrier of A1 -valued Function-like Element of bool [: the carrier' of A1, the carrier of A1:]
dom the Target of A1 is Element of bool the carrier' of A1
the Target of A1 | (dom the Target of A1) is Relation-like the carrier' of A1 -defined dom the Target of A1 -defined the carrier' of A1 -defined the carrier of A1 -valued Function-like Element of bool [: the carrier' of A1, the carrier of A1:]
the Target of A1 | the carrier' of (A1,A2) is Relation-like the carrier' of A1 -defined the carrier' of (A1,A2) -defined the carrier' of A1 -defined the carrier of A1 -valued Function-like Element of bool [: the carrier' of A1, the carrier of A1:]
G is Element of the carrier of A1
id G is Morphism of G,G
the carrier of C is non empty set
m is Element of the carrier of C
id m is Morphism of m,m
FG is Element of the carrier of A2
id FG is Morphism of FG,FG
the Comp of A1 || the carrier' of A1 is Relation-like Function-like set
the Comp of A1 | [: the carrier' of A1, the carrier' of A1:] is Relation-like [: the carrier' of A1, the carrier' of A1:] -defined [: the carrier' of A1, the carrier' of A1:] -defined the carrier' of A1 -valued Function-like set
[: the carrier' of A1, the carrier' of A1:] /\ [: the carrier' of A2, the carrier' of A2:] is Relation-like set
the Comp of A1 | ([: the carrier' of A1, the carrier' of A1:] /\ [: the carrier' of A2, the carrier' of A2:]) is Relation-like [: the carrier' of A1, the carrier' of A1:] -defined [: the carrier' of A1, the carrier' of A1:] /\ [: the carrier' of A2, the carrier' of A2:] -defined [: the carrier' of A1, the carrier' of A1:] -defined the carrier' of A1 -valued Function-like Element of bool [:[: the carrier' of A1, the carrier' of A1:], the carrier' of A1:]
the Comp of A1 || the carrier' of (A1,A2) is Relation-like Function-like set
the Comp of A1 | [: the carrier' of (A1,A2), the carrier' of (A1,A2):] is Relation-like [: the carrier' of (A1,A2), the carrier' of (A1,A2):] -defined [: the carrier' of A1, the carrier' of A1:] -defined the carrier' of A1 -valued Function-like set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of f is non empty set
the carrier of f is non empty set
g is Relation-like the carrier' of C -defined the carrier' of f -valued Function-like V21( the carrier' of C, the carrier' of f) Functor of C,f
Obj g is Relation-like the carrier of C -defined the carrier of f -valued Function-like V21( the carrier of C, the carrier of f) Element of bool [: the carrier of C, the carrier of f:]
the carrier of C is non empty set
[: the carrier of C, the carrier of f:] is non empty Relation-like set
bool [: the carrier of C, the carrier of f:] is non empty set
rng (Obj g) is Element of bool the carrier of f
bool the carrier of f is non empty set
rng g is Element of bool the carrier' of f
bool the carrier' of f is non empty set
the Element of the carrier of C is Element of the carrier of C
dom (Obj g) is Element of bool the carrier of C
bool the carrier of C is non empty set
(Obj g) . the Element of the carrier of C is Element of the carrier of f
A2 is non empty set
the Element of the carrier' of C is Element of the carrier' of C
dom g is Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
dom the Source of f is Element of bool the carrier' of f
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
dom the Target of f is Element of bool the carrier' of f
A3 is non empty Element of bool the carrier of f
bool the carrier' of f is non empty Element of bool (bool the carrier' of f)
bool (bool the carrier' of f) is non empty set
G is set
{ (Hom (b<sub>1</sub>,b<sub>2</sub>)) where b<sub>1</sub>, b<sub>2</sub> is Element of the carrier of f : ( b<sub>1</sub> in A3 & b<sub>2</sub> in A3 ) } is set
union { (Hom (b<sub>1</sub>,b<sub>2</sub>)) where b<sub>1</sub>, b<sub>2</sub> is Element of the carrier of f : ( b<sub>1</sub> in A3 & b<sub>2</sub> in A3 ) } is set
m is non empty Element of bool the carrier' of f
[:m,A3:] is non empty Relation-like set
bool [:m,A3:] is non empty set
the Source of f | m is Relation-like the carrier' of f -defined m -defined the carrier' of f -defined the carrier of f -valued Function-like Element of bool [: the carrier' of f, the carrier of f:]
the Target of f | m is Relation-like the carrier' of f -defined m -defined the carrier' of f -defined the carrier of f -valued Function-like Element of bool [: the carrier' of f, the carrier of f:]
[:m,m:] is non empty Relation-like the carrier' of f -defined the carrier' of f -valued Element of bool [: the carrier' of f, the carrier' of f:]
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier' of f:] is non empty set
[:[:m,m:],m:] is non empty Relation-like set
bool [:[:m,m:],m:] is non empty set
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
the Comp of f || m is Relation-like Function-like set
[:m,m:] is non empty Relation-like set
the Comp of f | [:m,m:] is Relation-like [:m,m:] -defined [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like set
g1 is Relation-like m -defined A3 -valued Function-like V21(m,A3) Element of bool [:m,A3:]
a2 is Relation-like m -defined A3 -valued Function-like V21(m,A3) Element of bool [:m,A3:]
b2 is Relation-like [:m,m:] -defined m -valued Function-like Element of bool [:[:m,m:],m:]
CatStr(# A3,m,g1,a2,b2 #) is non empty non void V58() strict CatStr
g2 is set
ha1 is set
g . ha1 is set
ha2 is Element of the carrier' of C
dom ha2 is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . ha2 is Element of the carrier of C
(Obj g) . (dom ha2) is Element of the carrier of f
cod ha2 is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . ha2 is Element of the carrier of C
(Obj g) . (cod ha2) is Element of the carrier of f
g . ha2 is Element of the carrier' of f
dom (g . ha2) is Element of the carrier of f
the Source of f . (g . ha2) is Element of the carrier of f
cod (g . ha2) is Element of the carrier of f
the Target of f . (g . ha2) is Element of the carrier of f
Hom ((dom (g . ha2)),(cod (g . ha2))) is Element of bool the carrier' of f
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of f : ( dom b<sub>1</sub> = dom (g . ha2) & cod b<sub>1</sub> = cod (g . ha2) ) } is set
meet G is set
ha1 is set
ha1 is set
g . the Element of the carrier' of C is Element of the carrier' of f
ha1 is non empty set
ha2 is set
ha2 is non empty Element of bool the carrier' of f
the Source of f | ha2 is Relation-like the carrier' of f -defined ha2 -defined the carrier' of f -defined the carrier of f -valued Function-like Element of bool [: the carrier' of f, the carrier of f:]
the Target of f | ha2 is Relation-like the carrier' of f -defined ha2 -defined the carrier' of f -defined the carrier of f -valued Function-like Element of bool [: the carrier' of f, the carrier of f:]
the Comp of f || ha2 is Relation-like Function-like set
[:ha2,ha2:] is non empty Relation-like set
the Comp of f | [:ha2,ha2:] is Relation-like [:ha2,ha2:] -defined [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like set
dom ( the Source of f | ha2) is Element of bool ha2
bool ha2 is non empty set
rng ( the Source of f | ha2) is Element of bool the carrier of f
F is set
G is set
( the Source of f | ha2) . G is set
COMP is Element of the carrier' of f
T is set
E is Element of the carrier of f
a is Element of the carrier of f
Hom (E,a) is Element of bool the carrier' of f
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of f : ( dom b<sub>1</sub> = E & cod b<sub>1</sub> = a ) } is set
dom COMP is Element of the carrier of f
the Source of f . COMP is Element of the carrier of f
[:ha2,A3:] is non empty Relation-like set
bool [:ha2,A3:] is non empty set
dom ( the Target of f | ha2) is Element of bool ha2
rng ( the Target of f | ha2) is Element of bool the carrier of f
G is set
COMP is set
( the Target of f | ha2) . COMP is set
T is Element of the carrier' of f
E is set
a is Element of the carrier of f
a9 is Element of the carrier of f
Hom (a,a9) is Element of bool the carrier' of f
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of f : ( dom b<sub>1</sub> = a & cod b<sub>1</sub> = a9 ) } is set
cod T is Element of the carrier of f
the Target of f . T is Element of the carrier of f
proj1 ( the Comp of f || ha2) is set
[:ha2,ha2:] is non empty Relation-like the carrier' of f -defined the carrier' of f -valued Element of bool [: the carrier' of f, the carrier' of f:]
proj2 ( the Comp of f || ha2) is set
COMP is set
T is set
( the Comp of f || ha2) . T is set
T `1 is set
T `2 is set
E is Element of ha2
a is Element of ha2
[E,a] is V18() Element of the carrier' of [:f,f:]
[:f,f:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of f, the carrier of f:] is non empty Relation-like set
[: the Source of f, the Source of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier of f, the carrier of f:] -valued Function-like V21([: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]) Element of bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:]
[:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:] is non empty set
[: the Target of f, the Target of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier of f, the carrier of f:] -valued Function-like V21([: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]) Element of bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:]
K222( the carrier' of f, the carrier' of f, the Comp of f, the Comp of f) is Relation-like [:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:] -defined [: the carrier' of f, the carrier' of f:] -valued Function-like Element of bool [:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:]
[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:] is non empty Relation-like set
[:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:] is non empty Relation-like set
bool [:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:] is non empty set
CatStr(# [: the carrier of f, the carrier of f:],[: the carrier' of f, the carrier' of f:],[: the Source of f, the Source of f:],[: the Target of f, the Target of f:],K222( the carrier' of f, the carrier' of f, the Comp of f, the Comp of f) #) is non empty non void V58() strict CatStr
the carrier' of [:f,f:] is non empty set
{E,a} is non empty set
{E} is non empty set
{{E,a},{E}} is non empty set
a9 is set
b is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of b is non empty set
the carrier' of b is non empty set
dom the Comp of f is Relation-like the carrier' of f -defined the carrier' of f -valued Element of bool [: the carrier' of f, the carrier' of f:]
(dom the Comp of f) /\ [:ha2,ha2:] is Relation-like the carrier' of f -defined the carrier' of f -valued Element of bool [: the carrier' of f, the carrier' of f:]
dom E is Element of the carrier of f
the Source of f . E is Element of the carrier of f
cod a is Element of the carrier of f
the Target of f . a is Element of the carrier of f
y1 is Element of the carrier' of b
dom y1 is Element of the carrier of b
the Source of b is Relation-like the carrier' of b -defined the carrier of b -valued Function-like V21( the carrier' of b, the carrier of b) 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 . y1 is Element of the carrier of b
y2 is Element of the carrier' of b
cod y2 is Element of the carrier of b
the Target of b is Relation-like the carrier' of b -defined the carrier of b -valued Function-like V21( the carrier' of b, the carrier of b) Element of bool [: the carrier' of b, the carrier of b:]
the Target of b . y2 is Element of the carrier of b
[: the carrier' of b, the carrier' of b:] is non empty Relation-like 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:], 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
dom the Comp of b is Relation-like the carrier' of b -defined the carrier' of b -valued Element of bool [: the carrier' of b, the carrier' of b:]
bool [: the carrier' of b, the carrier' of b:] is non empty set
the Comp of b . T is set
the Comp of f . T is set
rng the Comp of b is Element of bool the carrier' of b
bool the carrier' of b is non empty set
[:[:ha2,ha2:],ha2:] is non empty Relation-like set
bool [:[:ha2,ha2:],ha2:] is non empty set
T is Element of the carrier of f
id T is Morphism of T,T
E is set
a is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of a is non empty set
the carrier' of a is non empty set
a is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of a is non empty set
the carrier' of a is non empty set
a9 is Element of the carrier of a
id a9 is Morphism of a9,a9
F is Relation-like ha2 -defined A3 -valued Function-like V21(ha2,A3) Element of bool [:ha2,A3:]
G is Relation-like ha2 -defined A3 -valued Function-like V21(ha2,A3) Element of bool [:ha2,A3:]
COMP is Relation-like [:ha2,ha2:] -defined ha2 -valued Function-like Element of bool [:[:ha2,ha2:],ha2:]
CatStr(# A3,ha2,F,G,COMP #) is non empty non void V58() strict CatStr
T is non empty non void V58() strict Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of T is non empty set
the carrier' of T is non empty set
E is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of E is non empty set
the carrier' of E is non empty set
the Comp of T is Relation-like [: the carrier' of T, the carrier' of T:] -defined the carrier' of T -valued Function-like Element of bool [:[: the carrier' of T, the carrier' of T:], the carrier' of T:]
[: the carrier' of T, the carrier' of T:] is non empty Relation-like set
[:[: the carrier' of T, the carrier' of T:], the carrier' of T:] is non empty Relation-like set
bool [:[: the carrier' of T, the carrier' of T:], the carrier' of T:] is non empty set
the Comp of E is Relation-like [: the carrier' of E, the carrier' of E:] -defined the carrier' of E -valued Function-like Element of bool [:[: the carrier' of E, the carrier' of E:], the carrier' of E:]
[: the carrier' of E, the carrier' of E:] is non empty Relation-like set
[:[: the carrier' of E, the carrier' of E:], the carrier' of E:] is non empty Relation-like set
bool [:[: the carrier' of E, the carrier' of E:], the carrier' of E:] is non empty set
a is Element of the carrier of T
b is Element of the carrier of E
a9 is Element of the carrier of T
y1 is Element of the carrier of E
Hom (a,a9) is Element of bool the carrier' of T
bool the carrier' of T is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of T : ( dom b<sub>1</sub> = a & cod b<sub>1</sub> = a9 ) } is set
Hom (b,y1) is Element of bool the carrier' of E
bool the carrier' of E is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of E : ( dom b<sub>1</sub> = b & cod b<sub>1</sub> = y1 ) } is set
y2 is set
z1 is Element of the carrier' of T
dom z1 is Element of the carrier of T
the Source of T is Relation-like the carrier' of T -defined the carrier of T -valued Function-like V21( the carrier' of T, the carrier of T) Element of bool [: the carrier' of T, the carrier of T:]
[: the carrier' of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier' of T, the carrier of T:] is non empty set
the Source of T . z1 is Element of the carrier of T
cod z1 is Element of the carrier of T
the Target of T is Relation-like the carrier' of T -defined the carrier of T -valued Function-like V21( the carrier' of T, the carrier of T) Element of bool [: the carrier' of T, the carrier of T:]
the Target of T . z1 is Element of the carrier of T
z2 is Element of the carrier' of f
dom z2 is Element of the carrier of f
the Source of f . z2 is Element of the carrier of f
cod z2 is Element of the carrier of f
the Target of f . z2 is Element of the carrier of f
f is Element of the carrier' of E
dom f is Element of the carrier of E
the Source of E is Relation-like the carrier' of E -defined the carrier of E -valued Function-like V21( the carrier' of E, the carrier of E) Element of bool [: the carrier' of E, the carrier of E:]
[: the carrier' of E, the carrier of E:] is non empty Relation-like set
bool [: the carrier' of E, the carrier of E:] is non empty set
the Source of E . f is Element of the carrier of E
cod f is Element of the carrier of E
the Target of E is Relation-like the carrier' of E -defined the carrier of E -valued Function-like V21( the carrier' of E, the carrier of E) Element of bool [: the carrier' of E, the carrier of E:]
the Target of E . f is Element of the carrier of E
dom the Comp of T is Relation-like the carrier' of T -defined the carrier' of T -valued Element of bool [: the carrier' of T, the carrier' of T:]
bool [: the carrier' of T, the carrier' of T:] is non empty set
dom the Comp of E is Relation-like the carrier' of E -defined the carrier' of E -valued Element of bool [: the carrier' of E, the carrier' of E:]
bool [: the carrier' of E, the carrier' of E:] is non empty set
a is set
a `1 is set
a `2 is set
a9 is Element of ha2
b is Element of ha2
[a9,b] is V18() Element of the carrier' of [:f,f:]
[:f,f:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of f, the carrier of f:] is non empty Relation-like set
[: the Source of f, the Source of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier of f, the carrier of f:] -valued Function-like V21([: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]) Element of bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:]
[:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:] is non empty set
[: the Target of f, the Target of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier of f, the carrier of f:] -valued Function-like V21([: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]) Element of bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:]
K222( the carrier' of f, the carrier' of f, the Comp of f, the Comp of f) is Relation-like [:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:] -defined [: the carrier' of f, the carrier' of f:] -valued Function-like Element of bool [:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:]
[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:] is non empty Relation-like set
[:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:] is non empty Relation-like set
bool [:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:] is non empty set
CatStr(# [: the carrier of f, the carrier of f:],[: the carrier' of f, the carrier' of f:],[: the Source of f, the Source of f:],[: the Target of f, the Target of f:],K222( the carrier' of f, the carrier' of f, the Comp of f, the Comp of f) #) is non empty non void V58() strict CatStr
the carrier' of [:f,f:] is non empty set
{a9,b} is non empty set
{a9} is non empty set
{{a9,b},{a9}} is non empty set
y1 is Element of the carrier' of T
dom y1 is Element of the carrier of T
the Source of T is Relation-like the carrier' of T -defined the carrier of T -valued Function-like V21( the carrier' of T, the carrier of T) Element of bool [: the carrier' of T, the carrier of T:]
[: the carrier' of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier' of T, the carrier of T:] is non empty set
the Source of T . y1 is Element of the carrier of T
y2 is Element of the carrier' of T
cod y2 is Element of the carrier of T
the Target of T is Relation-like the carrier' of T -defined the carrier of T -valued Function-like V21( the carrier' of T, the carrier of T) Element of bool [: the carrier' of T, the carrier of T:]
the Target of T . y2 is Element of the carrier of T
dom a9 is Element of the carrier of f
the Source of f . a9 is Element of the carrier of f
z1 is Element of the carrier' of E
dom z1 is Element of the carrier of E
the Source of E is Relation-like the carrier' of E -defined the carrier of E -valued Function-like V21( the carrier' of E, the carrier of E) Element of bool [: the carrier' of E, the carrier of E:]
[: the carrier' of E, the carrier of E:] is non empty Relation-like set
bool [: the carrier' of E, the carrier of E:] is non empty set
the Source of E . z1 is Element of the carrier of E
cod b is Element of the carrier of f
the Target of f . b is Element of the carrier of f
z2 is Element of the carrier' of E
cod z2 is Element of the carrier of E
the Target of E is Relation-like the carrier' of E -defined the carrier of E -valued Function-like V21( the carrier' of E, the carrier of E) Element of bool [: the carrier' of E, the carrier of E:]
the Target of E . z2 is Element of the carrier of E
a is set
the Comp of T . a is set
the Comp of f . a is set
the Comp of E . a is set
a is Element of the carrier of T
id a is Morphism of a,a
a9 is Element of the carrier of E
id a9 is Morphism of a9,a9
b is Element of the carrier of f
id b is Morphism of b,b
A1 is non empty non void V58() strict Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of A1 is non empty set
the carrier' of A1 is non empty set
A2 is non empty non void V58() strict Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of A2 is non empty set
the carrier' of A2 is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
the carrier' of f is non empty set
g is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of f
the carrier' of g is non empty set
A1 is Relation-like the carrier' of C -defined the carrier' of f -valued Function-like V21( the carrier' of C, the carrier' of f) Functor of C,f
rng A1 is Element of bool the carrier' of f
bool the carrier' of f is non empty set
dom A1 is Element of bool the carrier' of C
bool the carrier' of C is non empty set
the carrier of C is non empty set
Obj A1 is Relation-like the carrier of C -defined the carrier of f -valued Function-like V21( the carrier of C, the carrier of f) Element of bool [: the carrier of C, the carrier of f:]
the carrier of f is non empty set
[: the carrier of C, the carrier of f:] is non empty Relation-like set
bool [: the carrier of C, the carrier of f:] is non empty set
dom (Obj A1) is Element of bool the carrier of C
bool the carrier of C is non empty set
[: the carrier' of C, the carrier' of g:] is non empty Relation-like set
bool [: the carrier' of C, the carrier' of g:] is non empty set
rng (Obj A1) is Element of bool the carrier of f
bool the carrier of f is non empty set
the carrier of g is non empty set
A3 is set
F is set
(Obj A1) . F is set
G is Element of the carrier of C
id G is Morphism of G,G
A1 . (id G) is Element of the carrier' of f
(Obj A1) . G is Element of the carrier of f
id ((Obj A1) . G) is Morphism of (Obj A1) . G,(Obj A1) . G
dom (id ((Obj A1) . G)) is Element of the carrier of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f . (id ((Obj A1) . G)) is Element of the carrier of f
FG is Element of the carrier' of g
dom FG is Element of the carrier of g
the Source of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
[: the carrier' of g, the carrier of g:] is non empty Relation-like set
bool [: the carrier' of g, the carrier of g:] is non empty set
the Source of g . FG is Element of the carrier of g
A3 is Element of the carrier of C
(Obj A1) . A3 is Element of the carrier of f
F is Element of the carrier of g
A2 is Relation-like the carrier' of C -defined the carrier' of g -valued Function-like V21( the carrier' of C, the carrier' of g) Element of bool [: the carrier' of C, the carrier' of g:]
id A3 is Morphism of A3,A3
A2 . (id A3) is Element of the carrier' of g
id ((Obj A1) . A3) is Morphism of (Obj A1) . A3,(Obj A1) . A3
G is Element of the carrier of g
id G is Morphism of G,G
A3 is Element of the carrier' of C
A1 . A3 is Element of the carrier' of f
dom (A1 . A3) is Element of the carrier of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f . (A1 . A3) is Element of the carrier of f
A2 . A3 is Element of the carrier' of g
dom (A2 . A3) is Element of the carrier of g
the Source of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
[: the carrier' of g, the carrier of g:] is non empty Relation-like set
bool [: the carrier' of g, the carrier of g:] is non empty set
the Source of g . (A2 . A3) is Element of the carrier of g
cod (A1 . A3) is Element of the carrier of f
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f . (A1 . A3) is Element of the carrier of f
cod (A2 . A3) is Element of the carrier of g
the Target of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
the Target of g . (A2 . A3) is Element of the carrier of g
dom A3 is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . A3 is Element of the carrier of C
id (dom A3) is Morphism of dom A3, dom A3
A2 . (id (dom A3)) is Element of the carrier' of g
A1 . (dom A3) is Element of the carrier of f
(Obj A1) . (dom A3) is Element of the carrier of f
id (A1 . (dom A3)) is Morphism of A1 . (dom A3),A1 . (dom A3)
id (dom (A1 . A3)) is Morphism of dom (A1 . A3), dom (A1 . A3)
id (dom (A2 . A3)) is Morphism of dom (A2 . A3), dom (A2 . A3)
cod A3 is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . A3 is Element of the carrier of C
id (cod A3) is Morphism of cod A3, cod A3
A2 . (id (cod A3)) is Element of the carrier' of g
A1 . (cod A3) is Element of the carrier of f
(Obj A1) . (cod A3) is Element of the carrier of f
id (A1 . (cod A3)) is Morphism of A1 . (cod A3),A1 . (cod A3)
id (cod (A1 . A3)) is Morphism of cod (A1 . A3), cod (A1 . A3)
id (cod (A2 . A3)) is Morphism of cod (A2 . A3), cod (A2 . A3)
F is Element of the carrier' of C
dom F is Element of the carrier of C
the Source of C . F is Element of the carrier of C
A3 is Element of the carrier' of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
F (*) A3 is Element of the carrier' of C
A1 . (F (*) A3) is Element of the carrier' of f
A1 . A3 is Element of the carrier' of f
A1 . F is Element of the carrier' of f
(A1 . F) (*) (A1 . A3) is Element of the carrier' of f
dom (A1 . F) is Element of the carrier of f
the Source of f . (A1 . F) is Element of the carrier of f
cod (A1 . A3) is Element of the carrier of f
the Target of f . (A1 . A3) is Element of the carrier of f
A2 . F is Element of the carrier' of g
dom (A2 . F) is Element of the carrier of g
the Source of g . (A2 . F) is Element of the carrier of g
A2 . A3 is Element of the carrier' of g
cod (A2 . A3) is Element of the carrier of g
the Target of g . (A2 . A3) is Element of the carrier of g
A2 . (F (*) A3) is Element of the carrier' of g
(A2 . F) (*) (A2 . A3) is Element of the carrier' of g
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of f is non empty set
g is Relation-like the carrier' of C -defined the carrier' of f -valued Function-like V21( the carrier' of C, the carrier' of f) Functor of C,f
(C,f,g) is non empty non void V58() strict Category-like transitive associative reflexive with_identities Subcategory of f
the carrier' of (C,f,g) is non empty set
rng g is Element of bool the carrier' of f
bool the carrier' of f is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
the carrier' of f is non empty set
g is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of f
the carrier' of g is non empty set
A1 is Relation-like the carrier' of C -defined the carrier' of g -valued Function-like V21( the carrier' of C, the carrier' of g) Functor of C,g
(C,g,A1) is non empty non void V58() strict Category-like transitive associative reflexive with_identities Subcategory of g
A2 is Relation-like the carrier' of C -defined the carrier' of f -valued Function-like V21( the carrier' of C, the carrier' of f) Functor of C,f
(C,f,A2) is non empty non void V58() strict Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of C is non empty set
Obj A1 is Relation-like the carrier of C -defined the carrier of g -valued Function-like V21( the carrier of C, the carrier of g) Element of bool [: the carrier of C, the carrier of g:]
the carrier of g is non empty set
[: the carrier of C, the carrier of g:] is non empty Relation-like set
bool [: the carrier of C, the carrier of g:] is non empty set
dom (Obj A1) is Element of bool the carrier of C
bool the carrier of C is non empty set
Obj A2 is Relation-like the carrier of C -defined the carrier of f -valued Function-like V21( the carrier of C, the carrier of f) Element of bool [: the carrier of C, the carrier of f:]
the carrier of f is non empty set
[: the carrier of C, the carrier of f:] is non empty Relation-like set
bool [: the carrier of C, the carrier of f:] is non empty set
dom (Obj A2) is Element of bool the carrier of C
F is set
G is Element of the carrier of C
(Obj A1) . G is Element of the carrier of g
id G is Morphism of G,G
A2 . (id G) is Element of the carrier' of f
id ((Obj A1) . G) is Morphism of (Obj A1) . G,(Obj A1) . G
FG is Element of the carrier of f
id FG is Morphism of FG,FG
(Obj A2) . F is set
(Obj A1) . F is set
A3 is non empty non void V58() strict Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of A3 is non empty set
rng (Obj A2) is Element of bool the carrier of f
bool the carrier of f is non empty set
rng A2 is Element of bool the carrier' of f
bool the carrier' of f is non empty set
the carrier' of A3 is non empty set
F is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of f
the carrier of F is non empty set
the carrier' of F is non empty set
the Element of the carrier of C is Element of the carrier of C
(Obj A2) . the Element of the carrier of C is Element of the carrier of f
(Obj A1) . the Element of the carrier of C is Element of the carrier of g
the carrier of F /\ the carrier of g is set
(F,g) is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
FG is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of g
the carrier of FG is non empty set
rng (Obj A1) is Element of bool the carrier of g
bool the carrier of g is non empty set
the carrier' of FG is non empty set
the carrier' of F /\ the carrier' of g is set
rng A1 is Element of bool the carrier' of g
bool the carrier' of g is non empty set
C is non empty set
f is Element of C
f is set
0 is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional Element of K158()
1Cat (0,1) is non empty trivial V52() non void 1 -element V58() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{0} is non empty functional set
{1} is non empty set
K262(1,0) is Relation-like {1} -defined {0} -valued Function-like V21({1},{0}) Element of bool [:{1},{0}:]
[:{1},{0}:] is non empty Relation-like set
bool [:{1},{0}:] is non empty set
K261(1,1,1) is Relation-like [:{1},{1}:] -defined {1} -valued Function-like V21([:{1},{1}:],{1}) Element of bool [:[:{1},{1}:],{1}:]
[:{1},{1}:] is non empty Relation-like set
[:[:{1},{1}:],{1}:] is non empty Relation-like set
bool [:[:{1},{1}:],{1}:] is non empty set
CatStr(# {0},{1},K262(1,0),K262(1,0),K261(1,1,1) #) is non empty non void V58() strict CatStr
{(1Cat (0,1))} is non empty set
C is non empty set
f is Element of C
C is non empty () set
f is Element of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
f is Element of the carrier' of C
dom f is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . f is Element of the carrier of C
[(dom f),(cod f)] is V18() Element of [: the carrier of C, the carrier of C:]
[: the carrier of C, the carrier of C:] is non empty Relation-like set
{(dom f),(cod f)} is non empty set
{(dom f)} is non empty set
{{(dom f),(cod f)},{(dom f)}} is non empty set
g is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of g is non empty set
A1 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A1 is non empty set
[g,A1] is V18() set
{g,A1} is non empty set
{g} is non empty set
{{g,A1},{g}} is non empty set
A2 is Relation-like the carrier' of g -defined the carrier' of A1 -valued Function-like V21( the carrier' of g, the carrier' of A1) Functor of g,A1
[[g,A1],A2] is V18() set
{[g,A1],A2} is non empty set
{[g,A1]} is non empty Relation-like Function-like set
{{[g,A1],A2},{[g,A1]}} is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
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
CatStr(# the carrier of C, the carrier' of C, the Source of C, the Target of C, the Comp of C #) is non empty non void V58() strict CatStr
f is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of f is non empty set
the carrier' of f is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
CatStr(# the carrier of f, the carrier' of f, the Source of f, the Target of f, the Comp of f #) is non empty non void V58() strict CatStr
g is Element of the carrier of f
id g is Morphism of g,g
A1 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[A1,A1] is V18() set
{A1,A1} is non empty set
{A1} is non empty set
{{A1,A1},{A1}} is non empty set
id A1 is Relation-like the carrier' of A1 -defined the carrier' of A1 -valued Function-like V21( the carrier' of A1, the carrier' of A1) Functor of A1,A1
the carrier' of A1 is non empty set
id the carrier' of A1 is non empty Relation-like the carrier' of A1 -defined the carrier' of A1 -valued Function-like one-to-one total Element of bool [: the carrier' of A1, the carrier' of A1:]
[: the carrier' of A1, the carrier' of A1:] is non empty Relation-like set
bool [: the carrier' of A1, the carrier' of A1:] is non empty set
[[A1,A1],(id A1)] is V18() set
{[A1,A1],(id A1)} is non empty set
{[A1,A1]} is non empty Relation-like Function-like set
{{[A1,A1],(id A1)},{[A1,A1]}} is non empty set
A2 is Element of the carrier of C
id A2 is Morphism of A2,A2
g is Element of the carrier' of f
A2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
dom g is Element of the carrier of f
the Source of f . g is Element of the carrier of f
A3 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
cod g is Element of the carrier of f
the Target of f . g is Element of the carrier of f
A1 is Element of the carrier' of C
dom A1 is Element of the carrier of C
the Source of C . A1 is Element of the carrier of C
cod A1 is Element of the carrier of C
the Target of C . A1 is Element of the carrier of C
the carrier' of A2 is non empty set
the carrier' of A3 is non empty set
[A2,A3] is V18() set
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
g is Element of the carrier' of f
A1 is Element of the carrier' of f
A1 (*) g is Element of the carrier' of f
F is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of G is non empty set
FG is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of FG is non empty set
[F,G] is V18() set
{F,G} is non empty set
{F} is non empty set
{{F,G},{F}} is non empty set
[G,FG] is V18() set
{G,FG} is non empty set
{G} is non empty set
{{G,FG},{G}} is non empty set
[F,FG] is V18() set
{F,FG} is non empty set
{{F,FG},{F}} is non empty set
m is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like V21( the carrier' of F, the carrier' of G) Functor of F,G
[[F,G],m] is V18() set
{[F,G],m} is non empty set
{[F,G]} is non empty Relation-like Function-like set
{{[F,G],m},{[F,G]}} is non empty set
g1 is Relation-like the carrier' of G -defined the carrier' of FG -valued Function-like V21( the carrier' of G, the carrier' of FG) Functor of G,FG
[[G,FG],g1] is V18() set
{[G,FG],g1} is non empty set
{[G,FG]} is non empty Relation-like Function-like set
{{[G,FG],g1},{[G,FG]}} is non empty set
g1 * m is Relation-like the carrier' of F -defined the carrier' of F -defined the carrier' of FG -valued the carrier' of FG -valued Function-like V21( the carrier' of F, the carrier' of FG) Functor of F,FG
[[F,FG],(g1 * m)] is V18() set
{[F,FG],(g1 * m)} is non empty set
{[F,FG]} is non empty Relation-like Function-like set
{{[F,FG],(g1 * m)},{[F,FG]}} is non empty set
A2 is Element of the carrier' of C
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
A3 is Element of the carrier' of C
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
a2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of a2 is non empty set
b2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of b2 is non empty set
[a2,b2] is V18() set
{a2,b2} is non empty set
{a2} is non empty set
{{a2,b2},{a2}} is non empty set
g2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of g2 is non empty set
ha1 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ha1 is non empty set
[g2,ha1] is V18() set
{g2,ha1} is non empty set
{g2} is non empty set
{{g2,ha1},{g2}} is non empty set
A1 `11 is set
ha2 is Relation-like the carrier' of g2 -defined the carrier' of ha1 -valued Function-like V21( the carrier' of g2, the carrier' of ha1) Functor of g2,ha1
[[g2,ha1],ha2] is V18() set
{[g2,ha1],ha2} is non empty set
{[g2,ha1]} is non empty Relation-like Function-like set
{{[g2,ha1],ha2},{[g2,ha1]}} is non empty set
g `12 is set
ha2 is Relation-like the carrier' of a2 -defined the carrier' of b2 -valued Function-like V21( the carrier' of a2, the carrier' of b2) Functor of a2,b2
[[a2,b2],ha2] is V18() set
{[a2,b2],ha2} is non empty set
{[a2,b2]} is non empty Relation-like Function-like set
{{[a2,b2],ha2},{[a2,b2]}} is non empty set
[A3,A2] is V18() Element of the carrier' of [:C,C:]
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:C,C:] is non empty set
{A3,A2} is non empty set
{A3} is non empty set
{{A3,A2},{A3}} is non empty set
dom the Comp of C is Relation-like the carrier' of C -defined the carrier' of C -valued Element of bool [: the carrier' of C, the carrier' of C:]
bool [: the carrier' of C, the carrier' of C:] is non empty set
the Comp of f . (A1,g) is set
[A1,g] is V18() set
{A1,g} is non empty set
{A1} is non empty set
{{A1,g},{A1}} is non empty set
the Comp of f . [A1,g] is set
A3 (*) A2 is Element of the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[C,C] is V18() set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
id C is Relation-like the carrier' of C -defined the carrier' of C -valued Function-like V21( the carrier' of C, the carrier' of C) Functor of C,C
the carrier' of C is non empty set
id the carrier' of C is non empty Relation-like the carrier' of C -defined the carrier' of C -valued Function-like one-to-one 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
[[C,C],(id C)] is V18() set
{[C,C],(id C)} is non empty set
{[C,C]} is non empty Relation-like Function-like set
{{[C,C],(id C)},{[C,C]}} is non empty set
1Cat (C,[[C,C],(id C)]) is non empty trivial V52() non void 1 -element V58() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{[[C,C],(id C)]} is non empty Relation-like Function-like set
K262([[C,C],(id C)],C) is Relation-like {[[C,C],(id C)]} -defined {C} -valued Function-like V21({[[C,C],(id C)]},{C}) Element of bool [:{[[C,C],(id C)]},{C}:]
[:{[[C,C],(id C)]},{C}:] is non empty Relation-like set
bool [:{[[C,C],(id C)]},{C}:] is non empty set
K261([[C,C],(id C)],[[C,C],(id C)],[[C,C],(id C)]) is Relation-like [:{[[C,C],(id C)]},{[[C,C],(id C)]}:] -defined {[[C,C],(id C)]} -valued Function-like V21([:{[[C,C],(id C)]},{[[C,C],(id C)]}:],{[[C,C],(id C)]}) Element of bool [:[:{[[C,C],(id C)]},{[[C,C],(id C)]}:],{[[C,C],(id C)]}:]
[:{[[C,C],(id C)]},{[[C,C],(id C)]}:] is non empty Relation-like set
[:[:{[[C,C],(id C)]},{[[C,C],(id C)]}:],{[[C,C],(id C)]}:] is non empty Relation-like set
bool [:[:{[[C,C],(id C)]},{[[C,C],(id C)]}:],{[[C,C],(id C)]}:] is non empty set
CatStr(# {C},{[[C,C],(id C)]},K262([[C,C],(id C)],C),K262([[C,C],(id C)],C),K261([[C,C],(id C)],[[C,C],(id C)],[[C,C],(id C)]) #) is non empty non void V58() strict CatStr
the carrier of (1Cat (C,[[C,C],(id C)])) is non empty trivial V34() set
A1 is Element of the carrier of (1Cat (C,[[C,C],(id C)]))
the carrier' of (1Cat (C,[[C,C],(id C)])) is non empty trivial set
A1 is Element of the carrier of (1Cat (C,[[C,C],(id C)]))
A2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
id A1 is Morphism of A1,A1
[A2,A2] is V18() set
{A2,A2} is non empty set
{A2} is non empty set
{{A2,A2},{A2}} is non empty set
id A2 is Relation-like the carrier' of A2 -defined the carrier' of A2 -valued Function-like V21( the carrier' of A2, the carrier' of A2) Functor of A2,A2
the carrier' of A2 is non empty set
id the carrier' of A2 is non empty Relation-like the carrier' of A2 -defined the carrier' of A2 -valued Function-like one-to-one total Element of bool [: the carrier' of A2, the carrier' of A2:]
[: the carrier' of A2, the carrier' of A2:] is non empty Relation-like set
bool [: the carrier' of A2, the carrier' of A2:] is non empty set
[[A2,A2],(id A2)] is V18() set
{[A2,A2],(id A2)} is non empty set
{[A2,A2]} is non empty Relation-like Function-like set
{{[A2,A2],(id A2)},{[A2,A2]}} is non empty set
A2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
A1 is Element of the carrier' of (1Cat (C,[[C,C],(id C)]))
dom A1 is Element of the carrier of (1Cat (C,[[C,C],(id C)]))
the Source of (1Cat (C,[[C,C],(id C)])) is Relation-like the carrier' of (1Cat (C,[[C,C],(id C)])) -defined the carrier of (1Cat (C,[[C,C],(id C)])) -valued Function-like V21( the carrier' of (1Cat (C,[[C,C],(id C)])), the carrier of (1Cat (C,[[C,C],(id C)]))) Element of bool [: the carrier' of (1Cat (C,[[C,C],(id C)])), the carrier of (1Cat (C,[[C,C],(id C)])):]
[: the carrier' of (1Cat (C,[[C,C],(id C)])), the carrier of (1Cat (C,[[C,C],(id C)])):] is non empty Relation-like set
bool [: the carrier' of (1Cat (C,[[C,C],(id C)])), the carrier of (1Cat (C,[[C,C],(id C)])):] is non empty set
the Source of (1Cat (C,[[C,C],(id C)])) . A1 is Element of the carrier of (1Cat (C,[[C,C],(id C)]))
A3 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
cod A1 is Element of the carrier of (1Cat (C,[[C,C],(id C)]))
the Target of (1Cat (C,[[C,C],(id C)])) is Relation-like the carrier' of (1Cat (C,[[C,C],(id C)])) -defined the carrier of (1Cat (C,[[C,C],(id C)])) -valued Function-like V21( the carrier' of (1Cat (C,[[C,C],(id C)])), the carrier of (1Cat (C,[[C,C],(id C)]))) Element of bool [: the carrier' of (1Cat (C,[[C,C],(id C)])), the carrier of (1Cat (C,[[C,C],(id C)])):]
the Target of (1Cat (C,[[C,C],(id C)])) . A1 is Element of the carrier of (1Cat (C,[[C,C],(id C)]))
the carrier' of A2 is non empty set
the carrier' of A3 is non empty set
F is Relation-like the carrier' of A2 -defined the carrier' of A3 -valued Function-like V21( the carrier' of A2, the carrier' of A3) Functor of A2,A3
[A2,A3] is V18() set
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
G is Relation-like the carrier' of A2 -defined the carrier' of A3 -valued Function-like V21( the carrier' of A2, the carrier' of A3) Functor of A2,A3
[[A2,A3],G] is V18() set
{[A2,A3],G} is non empty set
{[A2,A3]} is non empty Relation-like Function-like set
{{[A2,A3],G},{[A2,A3]}} is non empty set
A1 is Element of the carrier' of (1Cat (C,[[C,C],(id C)]))
A2 is Element of the carrier' of (1Cat (C,[[C,C],(id C)]))
A2 (*) A1 is Element of the carrier' of (1Cat (C,[[C,C],(id C)]))
A3 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A3 is non empty set
F is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of G is non empty set
[A3,F] is V18() set
{A3,F} is non empty set
{A3} is non empty set
{{A3,F},{A3}} is non empty set
[F,G] is V18() set
{F,G} is non empty set
{F} is non empty set
{{F,G},{F}} is non empty set
[A3,G] is V18() set
{A3,G} is non empty set
{{A3,G},{A3}} is non empty set
FG is Relation-like the carrier' of A3 -defined the carrier' of F -valued Function-like V21( the carrier' of A3, the carrier' of F) Functor of A3,F
[[A3,F],FG] is V18() set
{[A3,F],FG} is non empty set
{[A3,F]} is non empty Relation-like Function-like set
{{[A3,F],FG},{[A3,F]}} is non empty set
m is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like V21( the carrier' of F, the carrier' of G) Functor of F,G
[[F,G],m] is V18() set
{[F,G],m} is non empty set
{[F,G]} is non empty Relation-like Function-like set
{{[F,G],m},{[F,G]}} is non empty set
m * FG is Relation-like the carrier' of A3 -defined the carrier' of A3 -defined the carrier' of G -valued the carrier' of G -valued Function-like V21( the carrier' of A3, the carrier' of G) Functor of A3,G
[[A3,G],(m * FG)] is V18() set
{[A3,G],(m * FG)} is non empty set
{[A3,G]} is non empty Relation-like Function-like set
{{[A3,G],(m * FG)},{[A3,G]}} is non empty set
0 is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional Element of K158()
1Cat (0,1) is non empty trivial V52() non void 1 -element V58() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{0} is non empty functional set
{1} is non empty set
K262(1,0) is Relation-like {1} -defined {0} -valued Function-like V21({1},{0}) Element of bool [:{1},{0}:]
[:{1},{0}:] is non empty Relation-like set
bool [:{1},{0}:] is non empty set
K261(1,1,1) is Relation-like [:{1},{1}:] -defined {1} -valued Function-like V21([:{1},{1}:],{1}) Element of bool [:[:{1},{1}:],{1}:]
[:{1},{1}:] is non empty Relation-like set
[:[:{1},{1}:],{1}:] is non empty Relation-like set
bool [:[:{1},{1}:],{1}:] is non empty set
CatStr(# {0},{1},K262(1,0),K262(1,0),K261(1,1,1) #) is non empty non void V58() strict CatStr
[(1Cat (0,1)),(1Cat (0,1))] is V18() set
{(1Cat (0,1)),(1Cat (0,1))} is non empty set
{(1Cat (0,1))} is non empty set
{{(1Cat (0,1)),(1Cat (0,1))},{(1Cat (0,1))}} is non empty set
id (1Cat (0,1)) is Relation-like the carrier' of (1Cat (0,1)) -defined the carrier' of (1Cat (0,1)) -valued Function-like V21( the carrier' of (1Cat (0,1)), the carrier' of (1Cat (0,1))) Functor of 1Cat (0,1), 1Cat (0,1)
the carrier' of (1Cat (0,1)) is non empty trivial set
id the carrier' of (1Cat (0,1)) is non empty Relation-like the carrier' of (1Cat (0,1)) -defined the carrier' of (1Cat (0,1)) -valued Function-like one-to-one total Element of bool [: the carrier' of (1Cat (0,1)), the carrier' of (1Cat (0,1)):]
[: the carrier' of (1Cat (0,1)), the carrier' of (1Cat (0,1)):] is non empty Relation-like set
bool [: the carrier' of (1Cat (0,1)), the carrier' of (1Cat (0,1)):] is non empty set
[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))] is V18() set
{[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))} is non empty set
{[(1Cat (0,1)),(1Cat (0,1))]} is non empty Relation-like Function-like set
{{[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))},{[(1Cat (0,1)),(1Cat (0,1))]}} is non empty set
1Cat ((1Cat (0,1)),[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]) is non empty trivial V52() non void 1 -element V58() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]} is non empty Relation-like Function-like set
K262([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],(1Cat (0,1))) is Relation-like {[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]} -defined {(1Cat (0,1))} -valued Function-like V21({[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{(1Cat (0,1))}) Element of bool [:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{(1Cat (0,1))}:]
[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{(1Cat (0,1))}:] is non empty Relation-like set
bool [:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{(1Cat (0,1))}:] is non empty set
K261([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]) is Relation-like [:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:] -defined {[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]} -valued Function-like V21([:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:],{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}) Element of bool [:[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:],{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:]
[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:] is non empty Relation-like set
[:[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:],{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:] is non empty Relation-like set
bool [:[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:],{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:] is non empty set
CatStr(# {(1Cat (0,1))},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},K262([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],(1Cat (0,1))),K262([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],(1Cat (0,1))),K261([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]) #) is non empty non void V58() strict CatStr
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier of C is non empty set
f is Element of the carrier of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier' of C is non empty set
f is Element of the carrier' of C
dom f is Element of the carrier of C
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
(C,f) is Element of the carrier of C
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . f is Element of the carrier of C
(C,f) is Element of the carrier of C
g is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of g is non empty set
A1 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A1 is non empty set
[g,A1] is V18() set
{g,A1} is non empty set
{g} is non empty set
{{g,A1},{g}} is non empty set
A2 is Relation-like the carrier' of g -defined the carrier' of A1 -valued Function-like V21( the carrier' of g, the carrier' of A1) Functor of g,A1
[[g,A1],A2] is V18() set
{[g,A1],A2} is non empty set
{[g,A1]} is non empty Relation-like Function-like set
{{[g,A1],A2},{[g,A1]}} is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier' of C is non empty set
f is Element of the carrier' of C
f `11 is set
dom f is Element of the carrier of C
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
(C,f) is Element of the carrier of C
f `12 is set
cod f is Element of the carrier of C
the carrier of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C . f is Element of the carrier of C
(C,f) is Element of the carrier of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier of C is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier of f is non empty set
the carrier' of C is non empty set
the carrier' of f is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
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
CatStr(# the carrier of C, the carrier' of C, the Source of C, the Target of C, the Comp of C #) is non empty non void V58() strict CatStr
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
CatStr(# the carrier of f, the carrier' of f, the Source of f, the Target of f, the Comp of f #) is non empty non void V58() strict CatStr
dom the Source of C is Element of bool the carrier' of C
bool the carrier' of C is non empty set
dom the Source of f is Element of bool the carrier' of f
bool the carrier' of f is non empty set
dom the Target of C is Element of bool the carrier' of C
dom the Target of f is Element of bool the carrier' of f
g is set
A1 is Element of the carrier' of C
the Source of C . g is set
dom A1 is Element of the carrier of C
the Source of C . A1 is Element of the carrier of C
(C,A1) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
A2 is Element of the carrier' of f
dom A2 is Element of the carrier of f
the Source of f . A2 is Element of the carrier of f
the Source of f . g is set
g is set
A1 is Element of the carrier' of C
the Target of C . g is set
cod A1 is Element of the carrier of C
the Target of C . A1 is Element of the carrier of C
(C,A1) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
A2 is Element of the carrier' of f
cod A2 is Element of the carrier of f
the Target of f . A2 is Element of the carrier of f
the Target of f . g is set
dom the Comp of C is Relation-like the carrier' of C -defined the carrier' of C -valued Element of bool [: the carrier' of C, the carrier' of C:]
bool [: the carrier' of C, the carrier' of C:] is non empty set
dom the Comp of f is Relation-like the carrier' of f -defined the carrier' of f -valued Element of bool [: the carrier' of f, the carrier' of f:]
bool [: the carrier' of f, the carrier' of f:] is non empty set
g is set
A1 is Element of [: the carrier' of C, the carrier' of C:]
A2 is Element of [: the carrier' of f, the carrier' of f:]
A1 `1 is Element of the carrier' of C
A1 `2 is Element of the carrier' of C
[(A1 `1),(A1 `2)] is V18() Element of the carrier' of [:C,C:]
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:C,C:] is non empty set
{(A1 `1),(A1 `2)} is non empty set
{(A1 `1)} is non empty set
{{(A1 `1),(A1 `2)},{(A1 `1)}} is non empty set
dom (A1 `1) is Element of the carrier of C
the Source of C . (A1 `1) is Element of the carrier of C
cod (A1 `2) is Element of the carrier of C
the Target of C . (A1 `2) is Element of the carrier of C
A2 `1 is Element of the carrier' of f
dom (A2 `1) is Element of the carrier of f
the Source of f . (A2 `1) is Element of the carrier of f
A2 `2 is Element of the carrier' of f
cod (A2 `2) is Element of the carrier of f
the Target of f . (A2 `2) is Element of the carrier of f
g is set
A1 is Element of [: the carrier' of C, the carrier' of C:]
A2 is Element of [: the carrier' of f, the carrier' of f:]
A2 `1 is Element of the carrier' of f
A2 `2 is Element of the carrier' of f
[(A2 `1),(A2 `2)] is V18() Element of the carrier' of [:f,f:]
[:f,f:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of f, the carrier of f:] is non empty Relation-like set
[: the Source of f, the Source of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier of f, the carrier of f:] -valued Function-like V21([: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]) Element of bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:]
[:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:] is non empty set
[: the Target of f, the Target of f:] is Relation-like [: the carrier' of f, the carrier' of f:] -defined [: the carrier of f, the carrier of f:] -valued Function-like V21([: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]) Element of bool [:[: the carrier' of f, the carrier' of f:],[: the carrier of f, the carrier of f:]:]
K222( the carrier' of f, the carrier' of f, the Comp of f, the Comp of f) is Relation-like [:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:] -defined [: the carrier' of f, the carrier' of f:] -valued Function-like Element of bool [:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:]
[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:] is non empty Relation-like set
[:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:] is non empty Relation-like set
bool [:[:[: the carrier' of f, the carrier' of f:],[: the carrier' of f, the carrier' of f:]:],[: the carrier' of f, the carrier' of f:]:] is non empty set
CatStr(# [: the carrier of f, the carrier of f:],[: the carrier' of f, the carrier' of f:],[: the Source of f, the Source of f:],[: the Target of f, the Target of f:],K222( the carrier' of f, the carrier' of f, the Comp of f, the Comp of f) #) is non empty non void V58() strict CatStr
the carrier' of [:f,f:] is non empty set
{(A2 `1),(A2 `2)} is non empty set
{(A2 `1)} is non empty set
{{(A2 `1),(A2 `2)},{(A2 `1)}} is non empty set
dom (A2 `1) is Element of the carrier of f
the Source of f . (A2 `1) is Element of the carrier of f
cod (A2 `2) is Element of the carrier of f
the Target of f . (A2 `2) is Element of the carrier of f
A1 `1 is Element of the carrier' of C
dom (A1 `1) is Element of the carrier of C
the Source of C . (A1 `1) is Element of the carrier of C
A1 `2 is Element of the carrier' of C
cod (A1 `2) is Element of the carrier of C
the Target of C . (A1 `2) is Element of the carrier of C
g is set
A1 is set
[g,A1] is V18() set
{g,A1} is non empty set
{g} is non empty set
{{g,A1},{g}} is non empty set
A2 is Element of the carrier' of C
A3 is Element of the carrier' of C
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
FG is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of FG is non empty set
m is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of m is non empty set
[FG,m] is V18() set
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
g1 is Relation-like the carrier' of FG -defined the carrier' of m -valued Function-like V21( the carrier' of FG, the carrier' of m) Functor of FG,m
[[FG,m],g1] is V18() set
{[FG,m],g1} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],g1},{[FG,m]}} is non empty set
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
a2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of a2 is non empty set
b2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of b2 is non empty set
[a2,b2] is V18() set
{a2,b2} is non empty set
{a2} is non empty set
{{a2,b2},{a2}} is non empty set
g2 is Relation-like the carrier' of a2 -defined the carrier' of b2 -valued Function-like V21( the carrier' of a2, the carrier' of b2) Functor of a2,b2
[[a2,b2],g2] is V18() set
{[a2,b2],g2} is non empty set
{[a2,b2]} is non empty Relation-like Function-like set
{{[a2,b2],g2},{[a2,b2]}} is non empty set
the Comp of C . (g,A1) is set
the Comp of C . [g,A1] is set
A2 (*) A3 is Element of the carrier' of C
[a2,m] is V18() set
{a2,m} is non empty set
{{a2,m},{a2}} is non empty set
g1 * g2 is Relation-like the carrier' of a2 -defined the carrier' of m -valued Function-like Element of bool [: the carrier' of a2, the carrier' of m:]
[: the carrier' of a2, the carrier' of m:] is non empty Relation-like set
bool [: the carrier' of a2, the carrier' of m:] is non empty set
[[a2,m],(g1 * g2)] is V18() set
{[a2,m],(g1 * g2)} is non empty set
{[a2,m]} is non empty Relation-like Function-like set
{{[a2,m],(g1 * g2)},{[a2,m]}} is non empty set
G is Element of the carrier' of f
F is Element of the carrier' of f
F (*) G is Element of the carrier' of f
the Comp of f . (g,A1) is set
the Comp of f . [g,A1] is set
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
f is non empty non void V58() Category-like transitive associative reflexive with_identities Subcategory of C
the carrier of C is non empty set
the carrier of f is non empty set
g is Element of the carrier of f
the carrier' of f is non empty set
g is Element of the carrier of f
A1 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[A1,A1] is V18() set
{A1,A1} is non empty set
{A1} is non empty set
{{A1,A1},{A1}} is non empty set
id A1 is Relation-like the carrier' of A1 -defined the carrier' of A1 -valued Function-like V21( the carrier' of A1, the carrier' of A1) Functor of A1,A1
the carrier' of A1 is non empty set
id the carrier' of A1 is non empty Relation-like the carrier' of A1 -defined the carrier' of A1 -valued Function-like one-to-one total Element of bool [: the carrier' of A1, the carrier' of A1:]
[: the carrier' of A1, the carrier' of A1:] is non empty Relation-like set
bool [: the carrier' of A1, the carrier' of A1:] is non empty set
[[A1,A1],(id A1)] is V18() set
{[A1,A1],(id A1)} is non empty set
{[A1,A1]} is non empty Relation-like Function-like set
{{[A1,A1],(id A1)},{[A1,A1]}} is non empty set
A2 is Element of the carrier of C
id A2 is Morphism of A2,A2
id g is Morphism of g,g
the carrier' of C is non empty set
g is Element of the carrier' of f
A2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
dom g is Element of the carrier of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f . g is Element of the carrier of f
A3 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
cod g is Element of the carrier of f
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f . g is Element of the carrier of f
A1 is Element of the carrier' of C
dom A1 is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . A1 is Element of the carrier of C
cod A1 is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . A1 is Element of the carrier of C
the carrier' of A2 is non empty set
the carrier' of A3 is non empty set
[A2,A3] is V18() set
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
g is Element of the carrier' of f
A1 is Element of the carrier' of f
A1 (*) g is Element of the carrier' of f
A2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A2 is non empty set
A3 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A3 is non empty set
F is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of F is non empty set
[A2,A3] is V18() set
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
[A3,F] is V18() set
{A3,F} is non empty set
{A3} is non empty set
{{A3,F},{A3}} is non empty set
[A2,F] is V18() set
{A2,F} is non empty set
{{A2,F},{A2}} is non empty set
m is Relation-like the carrier' of A2 -defined the carrier' of A3 -valued Function-like V21( the carrier' of A2, the carrier' of A3) Functor of A2,A3
[[A2,A3],m] is V18() set
{[A2,A3],m} is non empty set
{[A2,A3]} is non empty Relation-like Function-like set
{{[A2,A3],m},{[A2,A3]}} is non empty set
g1 is Relation-like the carrier' of A3 -defined the carrier' of F -valued Function-like V21( the carrier' of A3, the carrier' of F) Functor of A3,F
[[A3,F],g1] is V18() set
{[A3,F],g1} is non empty set
{[A3,F]} is non empty Relation-like Function-like set
{{[A3,F],g1},{[A3,F]}} is non empty set
g1 * m is Relation-like the carrier' of A2 -defined the carrier' of A2 -defined the carrier' of F -valued the carrier' of F -valued Function-like V21( the carrier' of A2, the carrier' of F) Functor of A2,F
[[A2,F],(g1 * m)] is V18() set
{[A2,F],(g1 * m)} is non empty set
{[A2,F]} is non empty Relation-like Function-like set
{{[A2,F],(g1 * m)},{[A2,F]}} is non empty set
dom A1 is Element of the carrier of f
the Source of f . A1 is Element of the carrier of f
FG is Element of the carrier' of C
dom FG is Element of the carrier of C
the Source of C . FG is Element of the carrier of C
cod g is Element of the carrier of f
the Target of f . g is Element of the carrier of f
G is Element of the carrier' of C
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
A1 `11 is set
g `12 is set
FG (*) G is Element of the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier' of C is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier' of f is non empty set
the carrier of C is non empty set
the carrier of f is non empty set
g is set
A1 is Element of the carrier of C
id A1 is Morphism of A1,A1
A2 is Element of the carrier' of f
dom A2 is Element of the carrier of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f . A2 is Element of the carrier of f
(f,A2) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
dom (id A1) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . (id A1) is Element of the carrier of C
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
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
g is Element of the carrier of C
A2 is Element of the carrier of f
A1 is Element of the carrier of C
A3 is Element of the carrier of f
Hom (g,A1) is Element of bool the carrier' of C
bool the carrier' of C is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C : ( dom b<sub>1</sub> = g & cod b<sub>1</sub> = A1 ) } is set
Hom (A2,A3) is Element of bool the carrier' of f
bool the carrier' of f is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of f : ( dom b<sub>1</sub> = A2 & cod b<sub>1</sub> = A3 ) } is set
F is set
G is Element of the carrier' of C
dom G is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . G is Element of the carrier of C
cod G is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . G is Element of the carrier of C
FG is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of FG is non empty set
m is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of m is non empty set
[FG,m] is V18() set
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
g1 is Element of the carrier' of f
dom g1 is Element of the carrier of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f . g1 is Element of the carrier of f
(f,g1) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
cod g1 is Element of the carrier of f
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f . g1 is Element of the carrier of f
(f,g1) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
a2 is Relation-like the carrier' of FG -defined the carrier' of m -valued Function-like V21( the carrier' of FG, the carrier' of m) Functor of FG,m
[[FG,m],a2] is V18() set
{[FG,m],a2} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],a2},{[FG,m]}} is non empty set
a2 is Relation-like the carrier' of FG -defined the carrier' of m -valued Function-like V21( the carrier' of FG, the carrier' of m) Functor of FG,m
[[FG,m],a2] is V18() set
{[FG,m],a2} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],a2},{[FG,m]}} is non empty set
dom the Comp of C is Relation-like the carrier' of C -defined the carrier' of C -valued Element of bool [: the carrier' of C, the carrier' of C:]
bool [: the carrier' of C, the carrier' of C:] is non empty set
dom the Comp of f is Relation-like the carrier' of f -defined the carrier' of f -valued Element of bool [: the carrier' of f, the carrier' of f:]
bool [: the carrier' of f, the carrier' of f:] is non empty set
g is set
g `1 is set
g `2 is set
A1 is Element of the carrier' of C
A2 is Element of the carrier' of C
[A1,A2] is V18() Element of the carrier' of [:C,C:]
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:C,C:] is non empty set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
dom A1 is Element of the carrier of C
the Source of C . A1 is Element of the carrier of C
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
(C,A1) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
A3 is Element of the carrier' of f
dom A3 is Element of the carrier of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Source of f . A3 is Element of the carrier of f
(C,A2) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
F is Element of the carrier' of f
cod F is Element of the carrier of f
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f . F is Element of the carrier of f
g is set
g `1 is set
g `2 is set
A1 is Element of the carrier' of C
A2 is Element of the carrier' of C
[A1,A2] is V18() Element of the carrier' of [:C,C:]
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:C,C:] is non empty set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
dom A1 is Element of the carrier of C
the Source of C . A1 is Element of the carrier of C
(C,A1) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
cod A1 is Element of the carrier of C
the Target of C . A1 is Element of the carrier of C
(C,A1) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of (C,A1) is non empty set
the carrier' of (C,A1) is non empty set
[(C,A1),(C,A1)] is V18() set
{(C,A1),(C,A1)} is non empty set
{(C,A1)} is non empty set
{{(C,A1),(C,A1)},{(C,A1)}} is non empty set
G is Relation-like the carrier' of (C,A1) -defined the carrier' of (C,A1) -valued Function-like V21( the carrier' of (C,A1), the carrier' of (C,A1)) Functor of (C,A1),(C,A1)
[[(C,A1),(C,A1)],G] is V18() set
{[(C,A1),(C,A1)],G} is non empty set
{[(C,A1),(C,A1)]} is non empty Relation-like Function-like set
{{[(C,A1),(C,A1)],G},{[(C,A1),(C,A1)]}} is non empty set
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
(C,A2) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
the carrier' of (C,A2) is non empty set
[(C,A2),(C,A1)] is V18() set
{(C,A2),(C,A1)} is non empty set
{(C,A2)} is non empty set
{{(C,A2),(C,A1)},{(C,A2)}} is non empty set
FG is Relation-like the carrier' of (C,A2) -defined the carrier' of (C,A1) -valued Function-like V21( the carrier' of (C,A2), the carrier' of (C,A1)) Functor of (C,A2),(C,A1)
[[(C,A2),(C,A1)],FG] is V18() set
{[(C,A2),(C,A1)],FG} is non empty set
{[(C,A2),(C,A1)]} is non empty Relation-like Function-like set
{{[(C,A2),(C,A1)],FG},{[(C,A2),(C,A1)]}} is non empty set
the Comp of C . g is set
the Comp of C . (A1,A2) is set
[A1,A2] is V18() set
the Comp of C . [A1,A2] is set
A1 (*) A2 is Element of the carrier' of C
[(C,A2),(C,A1)] is V18() set
{(C,A2),(C,A1)} is non empty set
{{(C,A2),(C,A1)},{(C,A2)}} is non empty set
G * FG is Relation-like the carrier' of (C,A2) -defined the carrier' of (C,A2) -defined the carrier' of (C,A1) -valued the carrier' of (C,A1) -valued Function-like V21( the carrier' of (C,A2), the carrier' of (C,A1)) Functor of (C,A2),(C,A1)
[[(C,A2),(C,A1)],(G * FG)] is V18() set
{[(C,A2),(C,A1)],(G * FG)} is non empty set
{[(C,A2),(C,A1)]} is non empty Relation-like Function-like set
{{[(C,A2),(C,A1)],(G * FG)},{[(C,A2),(C,A1)]}} is non empty set
F is Element of the carrier' of f
A3 is Element of the carrier' of f
A3 (*) F is Element of the carrier' of f
the Comp of f . (A1,A2) is set
the Comp of f . [A1,A2] is set
the Comp of f . g is set
g is Element of the carrier of C
id g is Morphism of g,g
A1 is Element of the carrier of f
id A1 is Morphism of A1,A1
A2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[A2,A2] is V18() set
{A2,A2} is non empty set
{A2} is non empty set
{{A2,A2},{A2}} is non empty set
id A2 is Relation-like the carrier' of A2 -defined the carrier' of A2 -valued Function-like V21( the carrier' of A2, the carrier' of A2) Functor of A2,A2
the carrier' of A2 is non empty set
id the carrier' of A2 is non empty Relation-like the carrier' of A2 -defined the carrier' of A2 -valued Function-like one-to-one total Element of bool [: the carrier' of A2, the carrier' of A2:]
[: the carrier' of A2, the carrier' of A2:] is non empty Relation-like set
bool [: the carrier' of A2, the carrier' of A2:] is non empty set
[[A2,A2],(id A2)] is V18() set
{[A2,A2],(id A2)} is non empty set
{[A2,A2]} is non empty Relation-like Function-like set
{{[A2,A2],(id A2)},{[A2,A2]}} is non empty set
C is set
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier of C is non empty set
f is Element of the carrier of C
(f) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier' of C is non empty set
f is Element of the carrier' of C
f `2 is set
dom f is Element of the carrier of C
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
((dom f)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((dom f)) is non empty set
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . f is Element of the carrier of C
((cod f)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((cod f)) is non empty set
g is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of g is non empty set
A1 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A1 is non empty set
[g,A1] is V18() set
{g,A1} is non empty set
{g} is non empty set
{{g,A1},{g}} is non empty set
A2 is Relation-like the carrier' of g -defined the carrier' of A1 -valued Function-like V21( the carrier' of g, the carrier' of A1) Functor of g,A1
[[g,A1],A2] is V18() set
{[g,A1],A2} is non empty set
{[g,A1]} is non empty Relation-like Function-like set
{{[g,A1],A2},{[g,A1]}} is non empty set
(g) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
C is non empty () set
[:C,C:] is non empty Relation-like set
f is non empty set
{ b₁ where b₁ is Element of f : b₁ is Relation-like Function-like set } is set
the non empty non void V58() Category-like transitive associative reflexive with_identities (C) is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
id the non empty non void V58() Category-like transitive associative reflexive with_identities (C) is Relation-like the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) -defined the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) -valued Function-like V21( the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C)) Functor of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the non empty non void V58() Category-like transitive associative reflexive with_identities (C)
the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) is non empty set
id the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) is non empty Relation-like the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) -defined the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) -valued Function-like one-to-one total Element of bool [: the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C):]
[: the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C):] is non empty Relation-like set
bool [: the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C):] is non empty set
A2 is non empty set
A3 is set
F is Element of f
F is non empty () set
A3 is non empty functional set
G is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
FG is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
the carrier' of G is non empty set
the carrier' of FG is non empty set
m is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
the carrier' of m is non empty set
g1 is Relation-like Function-like Element of A3
a2 is Relation-like Function-like Element of A3
g1 * a2 is Relation-like Function-like set
b2 is Relation-like the carrier' of G -defined the carrier' of FG -valued Function-like V21( the carrier' of G, the carrier' of FG) Functor of G,FG
g2 is Relation-like the carrier' of FG -defined the carrier' of m -valued Function-like V21( the carrier' of FG, the carrier' of m) Functor of FG,m
g2 * b2 is Relation-like the carrier' of G -defined the carrier' of G -defined the carrier' of m -valued the carrier' of m -valued Function-like V21( the carrier' of G, the carrier' of m) Functor of G,m
ha1 is Element of f
ha2 is Element of f
G is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
the carrier' of G is non empty set
id G is Relation-like the carrier' of G -defined the carrier' of G -valued Function-like V21( the carrier' of G, the carrier' of G) Functor of G,G
id the carrier' of G is non empty Relation-like the carrier' of G -defined the carrier' of G -valued Function-like one-to-one total Element of bool [: the carrier' of G, the carrier' of G:]
[: the carrier' of G, the carrier' of G:] is non empty Relation-like set
bool [: the carrier' of G, the carrier' of G:] is non empty set
FG is Element of f
m is Relation-like Function-like Element of A3
g1 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
the carrier' of g1 is non empty set
a2 is Relation-like Function-like Element of A3
m * a2 is Relation-like Function-like set
a2 * m is Relation-like Function-like set
b2 is Relation-like the carrier' of g1 -defined the carrier' of G -valued Function-like V21( the carrier' of g1, the carrier' of G) Functor of g1,G
(id G) * b2 is Relation-like the carrier' of g1 -defined the carrier' of g1 -defined the carrier' of G -valued the carrier' of G -valued Function-like V21( the carrier' of g1, the carrier' of G) Functor of g1,G
a2 is Relation-like Function-like Element of A3
G is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
the carrier' of G is non empty set
FG is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
the carrier' of FG is non empty set
b2 is Relation-like Function-like Element of A3
m is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
the carrier' of m is non empty set
g2 is Relation-like Function-like Element of A3
g1 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
the carrier' of g1 is non empty set
a2 * b2 is Relation-like Function-like set
(a2 * b2) * g2 is Relation-like Function-like set
b2 * g2 is Relation-like Function-like set
a2 * (b2 * g2) is Relation-like Function-like set
[:F,F:] is non empty Relation-like set
G is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier of G is non empty set
the carrier' of G is non empty set
FG is Element of the carrier of G
m is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
id m is Relation-like the carrier' of m -defined the carrier' of m -valued Function-like V21( the carrier' of m, the carrier' of m) Functor of m,m
the carrier' of m is non empty set
id the carrier' of m is non empty Relation-like the carrier' of m -defined the carrier' of m -valued Function-like one-to-one total Element of bool [: the carrier' of m, the carrier' of m:]
[: the carrier' of m, the carrier' of m:] is non empty Relation-like set
bool [: the carrier' of m, the carrier' of m:] is non empty set
a2 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
[a2,a2] is V18() Element of [:F,F:]
{a2,a2} is non empty set
{a2} is non empty set
{{a2,a2},{a2}} is non empty set
g1 is Relation-like Function-like Element of A3
[[a2,a2],g1] is V18() Element of [:[:F,F:],A3:]
[:[:F,F:],A3:] is non empty Relation-like set
{[a2,a2],g1} is non empty set
{[a2,a2]} is non empty Relation-like Function-like set
{{[a2,a2],g1},{[a2,a2]}} is non empty set
id FG is Morphism of FG,FG
g2 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
ha1 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
[g2,ha1] is V18() Element of [:F,F:]
{g2,ha1} is non empty set
{g2} is non empty set
{{g2,ha1},{g2}} is non empty set
ha2 is Relation-like Function-like Element of A3
[[g2,ha1],ha2] is V18() Element of [:[:F,F:],A3:]
{[g2,ha1],ha2} is non empty set
{[g2,ha1]} is non empty Relation-like Function-like set
{{[g2,ha1],ha2},{[g2,ha1]}} is non empty set
the carrier' of g2 is non empty set
the carrier' of ha1 is non empty set
dom (id FG) is Element of the carrier of G
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V21( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is non empty Relation-like set
bool [: the carrier' of G, the carrier of G:] is non empty set
the Source of G . (id FG) is Element of the carrier of G
(G,(id FG)) is Element of the carrier of G
b2 is Element of the carrier' of G
cod b2 is Element of the carrier of G
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V21( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Target of G . b2 is Element of the carrier of G
(G,b2) is Element of the carrier of G
(id FG) (*) b2 is Element of the carrier' of G
[a2,ha1] is V18() Element of [:F,F:]
{a2,ha1} is non empty set
{{a2,ha1},{a2}} is non empty set
(id the carrier' of m) * ha2 is Relation-like the carrier' of m -defined Function-like set
[[a2,ha1],((id the carrier' of m) * ha2)] is V18() set
{[a2,ha1],((id the carrier' of m) * ha2)} is non empty set
{[a2,ha1]} is non empty Relation-like Function-like set
{{[a2,ha1],((id the carrier' of m) * ha2)},{[a2,ha1]}} is non empty set
[[a2,ha1],ha2] is V18() Element of [:[:F,F:],A3:]
{[a2,ha1],ha2} is non empty set
{{[a2,ha1],ha2},{[a2,ha1]}} is non empty set
[m,m] is V18() set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
[[m,m],(id m)] is V18() set
{[m,m],(id m)} is non empty set
{[m,m]} is non empty Relation-like Function-like set
{{[m,m],(id m)},{[m,m]}} is non empty set
FG is Element of the carrier' of G
m is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
g1 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
[m,g1] is V18() Element of [:F,F:]
{m,g1} is non empty set
{m} is non empty set
{{m,g1},{m}} is non empty set
a2 is Relation-like Function-like Element of A3
[[m,g1],a2] is V18() Element of [:[:F,F:],A3:]
{[m,g1],a2} is non empty set
{[m,g1]} is non empty Relation-like Function-like set
{{[m,g1],a2},{[m,g1]}} is non empty set
the carrier' of m is non empty set
the carrier' of g1 is non empty set
dom FG is Element of the carrier of G
the Source of G . FG is Element of the carrier of G
(G,FG) is Element of the carrier of G
cod FG is Element of the carrier of G
the Target of G . FG is Element of the carrier of G
(G,FG) is Element of the carrier of G
b2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
g2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of b2 is non empty set
the carrier' of g2 is non empty set
[b2,g2] is V18() set
{b2,g2} is non empty set
{b2} is non empty set
{{b2,g2},{b2}} is non empty set
FG is Element of the carrier' of G
m is Element of the carrier' of G
m (*) FG is Element of the carrier' of G
g1 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
a2 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
[g1,a2] is V18() Element of [:F,F:]
{g1,a2} is non empty set
{g1} is non empty set
{{g1,a2},{g1}} is non empty set
b2 is Relation-like Function-like Element of A3
[[g1,a2],b2] is V18() Element of [:[:F,F:],A3:]
{[g1,a2],b2} is non empty set
{[g1,a2]} is non empty Relation-like Function-like set
{{[g1,a2],b2},{[g1,a2]}} is non empty set
the carrier' of g1 is non empty set
the carrier' of a2 is non empty set
g2 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
ha1 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
[g2,ha1] is V18() Element of [:F,F:]
{g2,ha1} is non empty set
{g2} is non empty set
{{g2,ha1},{g2}} is non empty set
ha2 is Relation-like Function-like Element of A3
[[g2,ha1],ha2] is V18() Element of [:[:F,F:],A3:]
{[g2,ha1],ha2} is non empty set
{[g2,ha1]} is non empty Relation-like Function-like set
{{[g2,ha1],ha2},{[g2,ha1]}} is non empty set
the carrier' of g2 is non empty set
the carrier' of ha1 is non empty set
hb1 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of hb1 is non empty set
hb2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of hb2 is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
[hb1,hb2] is V18() set
{hb1,hb2} is non empty set
{hb1} is non empty set
{{hb1,hb2},{hb1}} is non empty set
[hb2,C] is V18() set
{hb2,C} is non empty set
{hb2} is non empty set
{{hb2,C},{hb2}} is non empty set
[hb1,C] is V18() set
{hb1,C} is non empty set
{{hb1,C},{hb1}} is non empty set
F is Relation-like the carrier' of hb1 -defined the carrier' of hb2 -valued Function-like V21( the carrier' of hb1, the carrier' of hb2) Functor of hb1,hb2
[[hb1,hb2],F] is V18() set
{[hb1,hb2],F} is non empty set
{[hb1,hb2]} is non empty Relation-like Function-like set
{{[hb1,hb2],F},{[hb1,hb2]}} is non empty set
G is Relation-like the carrier' of hb2 -defined the carrier' of C -valued Function-like V21( the carrier' of hb2, the carrier' of C) Functor of hb2,C
[[hb2,C],G] is V18() set
{[hb2,C],G} is non empty set
{[hb2,C]} is non empty Relation-like Function-like set
{{[hb2,C],G},{[hb2,C]}} is non empty set
G * F is Relation-like the carrier' of hb1 -defined the carrier' of hb1 -defined the carrier' of C -valued the carrier' of C -valued Function-like V21( the carrier' of hb1, the carrier' of C) Functor of hb1,C
[[hb1,C],(G * F)] is V18() set
{[hb1,C],(G * F)} is non empty set
{[hb1,C]} is non empty Relation-like Function-like set
{{[hb1,C],(G * F)},{[hb1,C]}} is non empty set
FG is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () CatStr
the carrier of FG is non empty set
the carrier' of FG is non empty set
m is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
the carrier' of m is non empty set
g1 is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
the carrier' of g1 is non empty set
[: the carrier' of m, the carrier' of g1:] is non empty Relation-like set
bool [: the carrier' of m, the carrier' of g1:] is non empty set
[m,g1] is V18() Element of [:C,C:]
{m,g1} is non empty set
{m} is non empty set
{{m,g1},{m}} is non empty set
a2 is Relation-like the carrier' of m -defined the carrier' of g1 -valued Function-like V21( the carrier' of m, the carrier' of g1) Functor of m,g1
[[m,g1],a2] is V18() Element of [:[:C,C:],(bool [: the carrier' of m, the carrier' of g1:]):]
[:[:C,C:],(bool [: the carrier' of m, the carrier' of g1:]):] is non empty Relation-like set
{[m,g1],a2} is non empty set
{[m,g1]} is non empty Relation-like Function-like set
{{[m,g1],a2},{[m,g1]}} is non empty set
b2 is Element of the carrier' of FG
g2 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
ha1 is non empty non void V58() Category-like transitive associative reflexive with_identities (F)
[g2,ha1] is V18() Element of [:F,F:]
{g2,ha1} is non empty set
{g2} is non empty set
{{g2,ha1},{g2}} is non empty set
ha2 is Relation-like Function-like Element of A3
[[g2,ha1],ha2] is V18() Element of [:[:F,F:],A3:]
[:[:F,F:],A3:] is non empty Relation-like set
{[g2,ha1],ha2} is non empty set
{[g2,ha1]} is non empty Relation-like Function-like set
{{[g2,ha1],ha2},{[g2,ha1]}} is non empty set
the carrier' of g2 is non empty set
the carrier' of ha1 is non empty set
dom b2 is Element of the carrier of FG
the Source of FG is Relation-like the carrier' of FG -defined the carrier of FG -valued Function-like V21( the carrier' of FG, the carrier of FG) Element of bool [: the carrier' of FG, the carrier of FG:]
[: the carrier' of FG, the carrier of FG:] is non empty Relation-like set
bool [: the carrier' of FG, the carrier of FG:] is non empty set
the Source of FG . b2 is Element of the carrier of FG
((dom b2)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((dom b2)) is non empty set
cod b2 is Element of the carrier of FG
the Target of FG is Relation-like the carrier' of FG -defined the carrier of FG -valued Function-like V21( the carrier' of FG, the carrier of FG) Element of bool [: the carrier' of FG, the carrier of FG:]
the Target of FG . b2 is Element of the carrier of FG
((cod b2)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((cod b2)) is non empty set
(FG,b2) is Relation-like the carrier' of ((dom b2)) -defined the carrier' of ((cod b2)) -valued Function-like V21( the carrier' of ((dom b2)), the carrier' of ((cod b2))) Functor of ((dom b2)),((cod b2))
hb1 is Element of f
C is non empty () set
[:C,C:] is non empty Relation-like set
f is non empty set
g is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () CatStr
the carrier of g is non empty set
the carrier' of g is non empty set
A1 is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () CatStr
the carrier of A1 is non empty set
the carrier' of A1 is non empty set
A2 is set
A3 is Element of the carrier' of g
dom A3 is Element of the carrier of g
the Source of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
[: the carrier' of g, the carrier of g:] is non empty Relation-like set
bool [: the carrier' of g, the carrier of g:] is non empty set
the Source of g . A3 is Element of the carrier of g
cod A3 is Element of the carrier of g
the Target of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
the Target of g . A3 is Element of the carrier of g
F is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of G is non empty set
[F,G] is V18() set
{F,G} is non empty set
{F} is non empty set
{{F,G},{F}} is non empty set
FG is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like V21( the carrier' of F, the carrier' of G) Functor of F,G
[[F,G],FG] is V18() set
{[F,G],FG} is non empty set
{[F,G]} is non empty Relation-like Function-like set
{{[F,G],FG},{[F,G]}} is non empty set
A2 is set
A3 is Element of the carrier' of A1
dom A3 is Element of the carrier of A1
the Source of A1 is Relation-like the carrier' of A1 -defined the carrier of A1 -valued Function-like V21( the carrier' of A1, the carrier of A1) Element of bool [: the carrier' of A1, the carrier of A1:]
[: the carrier' of A1, the carrier of A1:] is non empty Relation-like set
bool [: the carrier' of A1, the carrier of A1:] is non empty set
the Source of A1 . A3 is Element of the carrier of A1
cod A3 is Element of the carrier of A1
the Target of A1 is Relation-like the carrier' of A1 -defined the carrier of A1 -valued Function-like V21( the carrier' of A1, the carrier of A1) Element of bool [: the carrier' of A1, the carrier of A1:]
the Target of A1 . A3 is Element of the carrier of A1
F is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of F is non empty set
G is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of G is non empty set
[F,G] is V18() set
{F,G} is non empty set
{F} is non empty set
{{F,G},{F}} is non empty set
FG is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like V21( the carrier' of F, the carrier' of G) Functor of F,G
[[F,G],FG] is V18() set
{[F,G],FG} is non empty set
{[F,G]} is non empty Relation-like Function-like set
{{[F,G],FG},{[F,G]}} is non empty set
0 is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional Element of K158()
1Cat (0,1) is non empty trivial V52() non void 1 -element V58() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{0} is non empty functional set
{1} is non empty set
K262(1,0) is Relation-like {1} -defined {0} -valued Function-like V21({1},{0}) Element of bool [:{1},{0}:]
[:{1},{0}:] is non empty Relation-like set
bool [:{1},{0}:] is non empty set
K261(1,1,1) is Relation-like [:{1},{1}:] -defined {1} -valued Function-like V21([:{1},{1}:],{1}) Element of bool [:[:{1},{1}:],{1}:]
[:{1},{1}:] is non empty Relation-like set
[:[:{1},{1}:],{1}:] is non empty Relation-like set
bool [:[:{1},{1}:],{1}:] is non empty set
CatStr(# {0},{1},K262(1,0),K262(1,0),K261(1,1,1) #) is non empty non void V58() strict CatStr
[(1Cat (0,1)),(1Cat (0,1))] is V18() set
{(1Cat (0,1)),(1Cat (0,1))} is non empty set
{(1Cat (0,1))} is non empty set
{{(1Cat (0,1)),(1Cat (0,1))},{(1Cat (0,1))}} is non empty set
id (1Cat (0,1)) is Relation-like the carrier' of (1Cat (0,1)) -defined the carrier' of (1Cat (0,1)) -valued Function-like V21( the carrier' of (1Cat (0,1)), the carrier' of (1Cat (0,1))) Functor of 1Cat (0,1), 1Cat (0,1)
the carrier' of (1Cat (0,1)) is non empty trivial set
id the carrier' of (1Cat (0,1)) is non empty Relation-like the carrier' of (1Cat (0,1)) -defined the carrier' of (1Cat (0,1)) -valued Function-like one-to-one total Element of bool [: the carrier' of (1Cat (0,1)), the carrier' of (1Cat (0,1)):]
[: the carrier' of (1Cat (0,1)), the carrier' of (1Cat (0,1)):] is non empty Relation-like set
bool [: the carrier' of (1Cat (0,1)), the carrier' of (1Cat (0,1)):] is non empty set
[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))] is V18() set
{[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))} is non empty set
{[(1Cat (0,1)),(1Cat (0,1))]} is non empty Relation-like Function-like set
{{[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))},{[(1Cat (0,1)),(1Cat (0,1))]}} is non empty set
1Cat ((1Cat (0,1)),[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]) is non empty trivial V52() non void 1 -element V58() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]} is non empty Relation-like Function-like set
K262([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],(1Cat (0,1))) is Relation-like {[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]} -defined {(1Cat (0,1))} -valued Function-like V21({[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{(1Cat (0,1))}) Element of bool [:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{(1Cat (0,1))}:]
[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{(1Cat (0,1))}:] is non empty Relation-like set
bool [:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{(1Cat (0,1))}:] is non empty set
K261([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]) is Relation-like [:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:] -defined {[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]} -valued Function-like V21([:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:],{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}) Element of bool [:[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:],{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:]
[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:] is non empty Relation-like set
[:[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:],{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:] is non empty Relation-like set
bool [:[:{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:],{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]}:] is non empty set
CatStr(# {(1Cat (0,1))},{[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]},K262([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],(1Cat (0,1))),K262([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],(1Cat (0,1))),K261([[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))],[[(1Cat (0,1)),(1Cat (0,1))],(id (1Cat (0,1)))]) #) is non empty non void V58() strict CatStr
f is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () CatStr
g is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of f is non empty set
A1 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of g is non empty set
the carrier' of A1 is non empty set
[g,A1] is V18() set
{g,A1} is non empty set
{g} is non empty set
{{g,A1},{g}} is non empty set
the carrier' of f is non empty set
A2 is Relation-like the carrier' of g -defined the carrier' of A1 -valued Function-like V21( the carrier' of g, the carrier' of A1) Functor of g,A1
[[g,A1],A2] is V18() set
{[g,A1],A2} is non empty set
{[g,A1]} is non empty Relation-like Function-like set
{{[g,A1],A2},{[g,A1]}} is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () () CatStr
the carrier of C is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities () () () CatStr
the carrier of f is non empty set
the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
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
CatStr(# the carrier of C, the carrier' of C, the Source of C, the Target of C, the Comp of C #) is non empty non void V58() strict CatStr
the carrier' of f is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is non empty Relation-like set
bool [: the carrier' of f, the carrier of f:] is non empty set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V21( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Comp of f is Relation-like [: the carrier' of f, the carrier' of f:] -defined the carrier' of f -valued Function-like Element of bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:]
[: the carrier' of f, the carrier' of f:] is non empty Relation-like set
[:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty Relation-like set
bool [:[: the carrier' of f, the carrier' of f:], the carrier' of f:] is non empty set
CatStr(# the carrier of f, the carrier' of f, the Source of f, the Target of f, the Comp of f #) is non empty non void V58() strict CatStr
{ (C,b₁) where b₁ is Element of the carrier' of C : verum } is set
the Element of the carrier' of C is Element of the carrier' of C
(C, the Element of the carrier' of C) is Relation-like the carrier' of ((dom the Element of the carrier' of C)) -defined the carrier' of ((cod the Element of the carrier' of C)) -valued Function-like V21( the carrier' of ((dom the Element of the carrier' of C)), the carrier' of ((cod the Element of the carrier' of C))) Functor of ((dom the Element of the carrier' of C)),((cod the Element of the carrier' of C))
dom the Element of the carrier' of C is Element of the carrier of C
the Source of C . the Element of the carrier' of C is Element of the carrier of C
((dom the Element of the carrier' of C)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((dom the Element of the carrier' of C)) is non empty set
cod the Element of the carrier' of C is Element of the carrier of C
the Target of C . the Element of the carrier' of C is Element of the carrier of C
((cod the Element of the carrier' of C)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((cod the Element of the carrier' of C)) is non empty set
F is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
G is non empty non void V58() strict Category-like transitive associative reflexive with_identities CatStr
g is non empty () set
FG is non empty non void V58() Category-like transitive associative reflexive with_identities (g)
the carrier' of FG is non empty set
m is non empty non void V58() Category-like transitive associative reflexive with_identities (g)
the carrier' of m is non empty set
[:g,g:] is non empty Relation-like set
[: the carrier' of FG, the carrier' of m:] is non empty Relation-like set
bool [: the carrier' of FG, the carrier' of m:] is non empty set
[FG,m] is V18() Element of [:g,g:]
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
g1 is Relation-like the carrier' of FG -defined the carrier' of m -valued Function-like V21( the carrier' of FG, the carrier' of m) Functor of FG,m
[[FG,m],g1] is V18() Element of [:[:g,g:],(bool [: the carrier' of FG, the carrier' of m:]):]
[:[:g,g:],(bool [: the carrier' of FG, the carrier' of m:]):] is non empty Relation-like set
{[FG,m],g1} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],g1},{[FG,m]}} is non empty set
a2 is Element of the carrier' of C
dom a2 is Element of the carrier of C
the Source of C . a2 is Element of the carrier of C
((dom a2)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((dom a2)) is non empty set
cod a2 is Element of the carrier of C
the Target of C . a2 is Element of the carrier of C
((cod a2)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((cod a2)) is non empty set
(C,a2) is Relation-like the carrier' of ((dom a2)) -defined the carrier' of ((cod a2)) -valued Function-like V21( the carrier' of ((dom a2)), the carrier' of ((cod a2))) Functor of ((dom a2)),((cod a2))
the carrier' of CatStr(# the carrier of C, the carrier' of C, the Source of C, the Target of C, the Comp of C #) is non empty set
A3 is non empty set
FG is non empty non void V58() Category-like transitive associative reflexive with_identities (g)
the carrier' of FG is non empty set
m is non empty non void V58() Category-like transitive associative reflexive with_identities (g)
the carrier' of m is non empty set
a2 is Element of the carrier of f
(a2) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
b2 is Element of the carrier of f
(b2) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier' of FG, the carrier' of m:] is non empty Relation-like set
bool [: the carrier' of FG, the carrier' of m:] is non empty set
[FG,m] is V18() Element of [:g,g:]
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
g1 is Relation-like the carrier' of FG -defined the carrier' of m -valued Function-like V21( the carrier' of FG, the carrier' of m) Functor of FG,m
[[FG,m],g1] is V18() Element of [:[:g,g:],(bool [: the carrier' of FG, the carrier' of m:]):]
[:[:g,g:],(bool [: the carrier' of FG, the carrier' of m:]):] is non empty Relation-like set
{[FG,m],g1} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],g1},{[FG,m]}} is non empty set
ha1 is Element of the carrier' of C
dom ha1 is Element of the carrier of C
the Source of C . ha1 is Element of the carrier of C
((dom ha1)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((dom ha1)) is non empty set
cod ha1 is Element of the carrier of C
the Target of C . ha1 is Element of the carrier of C
((cod ha1)) is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of ((cod ha1)) is non empty set
(C,ha1) is Relation-like the carrier' of ((dom ha1)) -defined the carrier' of ((cod ha1)) -valued Function-like V21( the carrier' of ((dom ha1)), the carrier' of ((cod ha1))) Functor of ((dom ha1)),((cod ha1))
g2 is Element of the carrier' of f
the carrier' of CatStr(# the carrier of f, the carrier' of f, the Source of f, the Target of f, the Comp of f #) is non empty set
C is non empty () set
{ (Funct (b₁,b₂)) where b₁, b₂ is non empty non void V58() Category-like transitive associative reflexive with_identities (C) : verum } is set
the non empty non void V58() Category-like transitive associative reflexive with_identities (C) is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) is non empty set
the Relation-like the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) -defined the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) -valued Function-like V21( the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C)) Functor of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the non empty non void V58() Category-like transitive associative reflexive with_identities (C) is Relation-like the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) -defined the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C) -valued Function-like V21( the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the carrier' of the non empty non void V58() Category-like transitive associative reflexive with_identities (C)) Functor of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the non empty non void V58() Category-like transitive associative reflexive with_identities (C)
Funct ( the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the non empty non void V58() Category-like transitive associative reflexive with_identities (C)) is non empty FUNCTOR-DOMAIN of the non empty non void V58() Category-like transitive associative reflexive with_identities (C), the non empty non void V58() Category-like transitive associative reflexive with_identities (C)
union { (Funct (b₁,b₂)) where b₁, b₂ is non empty non void V58() Category-like transitive associative reflexive with_identities (C) : verum } is set
A3 is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
the carrier' of A3 is non empty set
F is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
the carrier' of F is non empty set
G is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
the carrier' of G is non empty set
FG is Relation-like the carrier' of A3 -defined the carrier' of F -valued Function-like V21( the carrier' of A3, the carrier' of F) Functor of A3,F
A2 is non empty set
m is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like V21( the carrier' of F, the carrier' of G) Functor of F,G
m * FG is Relation-like the carrier' of A3 -defined the carrier' of A3 -defined the carrier' of G -valued the carrier' of G -valued Function-like V21( the carrier' of A3, the carrier' of G) Functor of A3,G
Funct (A3,G) is non empty FUNCTOR-DOMAIN of A3,G
A3 is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
id A3 is Relation-like the carrier' of A3 -defined the carrier' of A3 -valued Function-like V21( the carrier' of A3, the carrier' of A3) Functor of A3,A3
the carrier' of A3 is non empty set
id the carrier' of A3 is non empty Relation-like the carrier' of A3 -defined the carrier' of A3 -valued Function-like one-to-one total Element of bool [: the carrier' of A3, the carrier' of A3:]
[: the carrier' of A3, the carrier' of A3:] is non empty Relation-like set
bool [: the carrier' of A3, the carrier' of A3:] is non empty set
Funct (A3,A3) is non empty FUNCTOR-DOMAIN of A3,A3
[:C,C:] is non empty Relation-like set
A3 is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () CatStr
the carrier of A3 is non empty set
the carrier' of A3 is non empty set
F is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
G is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of F is non empty set
the carrier' of G is non empty set
[F,G] is V18() set
{F,G} is non empty set
{F} is non empty set
{{F,G},{F}} is non empty set
g1 is Relation-like the carrier' of F -defined the carrier' of G -valued Function-like V21( the carrier' of F, the carrier' of G) Functor of F,G
[[F,G],g1] is V18() set
{[F,G],g1} is non empty set
{[F,G]} is non empty Relation-like Function-like set
{{[F,G],g1},{[F,G]}} is non empty set
FG is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
m is non empty non void V58() Category-like transitive associative reflexive with_identities (C)
Funct (FG,m) is non empty FUNCTOR-DOMAIN of FG,m
[: the carrier' of F, the carrier' of G:] is non empty Relation-like set
bool [: the carrier' of F, the carrier' of G:] is non empty set
[FG,m] is V18() Element of [:C,C:]
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
[[FG,m],g1] is V18() Element of [:[:C,C:],(bool [: the carrier' of F, the carrier' of G:]):]
[:[:C,C:],(bool [: the carrier' of F, the carrier' of G:]):] is non empty Relation-like set
{[FG,m],g1} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],g1},{[FG,m]}} is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier of C is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities () () () CatStr
the carrier of f is non empty set
the carrier' of C is non empty set
the carrier' of f is non empty set
g is set
A1 is Element of the carrier' of C
dom A1 is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . A1 is Element of the carrier of C
cod A1 is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . A1 is Element of the carrier of C
A2 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A2 is non empty set
A3 is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A3 is non empty set
[A2,A3] is V18() set
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
F is Relation-like the carrier' of A2 -defined the carrier' of A3 -valued Function-like V21( the carrier' of A2, the carrier' of A3) Functor of A2,A3
[[A2,A3],F] is V18() set
{[A2,A3],F} is non empty set
{[A2,A3]} is non empty Relation-like Function-like set
{{[A2,A3],F},{[A2,A3]}} is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
f is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier' of f is non empty set
g is non empty non void V58() Category-like transitive associative reflexive with_identities () () CatStr
the carrier' of g is non empty set
A1 is Relation-like the carrier' of C -defined the carrier' of f -valued Function-like V21( the carrier' of C, the carrier' of f) Functor of C,f
(C,f,A1) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () Subcategory of f
A2 is Relation-like the carrier' of C -defined the carrier' of g -valued Function-like V21( the carrier' of C, the carrier' of g) Functor of C,g
(C,g,A2) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () Subcategory of g
the carrier of f is non empty set
the carrier of g is non empty set
the carrier of f \/ the carrier of g is non empty set
A3 is non empty set
F is Element of A3
F is non empty () set
G is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () () CatStr
the carrier of G is non empty set
FG is non empty non void V58() Category-like transitive associative reflexive with_identities () () Subcategory of G
the carrier' of FG is non empty set
m is non empty non void V58() Category-like transitive associative reflexive with_identities () () Subcategory of G
the carrier' of m is non empty set
g1 is Relation-like the carrier' of C -defined the carrier' of FG -valued Function-like V21( the carrier' of C, the carrier' of FG) Functor of C,FG
rng g1 is Element of bool the carrier' of FG
bool the carrier' of FG is non empty set
the carrier' of G is non empty set
incl FG is Relation-like the carrier' of FG -defined the carrier' of G -valued Function-like V21( the carrier' of FG, the carrier' of G) Functor of FG,G
id FG is Relation-like the carrier' of FG -defined the carrier' of FG -valued Function-like V21( the carrier' of FG, the carrier' of FG) Functor of FG,FG
id the carrier' of FG is non empty Relation-like the carrier' of FG -defined the carrier' of FG -valued Function-like one-to-one total Element of bool [: the carrier' of FG, the carrier' of FG:]
[: the carrier' of FG, the carrier' of FG:] is non empty Relation-like set
bool [: the carrier' of FG, the carrier' of FG:] is non empty set
(incl FG) * g1 is Relation-like the carrier' of C -defined the carrier' of C -defined the carrier' of G -valued the carrier' of G -valued Function-like V21( the carrier' of C, the carrier' of G) Functor of C,G
(C,FG,g1) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () Subcategory of FG
b2 is Relation-like the carrier' of C -defined the carrier' of G -valued Function-like V21( the carrier' of C, the carrier' of G) Functor of C,G
(C,G,b2) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () Subcategory of G
a2 is Relation-like the carrier' of C -defined the carrier' of m -valued Function-like V21( the carrier' of C, the carrier' of m) Functor of C,m
(C,m,a2) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () () Subcategory of m
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
f is Element of the carrier of C
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {f} is Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C " {f} is Element of bool the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
f is Element of the carrier of C
(C,f) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {f} is Element of bool the carrier' of C
id f is Morphism of f,f
the Target of C . (id f) is Element of the carrier of C
cod (id f) is Element of the carrier of C
dom the Target of C is Element of bool the carrier' of C
(C,f) is Element of bool the carrier' of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C " {f} is Element of bool the carrier' of C
id f is Morphism of f,f
the Source of C . (id f) is Element of the carrier of C
dom (id f) is Element of the carrier of C
dom the Source of C is Element of bool the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
f is Element of the carrier of C
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {f} is Element of bool the carrier' of C
g is Element of the carrier' of C
cod g is Element of the carrier of C
the Target of C . g is Element of the carrier of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
f is Element of the carrier of C
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {f} is Element of bool the carrier' of C
g is Element of the carrier' of C
dom g is Element of the carrier of C
the Source of C . g is Element of the carrier of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
f is Element of the carrier of C
g is Element of the carrier of C
Hom (f,g) 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 = f & cod b₁ = g ) } is set
(C,f) is non empty Element of bool the carrier' of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {f} is Element of bool the carrier' of C
(C,g) is non empty Element of bool the carrier' of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
{g} is non empty Element of bool the carrier of C
the Target of C " {g} is Element of bool the carrier' of C
(C,f) /\ (C,g) is Element of bool the carrier' of C
A1 is set
A2 is Element of the carrier' of C
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
A1 is set
A2 is Element of the carrier' of C
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
g is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of g is non empty set
f is Element of the carrier' of C
dom f is Element of the carrier of C
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
(C,(dom f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(dom f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {(dom f)} is Element of bool the carrier' of C
A1 is Element of the carrier' of g
cod A1 is Element of the carrier of g
the carrier of g is non empty set
the Target of g is Relation-like the carrier' of g -defined the carrier of g -valued Function-like V21( the carrier' of g, the carrier of g) Element of bool [: the carrier' of g, the carrier of g:]
[: the carrier' of g, the carrier of g:] is non empty Relation-like set
bool [: the carrier' of g, the carrier of g:] is non empty set
the Target of g . A1 is Element of the carrier of g
(g,(cod A1)) is non empty Element of bool the carrier' of g
bool the carrier' of g is non empty set
{(cod A1)} is non empty Element of bool the carrier of g
bool the carrier of g is non empty set
the Target of g " {(cod A1)} is Element of bool the carrier' of g
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
f is Element of the carrier' of C
dom f is Element of the carrier of C
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
(C,(dom f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
{(dom f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {(dom f)} is Element of bool the carrier' of C
cod f is Element of the carrier of C
the Target of C . f is Element of the carrier of C
(C,(cod f)) is non empty Element of bool the carrier' of C
{(cod f)} is non empty Element of bool the carrier of C
the Target of C " {(cod f)} is Element of bool the carrier' of C
g is Element of (C,(dom f))
f (*) g is Element of the carrier' of C
cod g is Element of the carrier of C
the Target of C . g is Element of the carrier of C
cod (f (*) g) is Element of the carrier of C
the Target of C . (f (*) g) is Element of the carrier of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
f is Element of the carrier' of C
cod f is Element of the carrier of C
the carrier of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 Target of C . f is Element of the carrier of C
(C,(cod f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
{(cod f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {(cod f)} is Element of bool the carrier' of C
dom f is Element of the carrier of C
the Source of C . f is Element of the carrier of C
(C,(dom f)) is non empty Element of bool the carrier' of C
{(dom f)} is non empty Element of bool the carrier of C
the Source of C " {(dom f)} is Element of bool the carrier' of C
g is Element of (C,(cod f))
g (*) f is Element of the carrier' of C
dom g is Element of the carrier of C
the Source of C . g is Element of the carrier of C
dom (g (*) f) is Element of the carrier of C
the Source of C . (g (*) f) is Element of the carrier of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
f is Element of the carrier of C
(C,f) is non empty Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {f} is Element of bool the carrier' of C
A2 is Element of (C,f)
A3 is Element of (C,f)
dom A3 is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C . A3 is Element of the carrier of C
F is Element of (C,f)
dom F is Element of the carrier of C
the Source of C . F is Element of the carrier of C
G is Element of the carrier' of C
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
A3 (*) G is Element of the carrier' of C
FG is Element of the carrier' of C
cod FG is Element of the carrier of C
the Target of C . FG is Element of the carrier of C
F (*) FG is Element of the carrier' of C
FG (*) G is Element of the carrier' of C
cod H₁(FG,G) is Element of the carrier of C
the Target of C . (FG (*) G) is Element of the carrier of C
F (*) H₁(FG,G) is Element of the carrier' of C
dom FG is Element of the carrier of C
the Source of C . FG is Element of the carrier of C
A2 is Element of (C,f)
dom A2 is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C . A2 is Element of the carrier of C
id (dom A2) is Morphism of dom A2, dom A2
A3 is Morphism of dom A2, dom A2
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
A2 (*) A3 is Element of the carrier' of C
F is Element of (C,f)
dom F is Element of the carrier of C
the Source of C . F is Element of the carrier of C
G is Element of the carrier' of C
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
F (*) G is Element of the carrier' of C
G (*) A3 is Element of the carrier' of C
A2 (*) G is Element of the carrier' of C
A3 (*) G is Element of the carrier' of C
dom G is Element of the carrier of C
the Source of C . G is Element of the carrier of C
A2 is Element of (C,f)
A3 is Element of (C,f)
dom A3 is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C . A3 is Element of the carrier of C
F is Element of (C,f)
dom F is Element of the carrier of C
the Source of C . F is Element of the carrier of C
G is Element of (C,f)
dom G is Element of the carrier of C
the Source of C . G is Element of the carrier of C
FG is Element of the carrier' of C
cod FG is Element of the carrier of C
the Target of C . FG is Element of the carrier of C
A3 (*) FG is Element of the carrier' of C
m is Element of the carrier' of C
cod m is Element of the carrier of C
the Target of C . m is Element of the carrier of C
F (*) m is Element of the carrier' of C
g1 is Element of the carrier' of C
cod g1 is Element of the carrier of C
the Target of C . g1 is Element of the carrier of C
G (*) g1 is Element of the carrier' of C
m (*) FG is Element of the carrier' of C
g1 (*) H₁(m,FG) is Element of the carrier' of C
g1 (*) m is Element of the carrier' of C
H₁(g1,m) (*) FG is Element of the carrier' of C
dom m is Element of the carrier of C
the Source of C . m is Element of the carrier of C
dom g1 is Element of the carrier of C
the Source of C . g1 is Element of the carrier of C
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
(C,f) is non empty Element of bool the carrier' of C
the Source of C " {f} is Element of bool the carrier' of C
A3 is Element of (C,f)
F is Element of (C,f)
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
G is Element of (C,f)
cod F is Element of the carrier of C
the Target of C . F is Element of the carrier of C
FG is Element of the carrier' of C
dom FG is Element of the carrier of C
the Source of C . FG is Element of the carrier of C
FG (*) A3 is Element of the carrier' of C
m is Element of the carrier' of C
dom m is Element of the carrier of C
the Source of C . m is Element of the carrier of C
m (*) F is Element of the carrier' of C
m (*) FG is Element of the carrier' of C
dom H₁(m,FG) is Element of the carrier of C
the Source of C . (m (*) FG) is Element of the carrier of C
H₁(m,FG) (*) A3 is Element of the carrier' of C
cod FG is Element of the carrier of C
the Target of C . FG is Element of the carrier of C
A3 is Element of (C,f)
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
id (cod A3) is Morphism of cod A3, cod A3
F is Morphism of cod A3, cod A3
dom F is Element of the carrier of C
the Source of C . F is Element of the carrier of C
F (*) A3 is Element of the carrier' of C
G is Element of (C,f)
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
FG is Element of the carrier' of C
dom FG is Element of the carrier of C
the Source of C . FG is Element of the carrier of C
FG (*) A3 is Element of the carrier' of C
FG (*) F is Element of the carrier' of C
FG (*) G is Element of the carrier' of C
F (*) FG is Element of the carrier' of C
cod FG is Element of the carrier of C
the Target of C . FG is Element of the carrier of C
A3 is Element of (C,f)
F is Element of (C,f)
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
G is Element of (C,f)
cod F is Element of the carrier of C
the Target of C . F is Element of the carrier of C
FG is Element of (C,f)
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
m is Element of the carrier' of C
dom m is Element of the carrier of C
the Source of C . m is Element of the carrier of C
m (*) A3 is Element of the carrier' of C
g1 is Element of the carrier' of C
dom g1 is Element of the carrier of C
the Source of C . g1 is Element of the carrier of C
g1 (*) F is Element of the carrier' of C
a2 is Element of the carrier' of C
dom a2 is Element of the carrier of C
the Source of C . a2 is Element of the carrier of C
a2 (*) G is Element of the carrier' of C
g1 (*) m is Element of the carrier' of C
a2 (*) H₁(g1,m) is Element of the carrier' of C
a2 (*) g1 is Element of the carrier' of C
H₁(a2,g1) (*) m is Element of the carrier' of C
cod m is Element of the carrier of C
the Target of C . m is Element of the carrier of C
cod g1 is Element of the carrier of C
the Target of C . g1 is Element of the carrier of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
f is Element of the carrier of C
(C,f) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,f) is non empty set
g is Element of the carrier' of (C,f)
g `2 is set
the carrier' of C is non empty set
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {f} is Element of bool the carrier' of C
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
A1 is Element of (C,f)
A2 is Element of (C,f)
[A1,A2] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of the carrier' of C
[[A1,A2],A3] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
A2 (*) A3 is Element of the carrier' of C
g `11 is set
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {f} is Element of bool the carrier' of C
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
A1 is Element of (C,f)
A2 is Element of (C,f)
[A1,A2] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of the carrier' of C
[[A1,A2],A3] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
A2 (*) A3 is Element of the carrier' of C
g `12 is set
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
A1 is Element of (C,f)
A2 is Element of (C,f)
[A1,A2] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of the carrier' of C
[[A1,A2],A3] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
A2 (*) A3 is Element of the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
the carrier' of C is non empty set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
f is Element of the carrier of C
(C,f) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,f) is non empty set
g is Element of the carrier' of (C,f)
(C,f,g) is Element of (C,f)
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {f} is Element of bool the carrier' of C
(C,f,g) is Element of (C,f)
[(C,f,g),(C,f,g)] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{(C,f,g),(C,f,g)} is non empty set
{(C,f,g)} is non empty set
{{(C,f,g),(C,f,g)},{(C,f,g)}} is non empty set
(C,f,g) is Element of the carrier' of C
[[(C,f,g),(C,f,g)],(C,f,g)] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[(C,f,g),(C,f,g)],(C,f,g)} is non empty set
{[(C,f,g),(C,f,g)]} is non empty Relation-like Function-like set
{{[(C,f,g),(C,f,g)],(C,f,g)},{[(C,f,g),(C,f,g)]}} is non empty set
dom (C,f,g) is Element of the carrier of C
the Source of C . (C,f,g) is Element of the carrier of C
cod (C,f,g) is Element of the carrier of C
the Target of C . (C,f,g) is Element of the carrier of C
(C,f,g) (*) (C,f,g) is Element of the carrier' of C
dom g is Element of the carrier of (C,f)
the carrier of (C,f) is non empty set
the Source of (C,f) is Relation-like the carrier' of (C,f) -defined the carrier of (C,f) -valued Function-like V21( the carrier' of (C,f), the carrier of (C,f)) Element of bool [: the carrier' of (C,f), the carrier of (C,f):]
[: the carrier' of (C,f), the carrier of (C,f):] is non empty Relation-like set
bool [: the carrier' of (C,f), the carrier of (C,f):] is non empty set
the Source of (C,f) . g is Element of the carrier of (C,f)
cod g is Element of the carrier of (C,f)
the Target of (C,f) is Relation-like the carrier' of (C,f) -defined the carrier of (C,f) -valued Function-like V21( the carrier' of (C,f), the carrier of (C,f)) Element of bool [: the carrier' of (C,f), the carrier of (C,f):]
the Target of (C,f) . g is Element of the carrier of (C,f)
A1 is Element of (C,f)
A2 is Element of (C,f)
[A1,A2] is V18() Element of the carrier' of [:C,C:]
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of the carrier' of C
[[A1,A2],A3] is V18() Element of the carrier' of [:[:C,C:],C:]
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
dom A2 is Element of the carrier of C
the Source of C . A2 is Element of the carrier of C
cod A3 is Element of the carrier of C
the Target of C . A3 is Element of the carrier of C
A2 (*) A3 is Element of the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
f is Element of the carrier of C
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {f} is Element of bool the carrier' of C
(C,f) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier of (C,f) is non empty set
[:(C,f),(C,f):] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of (C,f), the carrier of (C,f):] is non empty Relation-like set
the carrier' of (C,f) is non empty set
[: the carrier' of (C,f), the carrier' of (C,f):] is non empty Relation-like set
the Source of (C,f) is Relation-like the carrier' of (C,f) -defined the carrier of (C,f) -valued Function-like V21( the carrier' of (C,f), the carrier of (C,f)) Element of bool [: the carrier' of (C,f), the carrier of (C,f):]
[: the carrier' of (C,f), the carrier of (C,f):] is non empty Relation-like set
bool [: the carrier' of (C,f), the carrier of (C,f):] is non empty set
[: the Source of (C,f), the Source of (C,f):] is Relation-like [: the carrier' of (C,f), the carrier' of (C,f):] -defined [: the carrier of (C,f), the carrier of (C,f):] -valued Function-like V21([: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]) Element of bool [:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]:]
[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]:] is non empty Relation-like set
bool [:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]:] is non empty set
the Target of (C,f) is Relation-like the carrier' of (C,f) -defined the carrier of (C,f) -valued Function-like V21( the carrier' of (C,f), the carrier of (C,f)) Element of bool [: the carrier' of (C,f), the carrier of (C,f):]
[: the Target of (C,f), the Target of (C,f):] is Relation-like [: the carrier' of (C,f), the carrier' of (C,f):] -defined [: the carrier of (C,f), the carrier of (C,f):] -valued Function-like V21([: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]) Element of bool [:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]:]
the Comp of (C,f) is Relation-like [: the carrier' of (C,f), the carrier' of (C,f):] -defined the carrier' of (C,f) -valued Function-like Element of bool [:[: the carrier' of (C,f), the carrier' of (C,f):], the carrier' of (C,f):]
[:[: the carrier' of (C,f), the carrier' of (C,f):], the carrier' of (C,f):] is non empty Relation-like set
bool [:[: the carrier' of (C,f), the carrier' of (C,f):], the carrier' of (C,f):] is non empty set
K222( the carrier' of (C,f), the carrier' of (C,f), the Comp of (C,f), the Comp of (C,f)) is Relation-like [:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:] -defined [: the carrier' of (C,f), the carrier' of (C,f):] -valued Function-like Element of bool [:[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:],[: the carrier' of (C,f), the carrier' of (C,f):]:]
[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:] is non empty Relation-like set
[:[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:],[: the carrier' of (C,f), the carrier' of (C,f):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:],[: the carrier' of (C,f), the carrier' of (C,f):]:] is non empty set
CatStr(# [: the carrier of (C,f), the carrier of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):],[: the Source of (C,f), the Source of (C,f):],[: the Target of (C,f), the Target of (C,f):],K222( the carrier' of (C,f), the carrier' of (C,f), the Comp of (C,f), the Comp of (C,f)) #) is non empty non void V58() strict CatStr
the carrier of [:(C,f),(C,f):] is non empty set
g is Element of (C,f)
dom g is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C . g is Element of the carrier of C
id (dom g) is Morphism of dom g, dom g
A1 is Element of the carrier of (C,f)
id A1 is Morphism of A1,A1
[A1,A1] is V18() Element of the carrier of [:(C,f),(C,f):]
{A1,A1} is non empty set
{A1} is non empty set
{{A1,A1},{A1}} is non empty set
[[A1,A1],(id (dom g))] is V18() Element of [: the carrier of [:(C,f),(C,f):], the carrier' of C:]
[: the carrier of [:(C,f),(C,f):], the carrier' of C:] is non empty Relation-like set
{[A1,A1],(id (dom g))} is non empty set
{[A1,A1]} is non empty Relation-like Function-like set
{{[A1,A1],(id (dom g))},{[A1,A1]}} is non empty set
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
A2 is Element of (C,f)
A3 is Element of (C,f)
[A2,A3] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
F is Element of the carrier' of C
[[A2,A3],F] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[A2,A3],F} is non empty set
{[A2,A3]} is non empty Relation-like Function-like set
{{[A2,A3],F},{[A2,A3]}} is non empty set
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
cod F is Element of the carrier of C
the Target of C . F is Element of the carrier of C
A3 (*) F is Element of the carrier' of C
cod (id (dom g)) is Element of the carrier of C
the Target of C . (id (dom g)) is Element of the carrier of C
g (*) (id (dom g)) is Element of the carrier' of C
[g,g] is V18() Element of the carrier' of [:C,C:]
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
[[g,g],(id (dom g))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[g,g],(id (dom g))} is non empty set
{[g,g]} is non empty Relation-like Function-like set
{{[g,g],(id (dom g))},{[g,g]}} is non empty set
(C,f,(id A1)) is Element of (C,f)
(C,f,(id A1)) is Element of (C,f)
dom (id A1) is Element of the carrier of (C,f)
the Source of (C,f) . (id A1) is Element of the carrier of (C,f)
cod (id A1) is Element of the carrier of (C,f)
the Target of (C,f) . (id A1) is Element of the carrier of (C,f)
G is Element of the carrier' of (C,f)
dom G is Element of the carrier of (C,f)
the Source of (C,f) . G is Element of the carrier of (C,f)
(C,f,G) is Element of (C,f)
G (*) (id A1) is Element of the carrier' of (C,f)
(id (dom g)) (*) F is Element of the carrier' of C
[[g,g],((id (dom g)) (*) F)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[g,g],((id (dom g)) (*) F)} is non empty set
{{[g,g],((id (dom g)) (*) F)},{[g,g]}} is non empty set
[[g,g],F] is V18() Element of the carrier' of [:[:C,C:],C:]
{[g,g],F} is non empty set
{{[g,g],F},{[g,g]}} is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
f is Element of the carrier of C
(C,f) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,f) is non empty set
g is Element of the carrier' of (C,f)
g `2 is set
the carrier' of C is non empty set
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {f} is Element of bool the carrier' of C
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
A1 is Element of (C,f)
A2 is Element of (C,f)
[A1,A2] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of the carrier' of C
[[A1,A2],A3] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
cod A1 is Element of the carrier of C
the Target of C . A1 is Element of the carrier of C
A3 (*) A1 is Element of the carrier' of C
g `11 is set
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {f} is Element of bool the carrier' of C
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
A1 is Element of (C,f)
A2 is Element of (C,f)
[A1,A2] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of the carrier' of C
[[A1,A2],A3] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
cod A1 is Element of the carrier of C
the Target of C . A1 is Element of the carrier of C
A3 (*) A1 is Element of the carrier' of C
g `12 is set
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
A1 is Element of (C,f)
A2 is Element of (C,f)
[A1,A2] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of the carrier' of C
[[A1,A2],A3] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
cod A1 is Element of the carrier of C
the Target of C . A1 is Element of the carrier of C
A3 (*) A1 is Element of the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
the carrier' of C is non empty set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
f is Element of the carrier of C
(C,f) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,f) is non empty set
g is Element of the carrier' of (C,f)
(C,f,g) is Element of (C,f)
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {f} is Element of bool the carrier' of C
(C,f,g) is Element of (C,f)
[(C,f,g),(C,f,g)] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{(C,f,g),(C,f,g)} is non empty set
{(C,f,g)} is non empty set
{{(C,f,g),(C,f,g)},{(C,f,g)}} is non empty set
(C,f,g) is Element of the carrier' of C
[[(C,f,g),(C,f,g)],(C,f,g)] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[(C,f,g),(C,f,g)],(C,f,g)} is non empty set
{[(C,f,g),(C,f,g)]} is non empty Relation-like Function-like set
{{[(C,f,g),(C,f,g)],(C,f,g)},{[(C,f,g),(C,f,g)]}} is non empty set
dom (C,f,g) is Element of the carrier of C
the Source of C . (C,f,g) is Element of the carrier of C
cod (C,f,g) is Element of the carrier of C
the Target of C . (C,f,g) is Element of the carrier of C
(C,f,g) (*) (C,f,g) is Element of the carrier' of C
dom g is Element of the carrier of (C,f)
the carrier of (C,f) is non empty set
the Source of (C,f) is Relation-like the carrier' of (C,f) -defined the carrier of (C,f) -valued Function-like V21( the carrier' of (C,f), the carrier of (C,f)) Element of bool [: the carrier' of (C,f), the carrier of (C,f):]
[: the carrier' of (C,f), the carrier of (C,f):] is non empty Relation-like set
bool [: the carrier' of (C,f), the carrier of (C,f):] is non empty set
the Source of (C,f) . g is Element of the carrier of (C,f)
cod g is Element of the carrier of (C,f)
the Target of (C,f) is Relation-like the carrier' of (C,f) -defined the carrier of (C,f) -valued Function-like V21( the carrier' of (C,f), the carrier of (C,f)) Element of bool [: the carrier' of (C,f), the carrier of (C,f):]
the Target of (C,f) . g is Element of the carrier of (C,f)
A1 is Element of (C,f)
A2 is Element of (C,f)
[A1,A2] is V18() Element of the carrier' of [:C,C:]
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
A3 is Element of the carrier' of C
[[A1,A2],A3] is V18() Element of the carrier' of [:[:C,C:],C:]
{[A1,A2],A3} is non empty set
{[A1,A2]} is non empty Relation-like Function-like set
{{[A1,A2],A3},{[A1,A2]}} is non empty set
dom A3 is Element of the carrier of C
the Source of C . A3 is Element of the carrier of C
cod A1 is Element of the carrier of C
the Target of C . A1 is Element of the carrier of C
A3 (*) A1 is Element of the carrier' of C
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
f is Element of the carrier of C
(C,f) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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
{f} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {f} is Element of bool the carrier' of C
(C,f) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier of (C,f) is non empty set
[:(C,f),(C,f):] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of (C,f), the carrier of (C,f):] is non empty Relation-like set
the carrier' of (C,f) is non empty set
[: the carrier' of (C,f), the carrier' of (C,f):] is non empty Relation-like set
the Source of (C,f) is Relation-like the carrier' of (C,f) -defined the carrier of (C,f) -valued Function-like V21( the carrier' of (C,f), the carrier of (C,f)) Element of bool [: the carrier' of (C,f), the carrier of (C,f):]
[: the carrier' of (C,f), the carrier of (C,f):] is non empty Relation-like set
bool [: the carrier' of (C,f), the carrier of (C,f):] is non empty set
[: the Source of (C,f), the Source of (C,f):] is Relation-like [: the carrier' of (C,f), the carrier' of (C,f):] -defined [: the carrier of (C,f), the carrier of (C,f):] -valued Function-like V21([: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]) Element of bool [:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]:]
[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]:] is non empty Relation-like set
bool [:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]:] is non empty set
the Target of (C,f) is Relation-like the carrier' of (C,f) -defined the carrier of (C,f) -valued Function-like V21( the carrier' of (C,f), the carrier of (C,f)) Element of bool [: the carrier' of (C,f), the carrier of (C,f):]
[: the Target of (C,f), the Target of (C,f):] is Relation-like [: the carrier' of (C,f), the carrier' of (C,f):] -defined [: the carrier of (C,f), the carrier of (C,f):] -valued Function-like V21([: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]) Element of bool [:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier of (C,f), the carrier of (C,f):]:]
the Comp of (C,f) is Relation-like [: the carrier' of (C,f), the carrier' of (C,f):] -defined the carrier' of (C,f) -valued Function-like Element of bool [:[: the carrier' of (C,f), the carrier' of (C,f):], the carrier' of (C,f):]
[:[: the carrier' of (C,f), the carrier' of (C,f):], the carrier' of (C,f):] is non empty Relation-like set
bool [:[: the carrier' of (C,f), the carrier' of (C,f):], the carrier' of (C,f):] is non empty set
K222( the carrier' of (C,f), the carrier' of (C,f), the Comp of (C,f), the Comp of (C,f)) is Relation-like [:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:] -defined [: the carrier' of (C,f), the carrier' of (C,f):] -valued Function-like Element of bool [:[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:],[: the carrier' of (C,f), the carrier' of (C,f):]:]
[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:] is non empty Relation-like set
[:[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:],[: the carrier' of (C,f), the carrier' of (C,f):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (C,f), the carrier' of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):]:],[: the carrier' of (C,f), the carrier' of (C,f):]:] is non empty set
CatStr(# [: the carrier of (C,f), the carrier of (C,f):],[: the carrier' of (C,f), the carrier' of (C,f):],[: the Source of (C,f), the Source of (C,f):],[: the Target of (C,f), the Target of (C,f):],K222( the carrier' of (C,f), the carrier' of (C,f), the Comp of (C,f), the Comp of (C,f)) #) is non empty non void V58() strict CatStr
the carrier of [:(C,f),(C,f):] is non empty set
g is Element of (C,f)
cod g is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . g is Element of the carrier of C
id (cod g) is Morphism of cod g, cod g
A1 is Element of the carrier of (C,f)
id A1 is Morphism of A1,A1
[A1,A1] is V18() Element of the carrier of [:(C,f),(C,f):]
{A1,A1} is non empty set
{A1} is non empty set
{{A1,A1},{A1}} is non empty set
[[A1,A1],(id (cod g))] is V18() Element of [: the carrier of [:(C,f),(C,f):], the carrier' of C:]
[: the carrier of [:(C,f),(C,f):], the carrier' of C:] is non empty Relation-like set
{[A1,A1],(id (cod g))} is non empty set
{[A1,A1]} is non empty Relation-like Function-like set
{{[A1,A1],(id (cod g))},{[A1,A1]}} is non empty set
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
A2 is Element of (C,f)
A3 is Element of (C,f)
[A2,A3] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{A2,A3} is non empty set
{A2} is non empty set
{{A2,A3},{A2}} is non empty set
F is Element of the carrier' of C
[[A2,A3],F] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[A2,A3],F} is non empty set
{[A2,A3]} is non empty Relation-like Function-like set
{{[A2,A3],F},{[A2,A3]}} is non empty set
dom F is Element of the carrier of C
the Source of C . F is Element of the carrier of C
cod A2 is Element of the carrier of C
the Target of C . A2 is Element of the carrier of C
F (*) A2 is Element of the carrier' of C
dom (id (cod g)) is Element of the carrier of C
the Source of C . (id (cod g)) is Element of the carrier of C
(id (cod g)) (*) g is Element of the carrier' of C
[g,g] is V18() Element of the carrier' of [:C,C:]
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
[[g,g],(id (cod g))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[g,g],(id (cod g))} is non empty set
{[g,g]} is non empty Relation-like Function-like set
{{[g,g],(id (cod g))},{[g,g]}} is non empty set
(C,f,(id A1)) is Element of (C,f)
(C,f,(id A1)) is Element of (C,f)
dom (id A1) is Element of the carrier of (C,f)
the Source of (C,f) . (id A1) is Element of the carrier of (C,f)
cod (id A1) is Element of the carrier of (C,f)
the Target of (C,f) . (id A1) is Element of the carrier of (C,f)
G is Element of the carrier' of (C,f)
cod G is Element of the carrier of (C,f)
the Target of (C,f) . G is Element of the carrier of (C,f)
(C,f,G) is Element of (C,f)
(id A1) (*) G is Element of the carrier' of (C,f)
F (*) (id (cod g)) is Element of the carrier' of C
[[g,g],(F (*) (id (cod g)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[g,g],(F (*) (id (cod g)))} is non empty set
{{[g,g],(F (*) (id (cod g)))},{[g,g]}} is non empty set
[[g,g],F] is V18() Element of the carrier' of [:[:C,C:],C:]
{[g,g],F} is non empty set
{{[g,g],F},{[g,g]}} is non empty set
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
f is Element of the carrier' of C
dom f is Element of the carrier of C
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . f is Element of the carrier of C
(C,(dom f)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(dom f)) is non empty set
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . f is Element of the carrier of C
(C,(cod f)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(cod f)) is non empty set
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
the carrier' of [:C,C:] is non empty set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
[: the carrier' of (C,(dom f)), the carrier' of [:[:C,C:],C:]:] is non empty Relation-like set
bool [: the carrier' of (C,(dom f)), the carrier' of [:[:C,C:],C:]:] is non empty set
A2 is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of [:[:C,C:],C:] -valued Function-like V21( the carrier' of (C,(dom f)), the carrier' of [:[:C,C:],C:]) Element of bool [: the carrier' of (C,(dom f)), the carrier' of [:[:C,C:],C:]:]
dom A2 is Element of bool the carrier' of (C,(dom f))
bool the carrier' of (C,(dom f)) is non empty set
rng A2 is Element of bool the carrier' of [:[:C,C:],C:]
bool the carrier' of [:[:C,C:],C:] is non empty set
A3 is set
F is set
A2 . F is set
G is Element of the carrier' of (C,(dom f))
(C,(dom f),G) is Element of (C,(dom f))
(C,(dom f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(dom f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {(dom f)} is Element of bool the carrier' of C
f (*) (C,(dom f),G) is Element of the carrier' of C
(C,(dom f),G) is Element of (C,(dom f))
f (*) (C,(dom f),G) is Element of the carrier' of C
[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))] is V18() Element of the carrier' of [:C,C:]
{(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))} is non empty set
{(f (*) (C,(dom f),G))} is non empty set
{{(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))},{(f (*) (C,(dom f),G))}} is non empty set
(C,(dom f),G) is Element of the carrier' of C
[[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))],(C,(dom f),G)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))],(C,(dom f),G)} is non empty set
{[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))]} is non empty Relation-like Function-like set
{{[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))],(C,(dom f),G)},{[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))]}} is non empty set
dom (C,(dom f),G) is Element of the carrier of C
the Source of C . (C,(dom f),G) is Element of the carrier of C
cod (C,(dom f),G) is Element of the carrier of C
the Target of C . (C,(dom f),G) is Element of the carrier of C
(C,(dom f),G) (*) (C,(dom f),G) is Element of the carrier' of C
cod (C,(dom f),G) is Element of the carrier of C
the Target of C . (C,(dom f),G) is Element of the carrier of C
(C,(cod f)) is non empty Element of bool the carrier' of C
{(cod f)} is non empty Element of bool the carrier of C
the Target of C " {(cod f)} is Element of bool the carrier' of C
dom (f (*) (C,(dom f),G)) is Element of the carrier of C
the Source of C . (f (*) (C,(dom f),G)) is Element of the carrier of C
(f (*) (C,(dom f),G)) (*) (C,(dom f),G) is Element of the carrier' of C
[: the carrier' of (C,(dom f)), the carrier' of (C,(cod f)):] is non empty Relation-like set
bool [: the carrier' of (C,(dom f)), the carrier' of (C,(cod f)):] is non empty set
the carrier of (C,(dom f)) is non empty set
(C,(dom f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(dom f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {(dom f)} is Element of bool the carrier' of C
F is Element of the carrier of (C,(dom f))
(C,(cod f)) is non empty Element of bool the carrier' of C
{(cod f)} is non empty Element of bool the carrier of C
the Target of C " {(cod f)} is Element of bool the carrier' of C
G is Element of (C,(dom f))
f (*) G is Element of the carrier' of C
the carrier of (C,(cod f)) is non empty set
FG is Element of (C,(cod f))
m is Element of the carrier of (C,(cod f))
id F is Morphism of F,F
[:(C,(dom f)),(C,(dom f)):] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):] is non empty Relation-like set
[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] is non empty Relation-like set
the Source of (C,(dom f)) is Relation-like the carrier' of (C,(dom f)) -defined the carrier of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier of (C,(dom f))) Element of bool [: the carrier' of (C,(dom f)), the carrier of (C,(dom f)):]
[: the carrier' of (C,(dom f)), the carrier of (C,(dom f)):] is non empty Relation-like set
bool [: the carrier' of (C,(dom f)), the carrier of (C,(dom f)):] is non empty set
[: the Source of (C,(dom f)), the Source of (C,(dom f)):] is Relation-like [: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] -defined [: the carrier of (C,(dom f)), the carrier of (C,(dom f)):] -valued Function-like V21([: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]) Element of bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]:]
[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]:] is non empty Relation-like set
bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]:] is non empty set
the Target of (C,(dom f)) is Relation-like the carrier' of (C,(dom f)) -defined the carrier of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier of (C,(dom f))) Element of bool [: the carrier' of (C,(dom f)), the carrier of (C,(dom f)):]
[: the Target of (C,(dom f)), the Target of (C,(dom f)):] is Relation-like [: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] -defined [: the carrier of (C,(dom f)), the carrier of (C,(dom f)):] -valued Function-like V21([: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]) Element of bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]:]
the Comp of (C,(dom f)) is Relation-like [: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] -defined the carrier' of (C,(dom f)) -valued Function-like Element of bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):], the carrier' of (C,(dom f)):]
[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):], the carrier' of (C,(dom f)):] is non empty Relation-like set
bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):], the carrier' of (C,(dom f)):] is non empty set
K222( the carrier' of (C,(dom f)), the carrier' of (C,(dom f)), the Comp of (C,(dom f)), the Comp of (C,(dom f))) is Relation-like [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:] -defined [: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] -valued Function-like Element of bool [:[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:]
[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:] is non empty Relation-like set
[:[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:] is non empty set
CatStr(# [: the carrier of (C,(dom f)), the carrier of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the Source of (C,(dom f)), the Source of (C,(dom f)):],[: the Target of (C,(dom f)), the Target of (C,(dom f)):],K222( the carrier' of (C,(dom f)), the carrier' of (C,(dom f)), the Comp of (C,(dom f)), the Comp of (C,(dom f))) #) is non empty non void V58() strict CatStr
the carrier of [:(C,(dom f)),(C,(dom f)):] is non empty set
[F,F] is V18() Element of the carrier of [:(C,(dom f)),(C,(dom f)):]
{F,F} is non empty set
{F} is non empty set
{{F,F},{F}} is non empty set
dom G is Element of the carrier of C
the Source of C . G is Element of the carrier of C
id (dom G) is Morphism of dom G, dom G
[[F,F],(id (dom G))] is V18() Element of [: the carrier of [:(C,(dom f)),(C,(dom f)):], the carrier' of C:]
[: the carrier of [:(C,(dom f)),(C,(dom f)):], the carrier' of C:] is non empty Relation-like set
{[F,F],(id (dom G))} is non empty set
{[F,F]} is non empty Relation-like Function-like set
{{[F,F],(id (dom G))},{[F,F]}} is non empty set
g1 is Element of the carrier of (C,(cod f))
id g1 is Morphism of g1,g1
[:(C,(cod f)),(C,(cod f)):] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):] is non empty Relation-like set
[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] is non empty Relation-like set
the Source of (C,(cod f)) is Relation-like the carrier' of (C,(cod f)) -defined the carrier of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier of (C,(cod f))) Element of bool [: the carrier' of (C,(cod f)), the carrier of (C,(cod f)):]
[: the carrier' of (C,(cod f)), the carrier of (C,(cod f)):] is non empty Relation-like set
bool [: the carrier' of (C,(cod f)), the carrier of (C,(cod f)):] is non empty set
[: the Source of (C,(cod f)), the Source of (C,(cod f)):] is Relation-like [: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] -defined [: the carrier of (C,(cod f)), the carrier of (C,(cod f)):] -valued Function-like V21([: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]) Element of bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]:]
[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]:] is non empty Relation-like set
bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]:] is non empty set
the Target of (C,(cod f)) is Relation-like the carrier' of (C,(cod f)) -defined the carrier of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier of (C,(cod f))) Element of bool [: the carrier' of (C,(cod f)), the carrier of (C,(cod f)):]
[: the Target of (C,(cod f)), the Target of (C,(cod f)):] is Relation-like [: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] -defined [: the carrier of (C,(cod f)), the carrier of (C,(cod f)):] -valued Function-like V21([: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]) Element of bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]:]
the Comp of (C,(cod f)) is Relation-like [: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] -defined the carrier' of (C,(cod f)) -valued Function-like Element of bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):], the carrier' of (C,(cod f)):]
[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):], the carrier' of (C,(cod f)):] is non empty Relation-like set
bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):], the carrier' of (C,(cod f)):] is non empty set
K222( the carrier' of (C,(cod f)), the carrier' of (C,(cod f)), the Comp of (C,(cod f)), the Comp of (C,(cod f))) is Relation-like [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:] -defined [: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] -valued Function-like Element of bool [:[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:]
[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:] is non empty Relation-like set
[:[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:] is non empty set
CatStr(# [: the carrier of (C,(cod f)), the carrier of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the Source of (C,(cod f)), the Source of (C,(cod f)):],[: the Target of (C,(cod f)), the Target of (C,(cod f)):],K222( the carrier' of (C,(cod f)), the carrier' of (C,(cod f)), the Comp of (C,(cod f)), the Comp of (C,(cod f))) #) is non empty non void V58() strict CatStr
the carrier of [:(C,(cod f)),(C,(cod f)):] is non empty set
[g1,g1] is V18() Element of the carrier of [:(C,(cod f)),(C,(cod f)):]
{g1,g1} is non empty set
{g1} is non empty set
{{g1,g1},{g1}} is non empty set
dom FG is Element of the carrier of C
the Source of C . FG is Element of the carrier of C
id (dom FG) is Morphism of dom FG, dom FG
[[g1,g1],(id (dom FG))] is V18() Element of [: the carrier of [:(C,(cod f)),(C,(cod f)):], the carrier' of C:]
[: the carrier of [:(C,(cod f)),(C,(cod f)):], the carrier' of C:] is non empty Relation-like set
{[g1,g1],(id (dom FG))} is non empty set
{[g1,g1]} is non empty Relation-like Function-like set
{{[g1,g1],(id (dom FG))},{[g1,g1]}} is non empty set
(C,(dom f),(id F)) is Element of (C,(dom f))
(C,(dom f),(id F)) is Element of (C,(dom f))
(C,(dom f),(id F)) is Element of the carrier' of C
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
A3 is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier' of (C,(cod f))) Element of bool [: the carrier' of (C,(dom f)), the carrier' of (C,(cod f)):]
A3 . (id F) is Element of the carrier' of (C,(cod f))
[FG,FG] is V18() Element of the carrier' of [:C,C:]
{FG,FG} is non empty set
{FG} is non empty set
{{FG,FG},{FG}} is non empty set
[[FG,FG],(C,(dom f),(id F))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,FG],(C,(dom f),(id F))} is non empty set
{[FG,FG]} is non empty Relation-like Function-like set
{{[FG,FG],(C,(dom f),(id F))},{[FG,FG]}} is non empty set
F is Element of the carrier' of (C,(dom f))
(C,(dom f),F) is Element of (C,(dom f))
f (*) (C,(dom f),F) is Element of the carrier' of C
(C,(dom f),F) is Element of (C,(dom f))
f (*) (C,(dom f),F) is Element of the carrier' of C
cod (C,(dom f),F) is Element of the carrier of C
the Target of C . (C,(dom f),F) is Element of the carrier of C
cod (C,(dom f),F) is Element of the carrier of C
the Target of C . (C,(dom f),F) is Element of the carrier of C
A3 . F is Element of the carrier' of (C,(cod f))
G is Element of (C,(cod f))
FG is Element of (C,(cod f))
[G,FG] is V18() Element of the carrier' of [:C,C:]
{G,FG} is non empty set
{G} is non empty set
{{G,FG},{G}} is non empty set
(C,(dom f),F) is Element of the carrier' of C
[[G,FG],(C,(dom f),F)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[G,FG],(C,(dom f),F)} is non empty set
{[G,FG]} is non empty Relation-like Function-like set
{{[G,FG],(C,(dom f),F)},{[G,FG]}} is non empty set
dom (A3 . F) is Element of the carrier of (C,(cod f))
the Source of (C,(cod f)) . (A3 . F) is Element of the carrier of (C,(cod f))
[[G,FG],(C,(dom f),F)] `11 is set
id (dom (A3 . F)) is Morphism of dom (A3 . F), dom (A3 . F)
[G,G] is V18() Element of the carrier' of [:C,C:]
{G,G} is non empty set
{{G,G},{G}} is non empty set
dom G is Element of the carrier of C
the Source of C . G is Element of the carrier of C
id (dom G) is Morphism of dom G, dom G
[[G,G],(id (dom G))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[G,G],(id (dom G))} is non empty set
{[G,G]} is non empty Relation-like Function-like set
{{[G,G],(id (dom G))},{[G,G]}} is non empty set
dom F is Element of the carrier of (C,(dom f))
the Source of (C,(dom f)) . F is Element of the carrier of (C,(dom f))
id (dom F) is Morphism of dom F, dom F
[(C,(dom f),F),(C,(dom f),F)] is V18() Element of the carrier' of [:C,C:]
{(C,(dom f),F),(C,(dom f),F)} is non empty set
{(C,(dom f),F)} is non empty set
{{(C,(dom f),F),(C,(dom f),F)},{(C,(dom f),F)}} is non empty set
dom (C,(dom f),F) is Element of the carrier of C
the Source of C . (C,(dom f),F) is Element of the carrier of C
id (dom (C,(dom f),F)) is Morphism of dom (C,(dom f),F), dom (C,(dom f),F)
[[(C,(dom f),F),(C,(dom f),F)],(id (dom (C,(dom f),F)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[(C,(dom f),F),(C,(dom f),F)],(id (dom (C,(dom f),F)))} is non empty set
{[(C,(dom f),F),(C,(dom f),F)]} is non empty Relation-like Function-like set
{{[(C,(dom f),F),(C,(dom f),F)],(id (dom (C,(dom f),F)))},{[(C,(dom f),F),(C,(dom f),F)]}} is non empty set
(C,(dom f),(id (dom F))) is Element of (C,(dom f))
(C,(dom f),(id (dom F))) is Element of (C,(dom f))
(C,(dom f),(id (dom F))) is Element of the carrier' of C
A3 . (id (dom F)) is Element of the carrier' of (C,(cod f))
[[G,G],(id (dom (C,(dom f),F)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[G,G],(id (dom (C,(dom f),F)))} is non empty set
{{[G,G],(id (dom (C,(dom f),F)))},{[G,G]}} is non empty set
cod (A3 . F) is Element of the carrier of (C,(cod f))
the Target of (C,(cod f)) . (A3 . F) is Element of the carrier of (C,(cod f))
[[G,FG],(C,(dom f),F)] `12 is set
id (cod (A3 . F)) is Morphism of cod (A3 . F), cod (A3 . F)
[FG,FG] is V18() Element of the carrier' of [:C,C:]
{FG,FG} is non empty set
{FG} is non empty set
{{FG,FG},{FG}} is non empty set
dom FG is Element of the carrier of C
the Source of C . FG is Element of the carrier of C
id (dom FG) is Morphism of dom FG, dom FG
[[FG,FG],(id (dom FG))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,FG],(id (dom FG))} is non empty set
{[FG,FG]} is non empty Relation-like Function-like set
{{[FG,FG],(id (dom FG))},{[FG,FG]}} is non empty set
cod F is Element of the carrier of (C,(dom f))
the Target of (C,(dom f)) . F is Element of the carrier of (C,(dom f))
id (cod F) is Morphism of cod F, cod F
[(C,(dom f),F),(C,(dom f),F)] is V18() Element of the carrier' of [:C,C:]
{(C,(dom f),F),(C,(dom f),F)} is non empty set
{(C,(dom f),F)} is non empty set
{{(C,(dom f),F),(C,(dom f),F)},{(C,(dom f),F)}} is non empty set
dom (C,(dom f),F) is Element of the carrier of C
the Source of C . (C,(dom f),F) is Element of the carrier of C
id (dom (C,(dom f),F)) is Morphism of dom (C,(dom f),F), dom (C,(dom f),F)
[[(C,(dom f),F),(C,(dom f),F)],(id (dom (C,(dom f),F)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[(C,(dom f),F),(C,(dom f),F)],(id (dom (C,(dom f),F)))} is non empty set
{[(C,(dom f),F),(C,(dom f),F)]} is non empty Relation-like Function-like set
{{[(C,(dom f),F),(C,(dom f),F)],(id (dom (C,(dom f),F)))},{[(C,(dom f),F),(C,(dom f),F)]}} is non empty set
(C,(dom f),(id (cod F))) is Element of (C,(dom f))
(C,(dom f),(id (cod F))) is Element of (C,(dom f))
(C,(dom f),(id (cod F))) is Element of the carrier' of C
A3 . (id (cod F)) is Element of the carrier' of (C,(cod f))
[[FG,FG],(id (dom (C,(dom f),F)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,FG],(id (dom (C,(dom f),F)))} is non empty set
{{[FG,FG],(id (dom (C,(dom f),F)))},{[FG,FG]}} is non empty set
F is Element of the carrier' of (C,(dom f))
FG is Element of (C,(dom f))
m is Element of (C,(dom f))
[FG,m] is V18() Element of the carrier' of [:C,C:]
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
g1 is Element of the carrier' of C
[[FG,m],g1] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,m],g1} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],g1},{[FG,m]}} is non empty set
dom m is Element of the carrier of C
the Source of C . m is Element of the carrier of C
cod g1 is Element of the carrier of C
the Target of C . g1 is Element of the carrier of C
m (*) g1 is Element of the carrier' of C
G is Element of the carrier' of (C,(dom f))
a2 is Element of (C,(dom f))
b2 is Element of (C,(dom f))
[a2,b2] is V18() Element of the carrier' of [:C,C:]
{a2,b2} is non empty set
{a2} is non empty set
{{a2,b2},{a2}} is non empty set
g2 is Element of the carrier' of C
[[a2,b2],g2] is V18() Element of the carrier' of [:[:C,C:],C:]
{[a2,b2],g2} is non empty set
{[a2,b2]} is non empty Relation-like Function-like set
{{[a2,b2],g2},{[a2,b2]}} is non empty set
dom b2 is Element of the carrier of C
the Source of C . b2 is Element of the carrier of C
cod g2 is Element of the carrier of C
the Target of C . g2 is Element of the carrier of C
b2 (*) g2 is Element of the carrier' of C
dom G is Element of the carrier of (C,(dom f))
the Source of (C,(dom f)) . G is Element of the carrier of (C,(dom f))
(C,(dom f),G) is Element of (C,(dom f))
cod F is Element of the carrier of (C,(dom f))
the Target of (C,(dom f)) . F is Element of the carrier of (C,(dom f))
(C,(dom f),F) is Element of (C,(dom f))
f (*) FG is Element of the carrier' of C
f (*) a2 is Element of the carrier' of C
f (*) m is Element of the carrier' of C
f (*) b2 is Element of the carrier' of C
(C,(dom f),F) is Element of (C,(dom f))
(C,(dom f),F) is Element of the carrier' of C
(C,(dom f),G) is Element of (C,(dom f))
(C,(dom f),G) is Element of the carrier' of C
A3 . F is Element of the carrier' of (C,(cod f))
ha1 is Element of (C,(cod f))
hb1 is Element of (C,(cod f))
[ha1,hb1] is V18() Element of the carrier' of [:C,C:]
{ha1,hb1} is non empty set
{ha1} is non empty set
{{ha1,hb1},{ha1}} is non empty set
[[ha1,hb1],g1] is V18() Element of the carrier' of [:[:C,C:],C:]
{[ha1,hb1],g1} is non empty set
{[ha1,hb1]} is non empty Relation-like Function-like set
{{[ha1,hb1],g1},{[ha1,hb1]}} is non empty set
A3 . G is Element of the carrier' of (C,(cod f))
ha2 is Element of (C,(cod f))
hb2 is Element of (C,(cod f))
[ha2,hb2] is V18() Element of the carrier' of [:C,C:]
{ha2,hb2} is non empty set
{ha2} is non empty set
{{ha2,hb2},{ha2}} is non empty set
[[ha2,hb2],g2] is V18() Element of the carrier' of [:[:C,C:],C:]
{[ha2,hb2],g2} is non empty set
{[ha2,hb2]} is non empty Relation-like Function-like set
{{[ha2,hb2],g2},{[ha2,hb2]}} is non empty set
G (*) F is Element of the carrier' of (C,(dom f))
[FG,b2] is V18() Element of the carrier' of [:C,C:]
{FG,b2} is non empty set
{{FG,b2},{FG}} is non empty set
g2 (*) g1 is Element of the carrier' of C
[[FG,b2],(g2 (*) g1)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,b2],(g2 (*) g1)} is non empty set
{[FG,b2]} is non empty Relation-like Function-like set
{{[FG,b2],(g2 (*) g1)},{[FG,b2]}} is non empty set
(A3 . G) (*) (A3 . F) is Element of the carrier' of (C,(cod f))
[ha1,hb2] is V18() Element of the carrier' of [:C,C:]
{ha1,hb2} is non empty set
{{ha1,hb2},{ha1}} is non empty set
[[ha1,hb2],(g2 (*) g1)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[ha1,hb2],(g2 (*) g1)} is non empty set
{[ha1,hb2]} is non empty Relation-like Function-like set
{{[ha1,hb2],(g2 (*) g1)},{[ha1,hb2]}} is non empty set
(C,(dom f),(G (*) F)) is Element of (C,(dom f))
(C,(dom f),(G (*) F)) is Element of (C,(dom f))
(C,(dom f),(G (*) F)) is Element of the carrier' of C
A3 . (G (*) F) is Element of the carrier' of (C,(cod f))
F is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier' of (C,(cod f))) Functor of (C,(dom f)),(C,(cod f))
G is Element of the carrier' of (C,(dom f))
F . G is Element of the carrier' of (C,(cod f))
(C,(dom f),G) is Element of (C,(dom f))
f (*) (C,(dom f),G) is Element of the carrier' of C
(C,(dom f),G) is Element of (C,(dom f))
f (*) (C,(dom f),G) is Element of the carrier' of C
[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))] is V18() Element of the carrier' of [:C,C:]
{(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))} is non empty set
{(f (*) (C,(dom f),G))} is non empty set
{{(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))},{(f (*) (C,(dom f),G))}} is non empty set
(C,(dom f),G) is Element of the carrier' of C
[[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))],(C,(dom f),G)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))],(C,(dom f),G)} is non empty set
{[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))]} is non empty Relation-like Function-like set
{{[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))],(C,(dom f),G)},{[(f (*) (C,(dom f),G)),(f (*) (C,(dom f),G))]}} is non empty set
g is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier' of (C,(cod f))) Functor of (C,(dom f)),(C,(cod f))
A1 is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier' of (C,(cod f))) Functor of (C,(dom f)),(C,(cod f))
A2 is Element of the carrier' of (C,(dom f))
g . A2 is Element of the carrier' of (C,(cod f))
(C,(dom f),A2) is Element of (C,(dom f))
(C,(dom f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(dom f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {(dom f)} is Element of bool the carrier' of C
f (*) (C,(dom f),A2) is Element of the carrier' of C
(C,(dom f),A2) is Element of (C,(dom f))
f (*) (C,(dom f),A2) is Element of the carrier' of C
[(f (*) (C,(dom f),A2)),(f (*) (C,(dom f),A2))] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{(f (*) (C,(dom f),A2)),(f (*) (C,(dom f),A2))} is non empty set
{(f (*) (C,(dom f),A2))} is non empty set
{{(f (*) (C,(dom f),A2)),(f (*) (C,(dom f),A2))},{(f (*) (C,(dom f),A2))}} is non empty set
(C,(dom f),A2) is Element of the carrier' of C
[[(f (*) (C,(dom f),A2)),(f (*) (C,(dom f),A2))],(C,(dom f),A2)] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[(f (*) (C,(dom f),A2)),(f (*) (C,(dom f),A2))],(C,(dom f),A2)} is non empty set
{[(f (*) (C,(dom f),A2)),(f (*) (C,(dom f),A2))]} is non empty Relation-like Function-like set
{{[(f (*) (C,(dom f),A2)),(f (*) (C,(dom f),A2))],(C,(dom f),A2)},{[(f (*) (C,(dom f),A2)),(f (*) (C,(dom f),A2))]}} is non empty set
A1 . A2 is Element of the carrier' of (C,(cod f))
(C,(cod f)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(cod f)) is non empty set
(C,(dom f)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(dom f)) is non empty set
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
the carrier' of [:C,C:] is non empty set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
[: the carrier' of (C,(cod f)), the carrier' of [:[:C,C:],C:]:] is non empty Relation-like set
bool [: the carrier' of (C,(cod f)), the carrier' of [:[:C,C:],C:]:] is non empty set
A2 is Relation-like the carrier' of (C,(cod f)) -defined the carrier' of [:[:C,C:],C:] -valued Function-like V21( the carrier' of (C,(cod f)), the carrier' of [:[:C,C:],C:]) Element of bool [: the carrier' of (C,(cod f)), the carrier' of [:[:C,C:],C:]:]
dom A2 is Element of bool the carrier' of (C,(cod f))
bool the carrier' of (C,(cod f)) is non empty set
rng A2 is Element of bool the carrier' of [:[:C,C:],C:]
bool the carrier' of [:[:C,C:],C:] is non empty set
A3 is set
F is set
A2 . F is set
G is Element of the carrier' of (C,(cod f))
(C,(cod f),G) is Element of (C,(cod f))
(C,(cod f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(cod f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {(cod f)} is Element of bool the carrier' of C
(C,(cod f),G) (*) f is Element of the carrier' of C
(C,(cod f),G) is Element of (C,(cod f))
(C,(cod f),G) (*) f is Element of the carrier' of C
[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)] is V18() Element of the carrier' of [:C,C:]
{((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)} is non empty set
{((C,(cod f),G) (*) f)} is non empty set
{{((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)},{((C,(cod f),G) (*) f)}} is non empty set
(C,(cod f),G) is Element of the carrier' of C
[[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)],(C,(cod f),G)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)],(C,(cod f),G)} is non empty set
{[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)]} is non empty Relation-like Function-like set
{{[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)],(C,(cod f),G)},{[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)]}} is non empty set
dom (C,(cod f),G) is Element of the carrier of C
the Source of C . (C,(cod f),G) is Element of the carrier of C
cod (C,(cod f),G) is Element of the carrier of C
the Target of C . (C,(cod f),G) is Element of the carrier of C
(C,(cod f),G) (*) (C,(cod f),G) is Element of the carrier' of C
dom (C,(cod f),G) is Element of the carrier of C
the Source of C . (C,(cod f),G) is Element of the carrier of C
(C,(dom f)) is non empty Element of bool the carrier' of C
{(dom f)} is non empty Element of bool the carrier of C
the Source of C " {(dom f)} is Element of bool the carrier' of C
cod ((C,(cod f),G) (*) f) is Element of the carrier of C
the Target of C . ((C,(cod f),G) (*) f) is Element of the carrier of C
(C,(cod f),G) (*) ((C,(cod f),G) (*) f) is Element of the carrier' of C
[: the carrier' of (C,(cod f)), the carrier' of (C,(dom f)):] is non empty Relation-like set
bool [: the carrier' of (C,(cod f)), the carrier' of (C,(dom f)):] is non empty set
the carrier of (C,(cod f)) is non empty set
(C,(cod f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(cod f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {(cod f)} is Element of bool the carrier' of C
F is Element of the carrier of (C,(cod f))
(C,(dom f)) is non empty Element of bool the carrier' of C
{(dom f)} is non empty Element of bool the carrier of C
the Source of C " {(dom f)} is Element of bool the carrier' of C
G is Element of (C,(cod f))
G (*) f is Element of the carrier' of C
the carrier of (C,(dom f)) is non empty set
FG is Element of (C,(dom f))
m is Element of the carrier of (C,(dom f))
id F is Morphism of F,F
[:(C,(cod f)),(C,(cod f)):] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):] is non empty Relation-like set
[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] is non empty Relation-like set
the Source of (C,(cod f)) is Relation-like the carrier' of (C,(cod f)) -defined the carrier of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier of (C,(cod f))) Element of bool [: the carrier' of (C,(cod f)), the carrier of (C,(cod f)):]
[: the carrier' of (C,(cod f)), the carrier of (C,(cod f)):] is non empty Relation-like set
bool [: the carrier' of (C,(cod f)), the carrier of (C,(cod f)):] is non empty set
[: the Source of (C,(cod f)), the Source of (C,(cod f)):] is Relation-like [: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] -defined [: the carrier of (C,(cod f)), the carrier of (C,(cod f)):] -valued Function-like V21([: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]) Element of bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]:]
[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]:] is non empty Relation-like set
bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]:] is non empty set
the Target of (C,(cod f)) is Relation-like the carrier' of (C,(cod f)) -defined the carrier of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier of (C,(cod f))) Element of bool [: the carrier' of (C,(cod f)), the carrier of (C,(cod f)):]
[: the Target of (C,(cod f)), the Target of (C,(cod f)):] is Relation-like [: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] -defined [: the carrier of (C,(cod f)), the carrier of (C,(cod f)):] -valued Function-like V21([: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]) Element of bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier of (C,(cod f)), the carrier of (C,(cod f)):]:]
the Comp of (C,(cod f)) is Relation-like [: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] -defined the carrier' of (C,(cod f)) -valued Function-like Element of bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):], the carrier' of (C,(cod f)):]
[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):], the carrier' of (C,(cod f)):] is non empty Relation-like set
bool [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):], the carrier' of (C,(cod f)):] is non empty set
K222( the carrier' of (C,(cod f)), the carrier' of (C,(cod f)), the Comp of (C,(cod f)), the Comp of (C,(cod f))) is Relation-like [:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:] -defined [: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):] -valued Function-like Element of bool [:[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:]
[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:] is non empty Relation-like set
[:[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):]:] is non empty set
CatStr(# [: the carrier of (C,(cod f)), the carrier of (C,(cod f)):],[: the carrier' of (C,(cod f)), the carrier' of (C,(cod f)):],[: the Source of (C,(cod f)), the Source of (C,(cod f)):],[: the Target of (C,(cod f)), the Target of (C,(cod f)):],K222( the carrier' of (C,(cod f)), the carrier' of (C,(cod f)), the Comp of (C,(cod f)), the Comp of (C,(cod f))) #) is non empty non void V58() strict CatStr
the carrier of [:(C,(cod f)),(C,(cod f)):] is non empty set
[F,F] is V18() Element of the carrier of [:(C,(cod f)),(C,(cod f)):]
{F,F} is non empty set
{F} is non empty set
{{F,F},{F}} is non empty set
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
id (cod G) is Morphism of cod G, cod G
[[F,F],(id (cod G))] is V18() Element of [: the carrier of [:(C,(cod f)),(C,(cod f)):], the carrier' of C:]
[: the carrier of [:(C,(cod f)),(C,(cod f)):], the carrier' of C:] is non empty Relation-like set
{[F,F],(id (cod G))} is non empty set
{[F,F]} is non empty Relation-like Function-like set
{{[F,F],(id (cod G))},{[F,F]}} is non empty set
g1 is Element of the carrier of (C,(dom f))
id g1 is Morphism of g1,g1
[:(C,(dom f)),(C,(dom f)):] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):] is non empty Relation-like set
[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] is non empty Relation-like set
the Source of (C,(dom f)) is Relation-like the carrier' of (C,(dom f)) -defined the carrier of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier of (C,(dom f))) Element of bool [: the carrier' of (C,(dom f)), the carrier of (C,(dom f)):]
[: the carrier' of (C,(dom f)), the carrier of (C,(dom f)):] is non empty Relation-like set
bool [: the carrier' of (C,(dom f)), the carrier of (C,(dom f)):] is non empty set
[: the Source of (C,(dom f)), the Source of (C,(dom f)):] is Relation-like [: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] -defined [: the carrier of (C,(dom f)), the carrier of (C,(dom f)):] -valued Function-like V21([: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]) Element of bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]:]
[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]:] is non empty Relation-like set
bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]:] is non empty set
the Target of (C,(dom f)) is Relation-like the carrier' of (C,(dom f)) -defined the carrier of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier of (C,(dom f))) Element of bool [: the carrier' of (C,(dom f)), the carrier of (C,(dom f)):]
[: the Target of (C,(dom f)), the Target of (C,(dom f)):] is Relation-like [: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] -defined [: the carrier of (C,(dom f)), the carrier of (C,(dom f)):] -valued Function-like V21([: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]) Element of bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier of (C,(dom f)), the carrier of (C,(dom f)):]:]
the Comp of (C,(dom f)) is Relation-like [: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] -defined the carrier' of (C,(dom f)) -valued Function-like Element of bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):], the carrier' of (C,(dom f)):]
[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):], the carrier' of (C,(dom f)):] is non empty Relation-like set
bool [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):], the carrier' of (C,(dom f)):] is non empty set
K222( the carrier' of (C,(dom f)), the carrier' of (C,(dom f)), the Comp of (C,(dom f)), the Comp of (C,(dom f))) is Relation-like [:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:] -defined [: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):] -valued Function-like Element of bool [:[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:]
[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:] is non empty Relation-like set
[:[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:] is non empty Relation-like set
bool [:[:[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):]:] is non empty set
CatStr(# [: the carrier of (C,(dom f)), the carrier of (C,(dom f)):],[: the carrier' of (C,(dom f)), the carrier' of (C,(dom f)):],[: the Source of (C,(dom f)), the Source of (C,(dom f)):],[: the Target of (C,(dom f)), the Target of (C,(dom f)):],K222( the carrier' of (C,(dom f)), the carrier' of (C,(dom f)), the Comp of (C,(dom f)), the Comp of (C,(dom f))) #) is non empty non void V58() strict CatStr
the carrier of [:(C,(dom f)),(C,(dom f)):] is non empty set
[g1,g1] is V18() Element of the carrier of [:(C,(dom f)),(C,(dom f)):]
{g1,g1} is non empty set
{g1} is non empty set
{{g1,g1},{g1}} is non empty set
cod FG is Element of the carrier of C
the Target of C . FG is Element of the carrier of C
id (cod FG) is Morphism of cod FG, cod FG
[[g1,g1],(id (cod FG))] is V18() Element of [: the carrier of [:(C,(dom f)),(C,(dom f)):], the carrier' of C:]
[: the carrier of [:(C,(dom f)),(C,(dom f)):], the carrier' of C:] is non empty Relation-like set
{[g1,g1],(id (cod FG))} is non empty set
{[g1,g1]} is non empty Relation-like Function-like set
{{[g1,g1],(id (cod FG))},{[g1,g1]}} is non empty set
(C,(cod f),(id F)) is Element of (C,(cod f))
(C,(cod f),(id F)) is Element of (C,(cod f))
(C,(cod f),(id F)) is Element of the carrier' of C
dom G is Element of the carrier of C
the Source of C . G is Element of the carrier of C
A3 is Relation-like the carrier' of (C,(cod f)) -defined the carrier' of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier' of (C,(dom f))) Element of bool [: the carrier' of (C,(cod f)), the carrier' of (C,(dom f)):]
A3 . (id F) is Element of the carrier' of (C,(dom f))
[FG,FG] is V18() Element of the carrier' of [:C,C:]
{FG,FG} is non empty set
{FG} is non empty set
{{FG,FG},{FG}} is non empty set
[[FG,FG],(C,(cod f),(id F))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,FG],(C,(cod f),(id F))} is non empty set
{[FG,FG]} is non empty Relation-like Function-like set
{{[FG,FG],(C,(cod f),(id F))},{[FG,FG]}} is non empty set
F is Element of the carrier' of (C,(cod f))
(C,(cod f),F) is Element of (C,(cod f))
(C,(cod f),F) (*) f is Element of the carrier' of C
(C,(cod f),F) is Element of (C,(cod f))
(C,(cod f),F) (*) f is Element of the carrier' of C
dom (C,(cod f),F) is Element of the carrier of C
the Source of C . (C,(cod f),F) is Element of the carrier of C
dom (C,(cod f),F) is Element of the carrier of C
the Source of C . (C,(cod f),F) is Element of the carrier of C
A3 . F is Element of the carrier' of (C,(dom f))
G is Element of (C,(dom f))
FG is Element of (C,(dom f))
[G,FG] is V18() Element of the carrier' of [:C,C:]
{G,FG} is non empty set
{G} is non empty set
{{G,FG},{G}} is non empty set
(C,(cod f),F) is Element of the carrier' of C
[[G,FG],(C,(cod f),F)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[G,FG],(C,(cod f),F)} is non empty set
{[G,FG]} is non empty Relation-like Function-like set
{{[G,FG],(C,(cod f),F)},{[G,FG]}} is non empty set
dom (A3 . F) is Element of the carrier of (C,(dom f))
the Source of (C,(dom f)) . (A3 . F) is Element of the carrier of (C,(dom f))
[[G,FG],(C,(cod f),F)] `11 is set
id (dom (A3 . F)) is Morphism of dom (A3 . F), dom (A3 . F)
[G,G] is V18() Element of the carrier' of [:C,C:]
{G,G} is non empty set
{{G,G},{G}} is non empty set
cod G is Element of the carrier of C
the Target of C . G is Element of the carrier of C
id (cod G) is Morphism of cod G, cod G
[[G,G],(id (cod G))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[G,G],(id (cod G))} is non empty set
{[G,G]} is non empty Relation-like Function-like set
{{[G,G],(id (cod G))},{[G,G]}} is non empty set
dom F is Element of the carrier of (C,(cod f))
the Source of (C,(cod f)) . F is Element of the carrier of (C,(cod f))
id (dom F) is Morphism of dom F, dom F
[(C,(cod f),F),(C,(cod f),F)] is V18() Element of the carrier' of [:C,C:]
{(C,(cod f),F),(C,(cod f),F)} is non empty set
{(C,(cod f),F)} is non empty set
{{(C,(cod f),F),(C,(cod f),F)},{(C,(cod f),F)}} is non empty set
cod (C,(cod f),F) is Element of the carrier of C
the Target of C . (C,(cod f),F) is Element of the carrier of C
id (cod (C,(cod f),F)) is Morphism of cod (C,(cod f),F), cod (C,(cod f),F)
[[(C,(cod f),F),(C,(cod f),F)],(id (cod (C,(cod f),F)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[(C,(cod f),F),(C,(cod f),F)],(id (cod (C,(cod f),F)))} is non empty set
{[(C,(cod f),F),(C,(cod f),F)]} is non empty Relation-like Function-like set
{{[(C,(cod f),F),(C,(cod f),F)],(id (cod (C,(cod f),F)))},{[(C,(cod f),F),(C,(cod f),F)]}} is non empty set
(C,(cod f),(id (dom F))) is Element of (C,(cod f))
(C,(cod f),(id (dom F))) is Element of (C,(cod f))
(C,(cod f),(id (dom F))) is Element of the carrier' of C
A3 . (id (dom F)) is Element of the carrier' of (C,(dom f))
[[G,G],(id (cod (C,(cod f),F)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[G,G],(id (cod (C,(cod f),F)))} is non empty set
{{[G,G],(id (cod (C,(cod f),F)))},{[G,G]}} is non empty set
cod (A3 . F) is Element of the carrier of (C,(dom f))
the Target of (C,(dom f)) . (A3 . F) is Element of the carrier of (C,(dom f))
[[G,FG],(C,(cod f),F)] `12 is set
id (cod (A3 . F)) is Morphism of cod (A3 . F), cod (A3 . F)
[FG,FG] is V18() Element of the carrier' of [:C,C:]
{FG,FG} is non empty set
{FG} is non empty set
{{FG,FG},{FG}} is non empty set
cod FG is Element of the carrier of C
the Target of C . FG is Element of the carrier of C
id (cod FG) is Morphism of cod FG, cod FG
[[FG,FG],(id (cod FG))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,FG],(id (cod FG))} is non empty set
{[FG,FG]} is non empty Relation-like Function-like set
{{[FG,FG],(id (cod FG))},{[FG,FG]}} is non empty set
cod F is Element of the carrier of (C,(cod f))
the Target of (C,(cod f)) . F is Element of the carrier of (C,(cod f))
id (cod F) is Morphism of cod F, cod F
[(C,(cod f),F),(C,(cod f),F)] is V18() Element of the carrier' of [:C,C:]
{(C,(cod f),F),(C,(cod f),F)} is non empty set
{(C,(cod f),F)} is non empty set
{{(C,(cod f),F),(C,(cod f),F)},{(C,(cod f),F)}} is non empty set
cod (C,(cod f),F) is Element of the carrier of C
the Target of C . (C,(cod f),F) is Element of the carrier of C
id (cod (C,(cod f),F)) is Morphism of cod (C,(cod f),F), cod (C,(cod f),F)
[[(C,(cod f),F),(C,(cod f),F)],(id (cod (C,(cod f),F)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[(C,(cod f),F),(C,(cod f),F)],(id (cod (C,(cod f),F)))} is non empty set
{[(C,(cod f),F),(C,(cod f),F)]} is non empty Relation-like Function-like set
{{[(C,(cod f),F),(C,(cod f),F)],(id (cod (C,(cod f),F)))},{[(C,(cod f),F),(C,(cod f),F)]}} is non empty set
(C,(cod f),(id (cod F))) is Element of (C,(cod f))
(C,(cod f),(id (cod F))) is Element of (C,(cod f))
(C,(cod f),(id (cod F))) is Element of the carrier' of C
A3 . (id (cod F)) is Element of the carrier' of (C,(dom f))
[[FG,FG],(id (cod (C,(cod f),F)))] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,FG],(id (cod (C,(cod f),F)))} is non empty set
{{[FG,FG],(id (cod (C,(cod f),F)))},{[FG,FG]}} is non empty set
F is Element of the carrier' of (C,(cod f))
FG is Element of (C,(cod f))
m is Element of (C,(cod f))
[FG,m] is V18() Element of the carrier' of [:C,C:]
{FG,m} is non empty set
{FG} is non empty set
{{FG,m},{FG}} is non empty set
g1 is Element of the carrier' of C
[[FG,m],g1] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,m],g1} is non empty set
{[FG,m]} is non empty Relation-like Function-like set
{{[FG,m],g1},{[FG,m]}} is non empty set
dom g1 is Element of the carrier of C
the Source of C . g1 is Element of the carrier of C
cod FG is Element of the carrier of C
the Target of C . FG is Element of the carrier of C
g1 (*) FG is Element of the carrier' of C
G is Element of the carrier' of (C,(cod f))
a2 is Element of (C,(cod f))
b2 is Element of (C,(cod f))
[a2,b2] is V18() Element of the carrier' of [:C,C:]
{a2,b2} is non empty set
{a2} is non empty set
{{a2,b2},{a2}} is non empty set
g2 is Element of the carrier' of C
[[a2,b2],g2] is V18() Element of the carrier' of [:[:C,C:],C:]
{[a2,b2],g2} is non empty set
{[a2,b2]} is non empty Relation-like Function-like set
{{[a2,b2],g2},{[a2,b2]}} is non empty set
dom g2 is Element of the carrier of C
the Source of C . g2 is Element of the carrier of C
cod a2 is Element of the carrier of C
the Target of C . a2 is Element of the carrier of C
g2 (*) a2 is Element of the carrier' of C
dom G is Element of the carrier of (C,(cod f))
the Source of (C,(cod f)) . G is Element of the carrier of (C,(cod f))
(C,(cod f),G) is Element of (C,(cod f))
cod F is Element of the carrier of (C,(cod f))
the Target of (C,(cod f)) . F is Element of the carrier of (C,(cod f))
(C,(cod f),F) is Element of (C,(cod f))
FG (*) f is Element of the carrier' of C
a2 (*) f is Element of the carrier' of C
m (*) f is Element of the carrier' of C
b2 (*) f is Element of the carrier' of C
(C,(cod f),F) is Element of (C,(cod f))
(C,(cod f),F) is Element of the carrier' of C
(C,(cod f),G) is Element of (C,(cod f))
(C,(cod f),G) is Element of the carrier' of C
A3 . F is Element of the carrier' of (C,(dom f))
ha1 is Element of (C,(dom f))
hb1 is Element of (C,(dom f))
[ha1,hb1] is V18() Element of the carrier' of [:C,C:]
{ha1,hb1} is non empty set
{ha1} is non empty set
{{ha1,hb1},{ha1}} is non empty set
[[ha1,hb1],g1] is V18() Element of the carrier' of [:[:C,C:],C:]
{[ha1,hb1],g1} is non empty set
{[ha1,hb1]} is non empty Relation-like Function-like set
{{[ha1,hb1],g1},{[ha1,hb1]}} is non empty set
A3 . G is Element of the carrier' of (C,(dom f))
ha2 is Element of (C,(dom f))
hb2 is Element of (C,(dom f))
[ha2,hb2] is V18() Element of the carrier' of [:C,C:]
{ha2,hb2} is non empty set
{ha2} is non empty set
{{ha2,hb2},{ha2}} is non empty set
[[ha2,hb2],g2] is V18() Element of the carrier' of [:[:C,C:],C:]
{[ha2,hb2],g2} is non empty set
{[ha2,hb2]} is non empty Relation-like Function-like set
{{[ha2,hb2],g2},{[ha2,hb2]}} is non empty set
G (*) F is Element of the carrier' of (C,(cod f))
[FG,b2] is V18() Element of the carrier' of [:C,C:]
{FG,b2} is non empty set
{{FG,b2},{FG}} is non empty set
g2 (*) g1 is Element of the carrier' of C
[[FG,b2],(g2 (*) g1)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[FG,b2],(g2 (*) g1)} is non empty set
{[FG,b2]} is non empty Relation-like Function-like set
{{[FG,b2],(g2 (*) g1)},{[FG,b2]}} is non empty set
(A3 . G) (*) (A3 . F) is Element of the carrier' of (C,(dom f))
[ha1,hb2] is V18() Element of the carrier' of [:C,C:]
{ha1,hb2} is non empty set
{{ha1,hb2},{ha1}} is non empty set
[[ha1,hb2],(g2 (*) g1)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[ha1,hb2],(g2 (*) g1)} is non empty set
{[ha1,hb2]} is non empty Relation-like Function-like set
{{[ha1,hb2],(g2 (*) g1)},{[ha1,hb2]}} is non empty set
(C,(cod f),(G (*) F)) is Element of (C,(cod f))
(C,(cod f),(G (*) F)) is Element of (C,(cod f))
(C,(cod f),(G (*) F)) is Element of the carrier' of C
A3 . (G (*) F) is Element of the carrier' of (C,(dom f))
F is Relation-like the carrier' of (C,(cod f)) -defined the carrier' of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier' of (C,(dom f))) Functor of (C,(cod f)),(C,(dom f))
G is Element of the carrier' of (C,(cod f))
F . G is Element of the carrier' of (C,(dom f))
(C,(cod f),G) is Element of (C,(cod f))
(C,(cod f),G) (*) f is Element of the carrier' of C
(C,(cod f),G) is Element of (C,(cod f))
(C,(cod f),G) (*) f is Element of the carrier' of C
[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)] is V18() Element of the carrier' of [:C,C:]
{((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)} is non empty set
{((C,(cod f),G) (*) f)} is non empty set
{{((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)},{((C,(cod f),G) (*) f)}} is non empty set
(C,(cod f),G) is Element of the carrier' of C
[[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)],(C,(cod f),G)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)],(C,(cod f),G)} is non empty set
{[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)]} is non empty Relation-like Function-like set
{{[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)],(C,(cod f),G)},{[((C,(cod f),G) (*) f),((C,(cod f),G) (*) f)]}} is non empty set
g is Relation-like the carrier' of (C,(cod f)) -defined the carrier' of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier' of (C,(dom f))) Functor of (C,(cod f)),(C,(dom f))
A1 is Relation-like the carrier' of (C,(cod f)) -defined the carrier' of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier' of (C,(dom f))) Functor of (C,(cod f)),(C,(dom f))
A2 is Element of the carrier' of (C,(cod f))
g . A2 is Element of the carrier' of (C,(dom f))
(C,(cod f),A2) is Element of (C,(cod f))
(C,(cod f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(cod f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {(cod f)} is Element of bool the carrier' of C
(C,(cod f),A2) (*) f is Element of the carrier' of C
(C,(cod f),A2) is Element of (C,(cod f))
(C,(cod f),A2) (*) f is Element of the carrier' of C
[((C,(cod f),A2) (*) f),((C,(cod f),A2) (*) f)] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{((C,(cod f),A2) (*) f),((C,(cod f),A2) (*) f)} is non empty set
{((C,(cod f),A2) (*) f)} is non empty set
{{((C,(cod f),A2) (*) f),((C,(cod f),A2) (*) f)},{((C,(cod f),A2) (*) f)}} is non empty set
(C,(cod f),A2) is Element of the carrier' of C
[[((C,(cod f),A2) (*) f),((C,(cod f),A2) (*) f)],(C,(cod f),A2)] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[((C,(cod f),A2) (*) f),((C,(cod f),A2) (*) f)],(C,(cod f),A2)} is non empty set
{[((C,(cod f),A2) (*) f),((C,(cod f),A2) (*) f)]} is non empty Relation-like Function-like set
{{[((C,(cod f),A2) (*) f),((C,(cod f),A2) (*) f)],(C,(cod f),A2)},{[((C,(cod f),A2) (*) f),((C,(cod f),A2) (*) f)]}} is non empty set
A1 . A2 is Element of the carrier' of (C,(dom f))
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
g is Element of the carrier' of C
dom g is Element of the carrier of C
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . g is Element of the carrier of C
f is Element of the carrier' of C
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . f is Element of the carrier of C
g (*) f is Element of the carrier' of C
(C,(g (*) f)) is Relation-like the carrier' of (C,(dom (g (*) f))) -defined the carrier' of (C,(cod (g (*) f))) -valued Function-like V21( the carrier' of (C,(dom (g (*) f))), the carrier' of (C,(cod (g (*) f)))) Functor of (C,(dom (g (*) f))),(C,(cod (g (*) f)))
dom (g (*) f) is Element of the carrier of C
the Source of C . (g (*) f) is Element of the carrier of C
(C,(dom (g (*) f))) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(dom (g (*) f))) is non empty set
cod (g (*) f) is Element of the carrier of C
the Target of C . (g (*) f) is Element of the carrier of C
(C,(cod (g (*) f))) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(cod (g (*) f))) is non empty set
dom f is Element of the carrier of C
the Source of C . f is Element of the carrier of C
(C,(dom f)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(dom f)) is non empty set
(C,(cod f)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(cod f)) is non empty set
(C,(dom g)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(dom g)) is non empty set
cod g is Element of the carrier of C
the Target of C . g is Element of the carrier of C
(C,(cod g)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(cod g)) is non empty set
(C,f) is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier' of (C,(cod f))) Functor of (C,(dom f)),(C,(cod f))
(C,g) is Relation-like the carrier' of (C,(dom g)) -defined the carrier' of (C,(cod g)) -valued Function-like V21( the carrier' of (C,(dom g)), the carrier' of (C,(cod g))) Functor of (C,(dom g)),(C,(cod g))
(C,g) * (C,f) is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of (C,(cod g)) -valued Function-like Element of bool [: the carrier' of (C,(dom f)), the carrier' of (C,(cod g)):]
[: the carrier' of (C,(dom f)), the carrier' of (C,(cod g)):] is non empty Relation-like set
bool [: the carrier' of (C,(dom f)), the carrier' of (C,(cod g)):] is non empty set
FG is Element of the carrier' of (C,(dom f))
(C,f) . FG is Element of the carrier' of (C,(cod f))
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
(C,(dom f),FG) is Element of (C,(dom f))
(C,(dom f)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(dom f)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Target of C " {(dom f)} is Element of bool the carrier' of C
f (*) (C,(dom f),FG) is Element of the carrier' of C
(C,(dom f),FG) is Element of (C,(dom f))
f (*) (C,(dom f),FG) is Element of the carrier' of C
[(f (*) (C,(dom f),FG)),(f (*) (C,(dom f),FG))] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{(f (*) (C,(dom f),FG)),(f (*) (C,(dom f),FG))} is non empty set
{(f (*) (C,(dom f),FG))} is non empty set
{{(f (*) (C,(dom f),FG)),(f (*) (C,(dom f),FG))},{(f (*) (C,(dom f),FG))}} is non empty set
(C,(dom f),FG) is Element of the carrier' of C
[[(f (*) (C,(dom f),FG)),(f (*) (C,(dom f),FG))],(C,(dom f),FG)] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[(f (*) (C,(dom f),FG)),(f (*) (C,(dom f),FG))],(C,(dom f),FG)} is non empty set
{[(f (*) (C,(dom f),FG)),(f (*) (C,(dom f),FG))]} is non empty Relation-like Function-like set
{{[(f (*) (C,(dom f),FG)),(f (*) (C,(dom f),FG))],(C,(dom f),FG)},{[(f (*) (C,(dom f),FG)),(f (*) (C,(dom f),FG))]}} is non empty set
(C,(cod f),((C,f) . FG)) is Element of (C,(cod f))
(C,(cod f)) is non empty Element of bool the carrier' of C
{(cod f)} is non empty Element of bool the carrier of C
the Target of C " {(cod f)} is Element of bool the carrier' of C
(C,(cod f),((C,f) . FG)) is Element of (C,(cod f))
(C,(cod f),((C,f) . FG)) is Element of the carrier' of C
cod (C,(dom f),FG) is Element of the carrier of C
the Target of C . (C,(dom f),FG) is Element of the carrier of C
cod (C,(dom f),FG) is Element of the carrier of C
the Target of C . (C,(dom f),FG) is Element of the carrier of C
g (*) (f (*) (C,(dom f),FG)) is Element of the carrier' of C
(g (*) f) (*) (C,(dom f),FG) is Element of the carrier' of C
g (*) (f (*) (C,(dom f),FG)) is Element of the carrier' of C
(g (*) f) (*) (C,(dom f),FG) is Element of the carrier' of C
F is Relation-like the carrier' of (C,(cod f)) -defined the carrier' of (C,(cod g)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier' of (C,(cod g))) Functor of (C,(cod f)),(C,(cod g))
F * (C,f) is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of (C,(dom f)) -defined the carrier' of (C,(cod g)) -valued the carrier' of (C,(cod g)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier' of (C,(cod g))) Functor of (C,(dom f)),(C,(cod g))
(F * (C,f)) . FG is Element of the carrier' of (C,(cod g))
F . ((C,f) . FG) is Element of the carrier' of (C,(cod g))
[(g (*) (f (*) (C,(dom f),FG))),(g (*) (f (*) (C,(dom f),FG)))] is V18() Element of the carrier' of [:C,C:]
{(g (*) (f (*) (C,(dom f),FG))),(g (*) (f (*) (C,(dom f),FG)))} is non empty set
{(g (*) (f (*) (C,(dom f),FG)))} is non empty set
{{(g (*) (f (*) (C,(dom f),FG))),(g (*) (f (*) (C,(dom f),FG)))},{(g (*) (f (*) (C,(dom f),FG)))}} is non empty set
[[(g (*) (f (*) (C,(dom f),FG))),(g (*) (f (*) (C,(dom f),FG)))],(C,(dom f),FG)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[(g (*) (f (*) (C,(dom f),FG))),(g (*) (f (*) (C,(dom f),FG)))],(C,(dom f),FG)} is non empty set
{[(g (*) (f (*) (C,(dom f),FG))),(g (*) (f (*) (C,(dom f),FG)))]} is non empty Relation-like Function-like set
{{[(g (*) (f (*) (C,(dom f),FG))),(g (*) (f (*) (C,(dom f),FG)))],(C,(dom f),FG)},{[(g (*) (f (*) (C,(dom f),FG))),(g (*) (f (*) (C,(dom f),FG)))]}} is non empty set
G is Relation-like the carrier' of (C,(dom f)) -defined the carrier' of (C,(cod g)) -valued Function-like V21( the carrier' of (C,(dom f)), the carrier' of (C,(cod g))) Functor of (C,(dom f)),(C,(cod g))
G . FG is Element of the carrier' of (C,(cod g))
C is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier' of C is non empty set
g is Element of the carrier' of C
dom g is Element of the carrier of C
the carrier of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) 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 . g is Element of the carrier of C
f is Element of the carrier' of C
cod f is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like V21( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . f is Element of the carrier of C
g (*) f is Element of the carrier' of C
(C,(g (*) f)) is Relation-like the carrier' of (C,(cod (g (*) f))) -defined the carrier' of (C,(dom (g (*) f))) -valued Function-like V21( the carrier' of (C,(cod (g (*) f))), the carrier' of (C,(dom (g (*) f)))) Functor of (C,(cod (g (*) f))),(C,(dom (g (*) f)))
cod (g (*) f) is Element of the carrier of C
the Target of C . (g (*) f) is Element of the carrier of C
(C,(cod (g (*) f))) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(cod (g (*) f))) is non empty set
dom (g (*) f) is Element of the carrier of C
the Source of C . (g (*) f) is Element of the carrier of C
(C,(dom (g (*) f))) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(dom (g (*) f))) is non empty set
cod g is Element of the carrier of C
the Target of C . g is Element of the carrier of C
(C,(cod g)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(cod g)) is non empty set
(C,(dom g)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(dom g)) is non empty set
(C,(cod f)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(cod f)) is non empty set
dom f is Element of the carrier of C
the Source of C . f is Element of the carrier of C
(C,(dom f)) is non empty non void V58() strict Category-like transitive associative reflexive with_identities () CatStr
the carrier' of (C,(dom f)) is non empty set
(C,g) is Relation-like the carrier' of (C,(cod g)) -defined the carrier' of (C,(dom g)) -valued Function-like V21( the carrier' of (C,(cod g)), the carrier' of (C,(dom g))) Functor of (C,(cod g)),(C,(dom g))
(C,f) is Relation-like the carrier' of (C,(cod f)) -defined the carrier' of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier' of (C,(dom f))) Functor of (C,(cod f)),(C,(dom f))
(C,f) * (C,g) is Relation-like the carrier' of (C,(cod g)) -defined the carrier' of (C,(dom f)) -valued Function-like Element of bool [: the carrier' of (C,(cod g)), the carrier' of (C,(dom f)):]
[: the carrier' of (C,(cod g)), the carrier' of (C,(dom f)):] is non empty Relation-like set
bool [: the carrier' of (C,(cod g)), the carrier' of (C,(dom f)):] is non empty set
G is Relation-like the carrier' of (C,(cod g)) -defined the carrier' of (C,(cod f)) -valued Function-like V21( the carrier' of (C,(cod g)), the carrier' of (C,(cod f))) Functor of (C,(cod g)),(C,(cod f))
m is Element of the carrier' of (C,(cod g))
G . m is Element of the carrier' of (C,(cod f))
[:C,C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of C, the carrier of C:] is non empty Relation-like set
[: the carrier' of C, the carrier' of C:] is non empty Relation-like set
[: the Source of C, the Source of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, 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
bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:] is non empty set
[: the Target of C, the Target of C:] is Relation-like [: the carrier' of C, the carrier' of C:] -defined [: the carrier of C, the carrier of C:] -valued Function-like V21([: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]) Element of bool [:[: the carrier' of C, the carrier' of C:],[: the carrier of C, the carrier of C:]:]
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:], 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
K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) is Relation-like [:[: the carrier' of C, the carrier' of C:],[: the carrier' of C, the carrier' of C:]:] -defined [: the carrier' of C, 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, 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, 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, the carrier' of C:]:],[: the carrier' of C, the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of C, the carrier of C:],[: the carrier' of C, the carrier' of C:],[: the Source of C, the Source of C:],[: the Target of C, the Target of C:],K222( the carrier' of C, the carrier' of C, the Comp of C, the Comp of C) #) is non empty non void V58() strict CatStr
(C,(cod g),m) is Element of (C,(cod g))
(C,(cod g)) is non empty Element of bool the carrier' of C
bool the carrier' of C is non empty set
{(cod g)} is non empty Element of bool the carrier of C
bool the carrier of C is non empty set
the Source of C " {(cod g)} is Element of bool the carrier' of C
(C,(cod g),m) (*) g is Element of the carrier' of C
(C,(cod g),m) is Element of (C,(cod g))
(C,(cod g),m) (*) g is Element of the carrier' of C
[((C,(cod g),m) (*) g),((C,(cod g),m) (*) g)] is V18() Element of the carrier' of [:C,C:]
the carrier' of [:C,C:] is non empty set
{((C,(cod g),m) (*) g),((C,(cod g),m) (*) g)} is non empty set
{((C,(cod g),m) (*) g)} is non empty set
{{((C,(cod g),m) (*) g),((C,(cod g),m) (*) g)},{((C,(cod g),m) (*) g)}} is non empty set
(C,(cod g),m) is Element of the carrier' of C
[[((C,(cod g),m) (*) g),((C,(cod g),m) (*) g)],(C,(cod g),m)] is V18() Element of the carrier' of [:[:C,C:],C:]
[:[:C,C:],C:] is non empty non void V58() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:C,C:] is non empty set
[: the carrier of [:C,C:], the carrier of C:] is non empty Relation-like set
[: the carrier' of [:C,C:], the carrier' of C:] is non empty Relation-like set
the Source of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty Relation-like set
bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:] is non empty set
[: the Source of [:C,C:], the Source of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:] is non empty set
the Target of [:C,C:] is Relation-like the carrier' of [:C,C:] -defined the carrier of [:C,C:] -valued Function-like V21( the carrier' of [:C,C:], the carrier of [:C,C:]) Element of bool [: the carrier' of [:C,C:], the carrier of [:C,C:]:]
[: the Target of [:C,C:], the Target of C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of C:] -defined [: the carrier of [:C,C:], the carrier of C:] -valued Function-like V21([: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]) Element of bool [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier of [:C,C:], the carrier of C:]:]
the Comp of [:C,C:] is Relation-like [: the carrier' of [:C,C:], the carrier' of [:C,C:]:] -defined the carrier' of [:C,C:] -valued Function-like Element of bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:]
[: the carrier' of [:C,C:], the carrier' of [:C,C:]:] is non empty Relation-like set
[:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty Relation-like set
bool [:[: the carrier' of [:C,C:], the carrier' of [:C,C:]:], the carrier' of [:C,C:]:] is non empty set
K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) is Relation-like [:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] -defined [: the carrier' of [:C,C:], the carrier' of C:] -valued Function-like Element of bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:]
[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
[:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty Relation-like set
bool [:[:[: the carrier' of [:C,C:], the carrier' of C:],[: the carrier' of [:C,C:], the carrier' of C:]:],[: the carrier' of [:C,C:], the carrier' of C:]:] is non empty set
CatStr(# [: the carrier of [:C,C:], the carrier of C:],[: the carrier' of [:C,C:], the carrier' of C:],[: the Source of [:C,C:], the Source of C:],[: the Target of [:C,C:], the Target of C:],K222( the carrier' of [:C,C:], the carrier' of C, the Comp of [:C,C:], the Comp of C) #) is non empty non void V58() strict CatStr
the carrier' of [:[:C,C:],C:] is non empty set
{[((C,(cod g),m) (*) g),((C,(cod g),m) (*) g)],(C,(cod g),m)} is non empty set
{[((C,(cod g),m) (*) g),((C,(cod g),m) (*) g)]} is non empty Relation-like Function-like set
{{[((C,(cod g),m) (*) g),((C,(cod g),m) (*) g)],(C,(cod g),m)},{[((C,(cod g),m) (*) g),((C,(cod g),m) (*) g)]}} is non empty set
(C,(cod f),(G . m)) is Element of (C,(cod f))
(C,(cod f)) is non empty Element of bool the carrier' of C
{(cod f)} is non empty Element of bool the carrier of C
the Source of C " {(cod f)} is Element of bool the carrier' of C
(C,(cod f),(G . m)) is Element of (C,(cod f))
(C,(cod f),(G . m)) is Element of the carrier' of C
dom (C,(cod g),m) is Element of the carrier of C
the Source of C . (C,(cod g),m) is Element of the carrier of C
dom (C,(cod g),m) is Element of the carrier of C
the Source of C . (C,(cod g),m) is Element of the carrier of C
(C,(cod g),m) (*) (g (*) f) is Element of the carrier' of C
((C,(cod g),m) (*) g) (*) f is Element of the carrier' of C
(C,(cod g),m) (*) (g (*) f) is Element of the carrier' of C
((C,(cod g),m) (*) g) (*) f is Element of the carrier' of C
F is Relation-like the carrier' of (C,(cod f)) -defined the carrier' of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(cod f)), the carrier' of (C,(dom f))) Functor of (C,(cod f)),(C,(dom f))
F * G is Relation-like the carrier' of (C,(cod g)) -defined the carrier' of (C,(cod g)) -defined the carrier' of (C,(dom f)) -valued the carrier' of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(cod g)), the carrier' of (C,(dom f))) Functor of (C,(cod g)),(C,(dom f))
(F * G) . m is Element of the carrier' of (C,(dom f))
F . (G . m) is Element of the carrier' of (C,(dom f))
[(((C,(cod g),m) (*) g) (*) f),(((C,(cod g),m) (*) g) (*) f)] is V18() Element of the carrier' of [:C,C:]
{(((C,(cod g),m) (*) g) (*) f),(((C,(cod g),m) (*) g) (*) f)} is non empty set
{(((C,(cod g),m) (*) g) (*) f)} is non empty set
{{(((C,(cod g),m) (*) g) (*) f),(((C,(cod g),m) (*) g) (*) f)},{(((C,(cod g),m) (*) g) (*) f)}} is non empty set
[[(((C,(cod g),m) (*) g) (*) f),(((C,(cod g),m) (*) g) (*) f)],(C,(cod g),m)] is V18() Element of the carrier' of [:[:C,C:],C:]
{[(((C,(cod g),m) (*) g) (*) f),(((C,(cod g),m) (*) g) (*) f)],(C,(cod g),m)} is non empty set
{[(((C,(cod g),m) (*) g) (*) f),(((C,(cod g),m) (*) g) (*) f)]} is non empty Relation-like Function-like set
{{[(((C,(cod g),m) (*) g) (*) f),(((C,(cod g),m) (*) g) (*) f)],(C,(cod g),m)},{[(((C,(cod g),m) (*) g) (*) f),(((C,(cod g),m) (*) g) (*) f)]}} is non empty set
FG is Relation-like the carrier' of (C,(cod g)) -defined the carrier' of (C,(dom f)) -valued Function-like V21( the carrier' of (C,(cod g)), the carrier' of (C,(dom f))) Functor of (C,(cod g)),(C,(dom f))
FG . m is Element of the carrier' of (C,(dom f))