:: NATTRA_1 semantic presentation

K149() is Element of bool K145()
K145() is set
bool K145() is non empty set
{} is Relation-like non-empty empty-yielding empty trivial finite finite-yielding V35() set
the Relation-like non-empty empty-yielding empty trivial finite finite-yielding V35() set is Relation-like non-empty empty-yielding empty trivial finite finite-yielding V35() set
1 is non empty set
{{},1} is non empty finite set
K144() is set
bool K144() is non empty set
bool K149() is non empty set
A is set
B is non empty set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
bool A is non empty set
OA is Relation-like A -defined B -valued Function-like quasi_total Element of bool [:A,B:]
AB is Element of bool A
OA | AB is Relation-like AB -defined A -defined B -valued set
[:AB,B:] is Relation-like set
bool [:AB,B:] is non empty set
A is non empty set
B is non empty set
[:A,B:] is Relation-like non empty set
OA is non empty set
[:OA,A:] is Relation-like non empty set
bool [:OA,A:] is non empty set
bool OA is non empty set
AB is non empty set
[:AB,B:] is Relation-like non empty set
bool [:AB,B:] is non empty set
bool AB is non empty set
[:OA,AB:] is Relation-like non empty set
MA is Relation-like OA -defined A -valued Function-like quasi_total Element of bool [:OA,A:]
MB is Relation-like AB -defined B -valued Function-like quasi_total Element of bool [:AB,B:]
[:MA,MB:] is Relation-like [:OA,AB:] -defined [:A,B:] -valued Function-like quasi_total Element of bool [:[:OA,AB:],[:A,B:]:]
[:[:OA,AB:],[:A,B:]:] is Relation-like non empty set
bool [:[:OA,AB:],[:A,B:]:] is non empty set
OB is non empty Element of bool OA
(OA,A,MA,OB) is Relation-like OB -defined OA -defined A -valued Function-like quasi_total Element of bool [:OB,A:]
[:OB,A:] is Relation-like non empty set
bool [:OB,A:] is non empty set
MB is non empty Element of bool AB
[:OB,MB:] is Relation-like OA -defined AB -valued non empty Element of bool [:OA,AB:]
bool [:OA,AB:] is non empty set
([:OA,AB:],[:A,B:],[:MA,MB:],[:OB,MB:]) is Relation-like [:OB,MB:] -defined [:OA,AB:] -defined [:A,B:] -valued Function-like quasi_total Element of bool [:[:OB,MB:],[:A,B:]:]
[:[:OB,MB:],[:A,B:]:] is Relation-like non empty set
bool [:[:OB,MB:],[:A,B:]:] is non empty set
(AB,B,MB,MB) is Relation-like MB -defined AB -defined B -valued Function-like quasi_total Element of bool [:MB,B:]
[:MB,B:] is Relation-like non empty set
bool [:MB,B:] is non empty set
[:(OA,A,MA,OB),(AB,B,MB,MB):] is Relation-like [:OB,MB:] -defined [:A,B:] -valued Function-like quasi_total Element of bool [:[:OB,MB:],[:A,B:]:]
[:OB,MB:] is Relation-like non empty set
[:[:OB,MB:],[:A,B:]:] is Relation-like non empty set
bool [:[:OB,MB:],[:A,B:]:] is non empty set
MA is Element of [:OB,MB:]
a is Element of OB
b is Element of MB
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
(AB,B,MB,MB) . b is Element of B
MB . b is Element of B
(OA,A,MA,OB) . a is Element of A
MA . a is Element of A
[:(OA,A,MA,OB),(AB,B,MB,MB):] . MA is Element of [:A,B:]
[:(OA,A,MA,OB),(AB,B,MB,MB):] . (a,b) is Element of [:A,B:]
[:(OA,A,MA,OB),(AB,B,MB,MB):] . [a,b] is set
[(MA . a),(MB . b)] is non empty V15() set
{(MA . a),(MB . b)} is non empty finite set
{(MA . a)} is non empty trivial finite set
{{(MA . a),(MB . b)},{(MA . a)}} is non empty finite V35() set
[:MA,MB:] . (a,b) is Element of [:A,B:]
[:MA,MB:] . [a,b] is set
([:OA,AB:],[:A,B:],[:MA,MB:],[:OB,MB:]) . MA is Element of [:A,B:]
A is non empty set
bool A is non empty set
B is non empty set
bool B is non empty set
OA is non empty Element of bool A
[:OA,OA:] is Relation-like A -defined A -valued non empty Element of bool [:A,A:]
[:A,A:] is Relation-like non empty set
bool [:A,A:] is non empty set
[:[:OA,OA:],OA:] is Relation-like non empty set
bool [:[:OA,OA:],OA:] is non empty set
AB is non empty Element of bool B
[:AB,AB:] is Relation-like B -defined B -valued non empty Element of bool [:B,B:]
[:B,B:] is Relation-like non empty set
bool [:B,B:] is non empty set
[:[:AB,AB:],AB:] is Relation-like non empty set
bool [:[:AB,AB:],AB:] is non empty set
MA is Relation-like [:OA,OA:] -defined OA -valued Function-like Element of bool [:[:OA,OA:],OA:]
MB is Relation-like [:AB,AB:] -defined AB -valued Function-like Element of bool [:[:AB,AB:],AB:]
|:MA,MB:| is Relation-like Function-like set
[:A,B:] is Relation-like non empty set
[:OA,AB:] is Relation-like A -defined B -valued non empty Element of bool [:A,B:]
bool [:A,B:] is non empty set
[:[:OA,AB:],[:OA,AB:]:] is Relation-like [:A,B:] -defined [:A,B:] -valued non empty Element of bool [:[:A,B:],[:A,B:]:]
[:[:A,B:],[:A,B:]:] is Relation-like non empty set
bool [:[:A,B:],[:A,B:]:] is non empty set
[:[:[:OA,AB:],[:OA,AB:]:],[:OA,AB:]:] is Relation-like non empty set
bool [:[:[:OA,AB:],[:OA,AB:]:],[:OA,AB:]:] is non empty set
A is non empty set
bool A is non empty set
[:A,A:] is Relation-like non empty set
[:[:A,A:],A:] is Relation-like non empty set
bool [:[:A,A:],A:] is non empty set
B is non empty set
bool B is non empty set
[:B,B:] is Relation-like non empty set
[:[:B,B:],B:] is Relation-like non empty set
bool [:[:B,B:],B:] is non empty set
OA is non empty Element of bool A
[:OA,OA:] is Relation-like A -defined A -valued non empty Element of bool [:A,A:]
bool [:A,A:] is non empty set
[:[:OA,OA:],OA:] is Relation-like non empty set
bool [:[:OA,OA:],OA:] is non empty set
AB is non empty Element of bool B
[:AB,AB:] is Relation-like B -defined B -valued non empty Element of bool [:B,B:]
bool [:B,B:] is non empty set
[:[:AB,AB:],AB:] is Relation-like non empty set
bool [:[:AB,AB:],AB:] is non empty set
[:OA,AB:] is Relation-like A -defined B -valued non empty Element of bool [:A,B:]
[:A,B:] is Relation-like non empty set
bool [:A,B:] is non empty set
MA is Relation-like [:A,A:] -defined A -valued Function-like Element of bool [:[:A,A:],A:]
MA || OA is Relation-like Function-like set
[:OA,OA:] is Relation-like non empty set
MA | [:OA,OA:] is Relation-like [:OA,OA:] -defined [:A,A:] -defined A -valued set
MB is Relation-like [:B,B:] -defined B -valued Function-like Element of bool [:[:B,B:],B:]
MB || AB is Relation-like Function-like set
[:AB,AB:] is Relation-like non empty set
MB | [:AB,AB:] is Relation-like [:AB,AB:] -defined [:B,B:] -defined B -valued set
|:MA,MB:| is Relation-like [:[:A,B:],[:A,B:]:] -defined [:A,B:] -valued Function-like Element of bool [:[:[:A,B:],[:A,B:]:],[:A,B:]:]
[:[:A,B:],[:A,B:]:] is Relation-like non empty set
[:[:[:A,B:],[:A,B:]:],[:A,B:]:] is Relation-like non empty set
bool [:[:[:A,B:],[:A,B:]:],[:A,B:]:] is non empty set
|:MA,MB:| || [:OA,AB:] is Relation-like Function-like set
[:[:OA,AB:],[:OA,AB:]:] is Relation-like non empty set
|:MA,MB:| | [:[:OA,AB:],[:OA,AB:]:] is Relation-like [:[:OA,AB:],[:OA,AB:]:] -defined [:[:A,B:],[:A,B:]:] -defined [:A,B:] -valued set
OB is Relation-like [:OA,OA:] -defined OA -valued Function-like Element of bool [:[:OA,OA:],OA:]
proj1 OB is Relation-like set
proj1 MA is Relation-like set
MB is Relation-like [:AB,AB:] -defined AB -valued Function-like Element of bool [:[:AB,AB:],AB:]
(A,B,OA,AB,OB,MB) is Relation-like [:[:OA,AB:],[:OA,AB:]:] -defined [:OA,AB:] -valued Function-like Element of bool [:[:[:OA,AB:],[:OA,AB:]:],[:OA,AB:]:]
[:[:OA,AB:],[:OA,AB:]:] is Relation-like [:A,B:] -defined [:A,B:] -valued non empty Element of bool [:[:A,B:],[:A,B:]:]
bool [:[:A,B:],[:A,B:]:] is non empty set
[:[:[:OA,AB:],[:OA,AB:]:],[:OA,AB:]:] is Relation-like non empty set
bool [:[:[:OA,AB:],[:OA,AB:]:],[:OA,AB:]:] is non empty set
proj1 (A,B,OA,AB,OB,MB) is Relation-like set
proj1 MB is Relation-like set
proj1 MB is Relation-like set
proj1 (|:MA,MB:| || [:OA,AB:]) is set
a is set
b is set
a is set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
a is set
t19 is set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
[[b,a],[a,t19]] is non empty V15() set
{[b,a],[a,t19]} is Relation-like non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],[a,t19]},{[b,a]}} is non empty finite V35() set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{{b,a},{b}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
proj1 |:MA,MB:| is Relation-like set
(proj1 |:MA,MB:|) /\ [:[:OA,AB:],[:OA,AB:]:] is Relation-like [:A,B:] -defined [:A,B:] -valued Element of bool [:[:A,B:],[:A,B:]:]
a is set
(proj1 MA) /\ [:OA,OA:] is Relation-like A -defined A -valued Element of bool [:A,A:]
proj1 |:MA,MB:| is Relation-like set
(proj1 |:MA,MB:|) /\ [:[:OA,AB:],[:OA,AB:]:] is Relation-like [:A,B:] -defined [:A,B:] -valued Element of bool [:[:A,B:],[:A,B:]:]
(proj1 MB) /\ [:AB,AB:] is Relation-like B -defined B -valued Element of bool [:B,B:]
b is set
a is set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
a is set
t19 is set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
[[b,a],[a,t19]] is non empty V15() set
{[b,a],[a,t19]} is Relation-like non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],[a,t19]},{[b,a]}} is non empty finite V35() set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{{b,a},{b}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
a is set
b is set
a is set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
a is set
t19 is set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
[[b,a],[a,t19]] is non empty V15() set
{[b,a],[a,t19]} is Relation-like non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],[a,t19]},{[b,a]}} is non empty finite V35() set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{{b,a},{b}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,OA,AB,OB,MB) . a is set
(A,B,OA,AB,OB,MB) . ([b,a],[a,t19]) is set
(A,B,OA,AB,OB,MB) . [[b,a],[a,t19]] is set
OB . (b,a) is set
OB . [b,a] is set
MB . (a,t19) is set
MB . [a,t19] is set
[(OB . (b,a)),(MB . (a,t19))] is non empty V15() set
{(OB . (b,a)),(MB . (a,t19))} is non empty finite set
{(OB . (b,a))} is non empty trivial finite set
{{(OB . (b,a)),(MB . (a,t19))},{(OB . (b,a))}} is non empty finite V35() set
MA . [b,a] is set
[(MA . [b,a]),(MB . [a,t19])] is non empty V15() set
{(MA . [b,a]),(MB . [a,t19])} is non empty finite set
{(MA . [b,a])} is non empty trivial finite set
{{(MA . [b,a]),(MB . [a,t19])},{(MA . [b,a])}} is non empty finite V35() set
MA . (b,a) is set
MB . (a,t19) is set
MB . [a,t19] is set
[(MA . (b,a)),(MB . (a,t19))] is non empty V15() set
{(MA . (b,a)),(MB . (a,t19))} is non empty finite set
{(MA . (b,a))} is non empty trivial finite set
{{(MA . (b,a)),(MB . (a,t19))},{(MA . (b,a))}} is non empty finite V35() set
|:MA,MB:| . ([b,a],[a,t19]) is set
|:MA,MB:| . [[b,a],[a,t19]] is set
(|:MA,MB:| || [:OA,AB:]) . a is set
a is Element of [:[:OA,AB:],[:OA,AB:]:]
(A,B,OA,AB,OB,MB) . a is set
(|:MA,MB:| || [:OA,AB:]) . a is set
proj2 (|:MA,MB:| || [:OA,AB:]) is set
proj2 (A,B,OA,AB,OB,MB) is Relation-like set
a is set
b is set
(|:MA,MB:| || [:OA,AB:]) . b is set
(A,B,OA,AB,OB,MB) . b is set
A is set
B is set
1Cat (A,B) is non empty trivial finite non void 1 -element V55() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{A} is non empty trivial finite set
{B} is non empty trivial finite set
K241(B,A) is Relation-like {B} -defined {A} -valued Function-like quasi_total finite Element of bool [:{B},{A}:]
[:{B},{A}:] is Relation-like non empty finite set
bool [:{B},{A}:] is non empty finite V35() set
K240(B,B,B) is Relation-like [:{B},{B}:] -defined {B} -valued Function-like quasi_total finite Element of bool [:[:{B},{B}:],{B}:]
[:{B},{B}:] is Relation-like non empty finite set
[:[:{B},{B}:],{B}:] is Relation-like non empty finite set
bool [:[:{B},{B}:],{B}:] is non empty finite V35() set
CatStr(# {A},{B},K241(B,A),K241(B,A),K240(B,B,B) #) is non empty non void V55() strict CatStr
the carrier' of (1Cat (A,B)) is non empty trivial finite set
OA is Element of the carrier' of (1Cat (A,B))
AB is Element of the carrier' of (1Cat (A,B))
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
[:A,A:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the carrier' of A is non empty set
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
[: the Source of A, the Source of A:] is Relation-like [: the carrier' of A, the carrier' of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:] is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the Target of A, the Target of A:] is Relation-like [: the carrier' of A, the carrier' of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
|: the Comp of A, the Comp of A:| is Relation-like [:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:] -defined [: the carrier' of A, the carrier' of A:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:]
[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:] is Relation-like non empty set
[:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:] is Relation-like non empty set
bool [:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of A:],[: the carrier' of A, the carrier' of A:],[: the Source of A, the Source of A:],[: the Target of A, the Target of A:],|: the Comp of A, the Comp of A:| #) is non empty non void V55() strict CatStr
B is Element of the carrier of A
id B is Morphism of B,B
[(id B),(id B)] is non empty V15() Element of the carrier' of [:A,A:]
the carrier' of [:A,A:] is non empty set
{(id B),(id B)} is non empty finite set
{(id B)} is non empty trivial finite set
{{(id B),(id B)},{(id B)}} is non empty finite V35() set
[[(id B),(id B)],(id B)] is non empty V15() Element of the carrier' of [:[:A,A:],A:]
[:[:A,A:],A:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:A,A:] is non empty set
[: the carrier of [:A,A:], the carrier of A:] is Relation-like non empty set
[: the carrier' of [:A,A:], the carrier' of A:] is Relation-like non empty set
the Source of [:A,A:] is Relation-like the carrier' of [:A,A:] -defined the carrier of [:A,A:] -valued Function-like quasi_total Element of bool [: the carrier' of [:A,A:], the carrier of [:A,A:]:]
[: the carrier' of [:A,A:], the carrier of [:A,A:]:] is Relation-like non empty set
bool [: the carrier' of [:A,A:], the carrier of [:A,A:]:] is non empty set
[: the Source of [:A,A:], the Source of A:] is Relation-like [: the carrier' of [:A,A:], the carrier' of A:] -defined [: the carrier of [:A,A:], the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier of [:A,A:], the carrier of A:]:]
[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier of [:A,A:], the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier of [:A,A:], the carrier of A:]:] is non empty set
the Target of [:A,A:] is Relation-like the carrier' of [:A,A:] -defined the carrier of [:A,A:] -valued Function-like quasi_total Element of bool [: the carrier' of [:A,A:], the carrier of [:A,A:]:]
[: the Target of [:A,A:], the Target of A:] is Relation-like [: the carrier' of [:A,A:], the carrier' of A:] -defined [: the carrier of [:A,A:], the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier of [:A,A:], the carrier of A:]:]
the Comp of [:A,A:] is Relation-like [: the carrier' of [:A,A:], the carrier' of [:A,A:]:] -defined the carrier' of [:A,A:] -valued Function-like Element of bool [:[: the carrier' of [:A,A:], the carrier' of [:A,A:]:], the carrier' of [:A,A:]:]
[: the carrier' of [:A,A:], the carrier' of [:A,A:]:] is Relation-like non empty set
[:[: the carrier' of [:A,A:], the carrier' of [:A,A:]:], the carrier' of [:A,A:]:] is Relation-like non empty set
bool [:[: the carrier' of [:A,A:], the carrier' of [:A,A:]:], the carrier' of [:A,A:]:] is non empty set
|: the Comp of [:A,A:], the Comp of A:| is Relation-like [:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:] -defined [: the carrier' of [:A,A:], the carrier' of A:] -valued Function-like Element of bool [:[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:],[: the carrier' of [:A,A:], the carrier' of A:]:]
[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:] is Relation-like non empty set
[:[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:],[: the carrier' of [:A,A:], the carrier' of A:]:] is Relation-like non empty set
bool [:[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:],[: the carrier' of [:A,A:], the carrier' of A:]:] is non empty set
CatStr(# [: the carrier of [:A,A:], the carrier of A:],[: the carrier' of [:A,A:], the carrier' of A:],[: the Source of [:A,A:], the Source of A:],[: the Target of [:A,A:], the Target of A:],|: the Comp of [:A,A:], the Comp of A:| #) is non empty non void V55() strict CatStr
the carrier' of [:[:A,A:],A:] is non empty set
{[(id B),(id B)],(id B)} is non empty finite set
{[(id B),(id B)]} is Relation-like non empty trivial finite set
{{[(id B),(id B)],(id B)},{[(id B),(id B)]}} is non empty finite V35() set
dom (id B) is Element of the carrier of A
the Source of A . (id B) is Element of the carrier of A
cod (id B) is Element of the carrier of A
the Target of A . (id B) is Element of the carrier of A
proj1 the Comp of A is Relation-like set
(id B) (*) (id B) is Element of the carrier' of A
the Comp of A . ((id B),(id B)) is set
[(id B),(id B)] is non empty V15() set
the Comp of A . [(id B),(id B)] is set
A is set
B is set
1Cat (A,B) is non empty trivial finite non void 1 -element V55() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{A} is non empty trivial finite set
{B} is non empty trivial finite set
K241(B,A) is Relation-like {B} -defined {A} -valued Function-like quasi_total finite Element of bool [:{B},{A}:]
[:{B},{A}:] is Relation-like non empty finite set
bool [:{B},{A}:] is non empty finite V35() set
K240(B,B,B) is Relation-like [:{B},{B}:] -defined {B} -valued Function-like quasi_total finite Element of bool [:[:{B},{B}:],{B}:]
[:{B},{B}:] is Relation-like non empty finite set
[:[:{B},{B}:],{B}:] is Relation-like non empty finite set
bool [:[:{B},{B}:],{B}:] is non empty finite V35() set
CatStr(# {A},{B},K241(B,A),K241(B,A),K240(B,B,B) #) is non empty non void V55() strict CatStr
the Comp of (1Cat (A,B)) is Relation-like [: the carrier' of (1Cat (A,B)), the carrier' of (1Cat (A,B)):] -defined the carrier' of (1Cat (A,B)) -valued Function-like finite Element of bool [:[: the carrier' of (1Cat (A,B)), the carrier' of (1Cat (A,B)):], the carrier' of (1Cat (A,B)):]
the carrier' of (1Cat (A,B)) is non empty trivial finite set
[: the carrier' of (1Cat (A,B)), the carrier' of (1Cat (A,B)):] is Relation-like non empty finite set
[:[: the carrier' of (1Cat (A,B)), the carrier' of (1Cat (A,B)):], the carrier' of (1Cat (A,B)):] is Relation-like non empty finite set
bool [:[: the carrier' of (1Cat (A,B)), the carrier' of (1Cat (A,B)):], the carrier' of (1Cat (A,B)):] is non empty finite V35() set
[B,B] is non empty V15() set
{B,B} is non empty finite set
{{B,B},{B}} is non empty finite V35() set
[[B,B],B] is non empty V15() set
{[B,B],B} is non empty finite set
{[B,B]} is Relation-like non empty trivial finite set
{{[B,B],B},{[B,B]}} is non empty finite V35() set
{[[B,B],B]} is Relation-like non empty trivial finite set
the carrier of (1Cat (A,B)) is non empty trivial finite set
the Element of the carrier of (1Cat (A,B)) is Element of the carrier of (1Cat (A,B))
OB is set
id the Element of the carrier of (1Cat (A,B)) is Morphism of the Element of the carrier of (1Cat (A,B)), the Element of the carrier of (1Cat (A,B))
dom (id the Element of the carrier of (1Cat (A,B))) is Element of the carrier of (1Cat (A,B))
the Source of (1Cat (A,B)) is Relation-like the carrier' of (1Cat (A,B)) -defined the carrier of (1Cat (A,B)) -valued Function-like quasi_total finite Element of bool [: the carrier' of (1Cat (A,B)), the carrier of (1Cat (A,B)):]
[: the carrier' of (1Cat (A,B)), the carrier of (1Cat (A,B)):] is Relation-like non empty finite set
bool [: the carrier' of (1Cat (A,B)), the carrier of (1Cat (A,B)):] is non empty finite V35() set
the Source of (1Cat (A,B)) . (id the Element of the carrier of (1Cat (A,B))) is Element of the carrier of (1Cat (A,B))
cod (id the Element of the carrier of (1Cat (A,B))) is Element of the carrier of (1Cat (A,B))
the Target of (1Cat (A,B)) is Relation-like the carrier' of (1Cat (A,B)) -defined the carrier of (1Cat (A,B)) -valued Function-like quasi_total finite Element of bool [: the carrier' of (1Cat (A,B)), the carrier of (1Cat (A,B)):]
the Target of (1Cat (A,B)) . (id the Element of the carrier of (1Cat (A,B))) is Element of the carrier of (1Cat (A,B))
MB is set
MA is set
[MB,MA] is non empty V15() set
{MB,MA} is non empty finite set
{MB} is non empty trivial finite set
{{MB,MA},{MB}} is non empty finite V35() set
proj1 the Comp of (1Cat (A,B)) is Relation-like finite set
a is set
b is set
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
the Comp of (1Cat (A,B)) . ((id the Element of the carrier of (1Cat (A,B))),(id the Element of the carrier of (1Cat (A,B)))) is set
[(id the Element of the carrier of (1Cat (A,B))),(id the Element of the carrier of (1Cat (A,B)))] is non empty V15() set
{(id the Element of the carrier of (1Cat (A,B))),(id the Element of the carrier of (1Cat (A,B)))} is non empty finite set
{(id the Element of the carrier of (1Cat (A,B)))} is non empty trivial finite set
{{(id the Element of the carrier of (1Cat (A,B))),(id the Element of the carrier of (1Cat (A,B)))},{(id the Element of the carrier of (1Cat (A,B)))}} is non empty finite V35() set
the Comp of (1Cat (A,B)) . [(id the Element of the carrier of (1Cat (A,B))),(id the Element of the carrier of (1Cat (A,B)))] is set
(id the Element of the carrier of (1Cat (A,B))) (*) (id the Element of the carrier of (1Cat (A,B))) is Element of the carrier' of (1Cat (A,B))
MB is set
AB is Element of the carrier' of (1Cat (A,B))
id the Element of the carrier of (1Cat (A,B)) is Morphism of the Element of the carrier of (1Cat (A,B)), the Element of the carrier of (1Cat (A,B))
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
B is Element of the carrier of A
id B is Morphism of B,B
1Cat (B,(id B)) is non empty trivial finite non void 1 -element V55() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{B} is non empty trivial finite set
{(id B)} is non empty trivial finite set
K241((id B),B) is Relation-like {(id B)} -defined {B} -valued Function-like quasi_total finite Element of bool [:{(id B)},{B}:]
[:{(id B)},{B}:] is Relation-like non empty finite set
bool [:{(id B)},{B}:] is non empty finite V35() set
K240((id B),(id B),(id B)) is Relation-like [:{(id B)},{(id B)}:] -defined {(id B)} -valued Function-like quasi_total finite Element of bool [:[:{(id B)},{(id B)}:],{(id B)}:]
[:{(id B)},{(id B)}:] is Relation-like non empty finite set
[:[:{(id B)},{(id B)}:],{(id B)}:] is Relation-like non empty finite set
bool [:[:{(id B)},{(id B)}:],{(id B)}:] is non empty finite V35() set
CatStr(# {B},{(id B)},K241((id B),B),K241((id B),B),K240((id B),(id B),(id B)) #) is non empty non void V55() strict CatStr
the carrier of (1Cat (B,(id B))) is non empty trivial finite set
OA is set
the Comp of (1Cat (B,(id B))) is Relation-like [: the carrier' of (1Cat (B,(id B))), the carrier' of (1Cat (B,(id B))):] -defined the carrier' of (1Cat (B,(id B))) -valued Function-like finite Element of bool [:[: the carrier' of (1Cat (B,(id B))), the carrier' of (1Cat (B,(id B))):], the carrier' of (1Cat (B,(id B))):]
the carrier' of (1Cat (B,(id B))) is non empty trivial finite set
[: the carrier' of (1Cat (B,(id B))), the carrier' of (1Cat (B,(id B))):] is Relation-like non empty finite set
[:[: the carrier' of (1Cat (B,(id B))), the carrier' of (1Cat (B,(id B))):], the carrier' of (1Cat (B,(id B))):] is Relation-like non empty finite set
bool [:[: the carrier' of (1Cat (B,(id B))), the carrier' of (1Cat (B,(id B))):], the carrier' of (1Cat (B,(id B))):] is non empty finite V35() set
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
the carrier' of A is non empty set
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
OA is Element of the carrier of (1Cat (B,(id B)))
AB is Element of the carrier of (1Cat (B,(id B)))
Hom (OA,AB) is trivial finite Element of bool the carrier' of (1Cat (B,(id B)))
bool the carrier' of (1Cat (B,(id B))) is non empty finite V35() set
{ b₁ where b₁ is Element of the carrier' of (1Cat (B,(id B))) : ( dom b₁ = OA & cod b₁ = AB ) } is set
MA is Element of the carrier of A
MB is Element of the carrier of A
Hom (MA,MB) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MA & cod b₁ = MB ) } is set
OB is set
OA is set
[:A,A:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
[: the Source of A, the Source of A:] is Relation-like [: the carrier' of A, the carrier' of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:] is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the Target of A, the Target of A:] is Relation-like [: the carrier' of A, the carrier' of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:]
|: the Comp of A, the Comp of A:| is Relation-like [:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:] -defined [: the carrier' of A, the carrier' of A:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:]
[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:] is Relation-like non empty set
[:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:] is Relation-like non empty set
bool [:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of A:],[: the carrier' of A, the carrier' of A:],[: the Source of A, the Source of A:],[: the Target of A, the Target of A:],|: the Comp of A, the Comp of A:| #) is non empty non void V55() strict CatStr
[(id B),(id B)] is non empty V15() Element of the carrier' of [:A,A:]
the carrier' of [:A,A:] is non empty set
{(id B),(id B)} is non empty finite set
{{(id B),(id B)},{(id B)}} is non empty finite V35() set
[[(id B),(id B)],(id B)] is non empty V15() Element of the carrier' of [:[:A,A:],A:]
[:[:A,A:],A:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of [:A,A:] is non empty set
[: the carrier of [:A,A:], the carrier of A:] is Relation-like non empty set
[: the carrier' of [:A,A:], the carrier' of A:] is Relation-like non empty set
the Source of [:A,A:] is Relation-like the carrier' of [:A,A:] -defined the carrier of [:A,A:] -valued Function-like quasi_total Element of bool [: the carrier' of [:A,A:], the carrier of [:A,A:]:]
[: the carrier' of [:A,A:], the carrier of [:A,A:]:] is Relation-like non empty set
bool [: the carrier' of [:A,A:], the carrier of [:A,A:]:] is non empty set
[: the Source of [:A,A:], the Source of A:] is Relation-like [: the carrier' of [:A,A:], the carrier' of A:] -defined [: the carrier of [:A,A:], the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier of [:A,A:], the carrier of A:]:]
[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier of [:A,A:], the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier of [:A,A:], the carrier of A:]:] is non empty set
the Target of [:A,A:] is Relation-like the carrier' of [:A,A:] -defined the carrier of [:A,A:] -valued Function-like quasi_total Element of bool [: the carrier' of [:A,A:], the carrier of [:A,A:]:]
[: the Target of [:A,A:], the Target of A:] is Relation-like [: the carrier' of [:A,A:], the carrier' of A:] -defined [: the carrier of [:A,A:], the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier of [:A,A:], the carrier of A:]:]
the Comp of [:A,A:] is Relation-like [: the carrier' of [:A,A:], the carrier' of [:A,A:]:] -defined the carrier' of [:A,A:] -valued Function-like Element of bool [:[: the carrier' of [:A,A:], the carrier' of [:A,A:]:], the carrier' of [:A,A:]:]
[: the carrier' of [:A,A:], the carrier' of [:A,A:]:] is Relation-like non empty set
[:[: the carrier' of [:A,A:], the carrier' of [:A,A:]:], the carrier' of [:A,A:]:] is Relation-like non empty set
bool [:[: the carrier' of [:A,A:], the carrier' of [:A,A:]:], the carrier' of [:A,A:]:] is non empty set
|: the Comp of [:A,A:], the Comp of A:| is Relation-like [:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:] -defined [: the carrier' of [:A,A:], the carrier' of A:] -valued Function-like Element of bool [:[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:],[: the carrier' of [:A,A:], the carrier' of A:]:]
[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:] is Relation-like non empty set
[:[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:],[: the carrier' of [:A,A:], the carrier' of A:]:] is Relation-like non empty set
bool [:[:[: the carrier' of [:A,A:], the carrier' of A:],[: the carrier' of [:A,A:], the carrier' of A:]:],[: the carrier' of [:A,A:], the carrier' of A:]:] is non empty set
CatStr(# [: the carrier of [:A,A:], the carrier of A:],[: the carrier' of [:A,A:], the carrier' of A:],[: the Source of [:A,A:], the Source of A:],[: the Target of [:A,A:], the Target of A:],|: the Comp of [:A,A:], the Comp of A:| #) is non empty non void V55() strict CatStr
the carrier' of [:[:A,A:],A:] is non empty set
{[(id B),(id B)],(id B)} is non empty finite set
{[(id B),(id B)]} is Relation-like non empty trivial finite set
{{[(id B),(id B)],(id B)},{[(id B),(id B)]}} is non empty finite V35() set
{[[(id B),(id B)],(id B)]} is Relation-like non empty trivial finite set
OA is Element of the carrier of (1Cat (B,(id B)))
id OA is Morphism of OA,OA
AB is Element of the carrier of A
id AB is Morphism of AB,AB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the carrier' of A is non empty set
the carrier of A is non empty set
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities Subcategory of A
the Source of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the carrier' of B is non empty set
the carrier of B is non empty set
[: the carrier' of B, the carrier of B:] is Relation-like non empty set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of A | the carrier' of B is Relation-like the carrier' of B -defined the carrier' of A -defined the carrier of A -valued set
the Target of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of A | the carrier' of B is Relation-like the carrier' of B -defined the carrier' of A -defined the carrier of A -valued set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is Relation-like non empty set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is Relation-like non empty set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of A || the carrier' of B is Relation-like Function-like set
the Comp of A | [: the carrier' of B, the carrier' of B:] is Relation-like [: the carrier' of B, the carrier' of B:] -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
proj1 the Source of A is set
OA is set
proj1 the Source of B is set
AB is Element of the carrier' of B
the Source of B . OA is set
dom AB is Element of the carrier of B
the Source of B . AB is Element of the carrier of B
MA is Element of the carrier' of A
dom MA is Element of the carrier of A
the Source of A . MA is Element of the carrier of A
the Source of A . OA is set
OA is set
proj1 the Target of B is set
AB is Element of the carrier' of B
the Target of B . OA is set
cod AB is Element of the carrier of B
the Target of B . AB is Element of the carrier of B
MA is Element of the carrier' of A
cod MA is Element of the carrier of A
the Target of A . MA is Element of the carrier of A
the Target of A . OA is set
(proj1 the Source of A) /\ the carrier' of B is set
proj1 the Target of A is set
(proj1 the Target of A) /\ the carrier' of B is set
proj1 the Comp of B is Relation-like set
proj1 the Comp of A is Relation-like set
(proj1 the Comp of A) /\ [: the carrier' of B, the carrier' of B:] is Relation-like set
OA is set
OA `1 is set
OA `2 is set
AB is Element of the carrier' of B
MA is Element of the carrier' of B
MB is Element of the carrier' of A
OB is Element of the carrier' of A
[MB,OB] is non empty V15() Element of the carrier' of [:A,A:]
[:A,A:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[: the Source of A, the Source of A:] is Relation-like [: the carrier' of A, the carrier' of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:] is non empty set
[: the Target of A, the Target of A:] is Relation-like [: the carrier' of A, the carrier' of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:]
|: the Comp of A, the Comp of A:| is Relation-like [:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:] -defined [: the carrier' of A, the carrier' of A:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:]
[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:] is Relation-like non empty set
[:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:] is Relation-like non empty set
bool [:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of A:],[: the carrier' of A, the carrier' of A:],[: the Source of A, the Source of A:],[: the Target of A, the Target of A:],|: the Comp of A, the Comp of A:| #) is non empty non void V55() strict CatStr
the carrier' of [:A,A:] is non empty set
{MB,OB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,OB},{MB}} is non empty finite V35() set
dom AB is Element of the carrier of B
the Source of B . AB is Element of the carrier of B
dom MB is Element of the carrier of A
the Source of A . MB is Element of the carrier of A
cod OB is Element of the carrier of A
the Target of A . OB is Element of the carrier of A
cod MA is Element of the carrier of B
the Target of B . MA is Element of the carrier of B
[AB,MA] is non empty V15() Element of the carrier' of [:B,B:]
[:B,B:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[: the Source of B, the Source of B:] is Relation-like [: the carrier' of B, the carrier' of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total 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:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier' of B, the carrier' of B:],[: the carrier of B, the carrier of B:]:] is non empty set
[: the Target of B, the Target of B:] is Relation-like [: the carrier' of B, the carrier' of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier' of B, the carrier' of B:],[: the carrier of B, the carrier of B:]:]
|: the Comp of B, the Comp of B:| is Relation-like [:[: the carrier' of B, the carrier' of B:],[: the carrier' of B, the carrier' of B:]:] -defined [: the carrier' of B, 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:]:]
[:[: the carrier' of B, the carrier' of B:],[: the carrier' of B, the carrier' of B:]:] is Relation-like non empty set
[:[:[: 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 Relation-like non empty set
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 set
CatStr(# [: the carrier of B, the carrier of B:],[: the carrier' of B, the carrier' of B:],[: the Source of B, the Source of B:],[: the Target of B, the Target of B:],|: the Comp of B, the Comp of B:| #) is non empty non void V55() strict CatStr
the carrier' of [:B,B:] is non empty set
{AB,MA} is non empty finite set
{AB} is non empty trivial finite set
{{AB,MA},{AB}} is non empty finite V35() set
the Comp of A | ((proj1 the Comp of A) /\ [: the carrier' of B, the carrier' of B:]) is Relation-like (proj1 the Comp of A) /\ [: the carrier' of B, the carrier' of B:] -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
the Comp of A | (proj1 the Comp of A) is Relation-like proj1 the Comp of A -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
( the Comp of A | (proj1 the Comp of A)) | [: the carrier' of B, the carrier' of B:] is Relation-like [: the carrier' of B, the carrier' of B:] -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
bool the carrier of A is non empty set
the carrier' of A is non empty set
bool the carrier' of A is non empty set
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
B is non empty Element of bool the carrier of A
OA is non empty Element of bool the carrier' of A
[:OA,B:] is Relation-like non empty set
bool [:OA,B:] is non empty set
( the carrier' of A, the carrier of A, the Source of A,OA) is Relation-like OA -defined the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [:OA, the carrier of A:]
[:OA, the carrier of A:] is Relation-like non empty set
bool [:OA, the carrier of A:] is non empty set
( the carrier' of A, the carrier of A, the Target of A,OA) is Relation-like OA -defined the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [:OA, the carrier of A:]
[:OA,OA:] is Relation-like non empty set
[:[:OA,OA:],OA:] is Relation-like non empty set
bool [:[:OA,OA:],OA:] is non empty set
the Comp of A || OA is Relation-like Function-like set
the Comp of A | [:OA,OA:] is Relation-like [:OA,OA:] -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
AB is Relation-like OA -defined B -valued Function-like quasi_total Element of bool [:OA,B:]
MA is Relation-like OA -defined B -valued Function-like quasi_total Element of bool [:OA,B:]
MB is Relation-like [:OA,OA:] -defined OA -valued Function-like Element of bool [:[:OA,OA:],OA:]
CatStr(# B,OA,AB,MA,MB #) is non empty non void V55() strict CatStr
the carrier' of CatStr(# B,OA,AB,MA,MB #) is non empty set
MB is Element of the carrier' of A
MA is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) is Relation-like the carrier' of CatStr(# B,OA,AB,MA,MB #) -defined the carrier of CatStr(# B,OA,AB,MA,MB #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier of CatStr(# B,OA,AB,MA,MB #):]
the carrier of CatStr(# B,OA,AB,MA,MB #) is non empty set
[: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier of CatStr(# B,OA,AB,MA,MB #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier of CatStr(# B,OA,AB,MA,MB #):] is non empty set
proj1 the Source of CatStr(# B,OA,AB,MA,MB #) is set
dom MB is Element of the carrier of A
the Source of A . MB is Element of the carrier of A
dom MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) is Relation-like the carrier' of CatStr(# B,OA,AB,MA,MB #) -defined the carrier of CatStr(# B,OA,AB,MA,MB #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier of CatStr(# B,OA,AB,MA,MB #):]
proj1 the Target of CatStr(# B,OA,AB,MA,MB #) is set
cod MB is Element of the carrier of A
the Target of A . MB is Element of the carrier of A
cod MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Comp of CatStr(# B,OA,AB,MA,MB #) is Relation-like [: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier' of CatStr(# B,OA,AB,MA,MB #):] -defined the carrier' of CatStr(# B,OA,AB,MA,MB #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier' of CatStr(# B,OA,AB,MA,MB #):], the carrier' of CatStr(# B,OA,AB,MA,MB #):]
[: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier' of CatStr(# B,OA,AB,MA,MB #):] is Relation-like non empty set
[:[: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier' of CatStr(# B,OA,AB,MA,MB #):], the carrier' of CatStr(# B,OA,AB,MA,MB #):] is Relation-like non empty set
bool [:[: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier' of CatStr(# B,OA,AB,MA,MB #):], the carrier' of CatStr(# B,OA,AB,MA,MB #):] is non empty set
proj1 the Comp of CatStr(# B,OA,AB,MA,MB #) is Relation-like set
proj1 the Comp of A is Relation-like set
(proj1 the Comp of A) /\ [: the carrier' of CatStr(# B,OA,AB,MA,MB #), the carrier' of CatStr(# B,OA,AB,MA,MB #):] is Relation-like set
MA is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
MB is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
dom MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
cod MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
a is Element of the carrier' of A
dom a is Element of the carrier of A
the Source of A . a is Element of the carrier of A
b is Element of the carrier' of A
cod b is Element of the carrier of A
the Target of A . b is Element of the carrier of A
[a,b] is non empty V15() Element of the carrier' of [:A,A:]
[:A,A:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[: the Source of A, the Source of A:] is Relation-like [: the carrier' of A, the carrier' of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:] is non empty set
[: the Target of A, the Target of A:] is Relation-like [: the carrier' of A, the carrier' of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of A:],[: the carrier of A, the carrier of A:]:]
|: the Comp of A, the Comp of A:| is Relation-like [:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:] -defined [: the carrier' of A, the carrier' of A:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:]
[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:] is Relation-like non empty set
[:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:] is Relation-like non empty set
bool [:[:[: the carrier' of A, the carrier' of A:],[: the carrier' of A, the carrier' of A:]:],[: the carrier' of A, the carrier' of A:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of A:],[: the carrier' of A, the carrier' of A:],[: the Source of A, the Source of A:],[: the Target of A, the Target of A:],|: the Comp of A, the Comp of A:| #) is non empty non void V55() strict CatStr
the carrier' of [:A,A:] is non empty set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
MA is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
MB is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
dom MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
cod MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
a is Element of the carrier' of A
dom a is Element of the carrier of A
the Source of A . a is Element of the carrier of A
b is Element of the carrier' of A
cod b is Element of the carrier of A
the Target of A . b is Element of the carrier of A
MA is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
dom MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MB is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
cod MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MA (*) MB is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
dom (MA (*) MB) is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . (MA (*) MB) is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
dom MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
cod (MA (*) MB) is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . (MA (*) MB) is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
cod MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
the Comp of CatStr(# B,OA,AB,MA,MB #) . (MA,MB) is set
the Comp of CatStr(# B,OA,AB,MA,MB #) . [MA,MB] is set
a is Element of the carrier' of A
dom a is Element of the carrier of A
the Source of A . a is Element of the carrier of A
b is Element of the carrier' of A
cod b is Element of the carrier of A
the Target of A . b is Element of the carrier of A
[a,b] is non empty V15() Element of the carrier' of [:A,A:]
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
the Comp of A . (a,b) is set
[a,b] is non empty V15() set
the Comp of A . [a,b] is set
a (*) b is Element of the carrier' of A
dom (a (*) b) is Element of the carrier of A
the Source of A . (a (*) b) is Element of the carrier of A
dom b is Element of the carrier of A
the Source of A . b is Element of the carrier of A
cod (a (*) b) is Element of the carrier of A
the Target of A . (a (*) b) is Element of the carrier of A
cod a is Element of the carrier of A
the Target of A . a is Element of the carrier of A
MA is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
cod MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MB is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
dom MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MB (*) MA is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
a is Element of the carrier' of A
b is Element of the carrier' of A
a (*) b is Element of the carrier' of A
cod b is Element of the carrier of A
the Target of A . b is Element of the carrier of A
dom a is Element of the carrier of A
the Source of A . a is Element of the carrier of A
[MB,MA] is non empty V15() set
{MB,MA} is non empty finite set
{MB} is non empty trivial finite set
{{MB,MA},{MB}} is non empty finite V35() set
the Comp of CatStr(# B,OA,AB,MA,MB #) . (MB,MA) is set
the Comp of CatStr(# B,OA,AB,MA,MB #) . [MB,MA] is set
the Comp of A . (a,b) is set
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
the Comp of A . [a,b] is set
a is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
dom a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MA is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
cod MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
dom MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . MA is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MB is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
cod MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MA (*) MB is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
a (*) (MA (*) MB) is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
a (*) MA is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
(a (*) MA) (*) MB is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
the Comp of CatStr(# B,OA,AB,MA,MB #) . (MA,MB) is set
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
the Comp of CatStr(# B,OA,AB,MA,MB #) . [MA,MB] is set
[a,MA] is non empty V15() set
{a,MA} is non empty finite set
{a} is non empty trivial finite set
{{a,MA},{a}} is non empty finite V35() set
the Comp of CatStr(# B,OA,AB,MA,MB #) . [a,MA] is set
a is Element of the carrier' of A
dom a is Element of the carrier of A
the Source of A . a is Element of the carrier of A
b is Element of the carrier' of A
cod b is Element of the carrier of A
the Target of A . b is Element of the carrier of A
[a,b] is non empty V15() Element of the carrier' of [:A,A:]
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
dom b is Element of the carrier of A
the Source of A . b is Element of the carrier of A
a is Element of the carrier' of A
cod a is Element of the carrier of A
the Target of A . a is Element of the carrier of A
[b,a] is non empty V15() Element of the carrier' of [:A,A:]
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
b (*) a is Element of the carrier' of A
a (*) b is Element of the carrier' of A
the Comp of CatStr(# B,OA,AB,MA,MB #) . (a,MA) is set
the Comp of A . (a,b) is set
[a,b] is non empty V15() set
the Comp of A . [a,b] is set
t19 is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
dom t19 is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . t19 is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
F2 is Element of the carrier' of A
dom F2 is Element of the carrier of A
the Source of A . F2 is Element of the carrier of A
the Comp of A . (b,a) is set
[b,a] is non empty V15() set
the Comp of A . [b,a] is set
t19 is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
F1 is Element of the carrier' of A
cod F1 is Element of the carrier of A
the Target of A . F1 is Element of the carrier of A
cod t19 is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . t19 is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
a (*) (b (*) a) is Element of the carrier' of A
(a (*) b) (*) a is Element of the carrier' of A
MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
Hom (MB,MB) is Element of bool the carrier' of CatStr(# B,OA,AB,MA,MB #)
bool the carrier' of CatStr(# B,OA,AB,MA,MB #) is non empty set
{ b₁ where b₁ is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #) : ( dom b₁ = MB & cod b₁ = MB ) } is set
MA is Element of the carrier of A
id MA is Morphism of MA,MA
a is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
cod a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
cod (id MA) is Element of the carrier of A
the Target of A . (id MA) is Element of the carrier of A
dom a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
dom (id MA) is Element of the carrier of A
the Source of A . (id MA) is Element of the carrier of A
MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MA is Element of the carrier of A
id MA is Morphism of MA,MA
a is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
b is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
Hom (MB,b) is Element of bool the carrier' of CatStr(# B,OA,AB,MA,MB #)
bool the carrier' of CatStr(# B,OA,AB,MA,MB #) is non empty set
{ b₁ where b₁ is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #) : ( dom b₁ = MB & cod b₁ = b ) } is set
Hom (b,MB) is Element of bool the carrier' of CatStr(# B,OA,AB,MA,MB #)
{ b₁ where b₁ is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #) : ( dom b₁ = b & cod b₁ = MB ) } is set
a is Morphism of MB,b
a (*) a is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
dom a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
t19 is Element of the carrier' of A
dom t19 is Element of the carrier of A
the Source of A . t19 is Element of the carrier of A
cod (id MA) is Element of the carrier of A
the Target of A . (id MA) is Element of the carrier of A
cod a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
t19 (*) (id MA) is Element of the carrier' of A
a is Morphism of b,MB
a (*) a is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
cod a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
t19 is Element of the carrier' of A
cod t19 is Element of the carrier of A
the Target of A . t19 is Element of the carrier of A
dom a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
dom t19 is Element of the carrier of A
the Source of A . t19 is Element of the carrier of A
a is Element of the carrier of A
Hom (a,MA) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = a & cod b₁ = MA ) } is set
Hom (MA,MA) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MA & cod b₁ = MA ) } is set
dom (id MA) is Element of the carrier of A
the Source of A . (id MA) is Element of the carrier of A
dom a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
t19 is Morphism of a,MA
(id MA) (*) t19 is Element of the carrier' of A
(id MA) * t19 is Morphism of a,MA
MB is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
MA is Element of the carrier of A
id MA is Morphism of MA,MA
a is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
cod a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Target of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
cod (id MA) is Element of the carrier of A
the Target of A . (id MA) is Element of the carrier of A
dom a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
the Source of CatStr(# B,OA,AB,MA,MB #) . a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
dom (id MA) is Element of the carrier of A
the Source of A . (id MA) is Element of the carrier of A
Hom (MB,MB) is Element of bool the carrier' of CatStr(# B,OA,AB,MA,MB #)
bool the carrier' of CatStr(# B,OA,AB,MA,MB #) is non empty set
{ b₁ where b₁ is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #) : ( dom b₁ = MB & cod b₁ = MB ) } is set
b is Morphism of MB,MB
a is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
t19 is Element of the carrier of CatStr(# B,OA,AB,MA,MB #)
Hom (MB,a) is Element of bool the carrier' of CatStr(# B,OA,AB,MA,MB #)
{ b₁ where b₁ is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #) : ( dom b₁ = MB & cod b₁ = a ) } is set
a is Morphism of MB,a
a (*) b is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
Hom (t19,MB) is Element of bool the carrier' of CatStr(# B,OA,AB,MA,MB #)
{ b₁ where b₁ is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #) : ( dom b₁ = t19 & cod b₁ = MB ) } is set
t19 is Morphism of t19,MB
b (*) t19 is Element of the carrier' of CatStr(# B,OA,AB,MA,MB #)
MB is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of MB is non empty set
the Comp of MB is Relation-like [: the carrier' of MB, the carrier' of MB:] -defined the carrier' of MB -valued Function-like Element of bool [:[: the carrier' of MB, the carrier' of MB:], the carrier' of MB:]
the carrier' of MB is non empty set
[: the carrier' of MB, the carrier' of MB:] is Relation-like non empty set
[:[: the carrier' of MB, the carrier' of MB:], the carrier' of MB:] is Relation-like non empty set
bool [:[: the carrier' of MB, the carrier' of MB:], the carrier' of MB:] is non empty set
MA is Element of the carrier of MB
a is Element of the carrier of MB
Hom (MA,a) is Element of bool the carrier' of MB
bool the carrier' of MB is non empty set
{ b₁ where b₁ is Element of the carrier' of MB : ( dom b₁ = MA & cod b₁ = a ) } is set
b is Element of the carrier of A
a is Element of the carrier of A
Hom (b,a) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = b & cod b₁ = a ) } is set
a is set
t19 is Element of the carrier' of MB
dom t19 is Element of the carrier of MB
the Source of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
[: the carrier' of MB, the carrier of MB:] is Relation-like non empty set
bool [: the carrier' of MB, the carrier of MB:] is non empty set
the Source of MB . t19 is Element of the carrier of MB
cod t19 is Element of the carrier of MB
the Target of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
the Target of MB . t19 is Element of the carrier of MB
t19 is Element of the carrier' of A
cod t19 is Element of the carrier of A
the Target of A . t19 is Element of the carrier of A
dom t19 is Element of the carrier of A
the Source of A . t19 is Element of the carrier of A
MA is Element of the carrier of MB
id MA is Morphism of MA,MA
a is Element of the carrier of A
id a is Morphism of a,a
b is Element of the carrier' of MB
cod b is Element of the carrier of MB
the Target of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
[: the carrier' of MB, the carrier of MB:] is Relation-like non empty set
bool [: the carrier' of MB, the carrier of MB:] is non empty set
the Target of MB . b is Element of the carrier of MB
cod (id a) is Element of the carrier of A
the Target of A . (id a) is Element of the carrier of A
dom b is Element of the carrier of MB
the Source of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
the Source of MB . b is Element of the carrier of MB
dom (id a) is Element of the carrier of A
the Source of A . (id a) is Element of the carrier of A
Hom (MA,MA) is non empty Element of bool the carrier' of MB
bool the carrier' of MB is non empty set
{ b₁ where b₁ is Element of the carrier' of MB : ( dom b₁ = MA & cod b₁ = MA ) } is set
a is Morphism of MA,MA
a is Element of the carrier of MB
t19 is Element of the carrier of MB
Hom (MA,a) is Element of bool the carrier' of MB
{ b₁ where b₁ is Element of the carrier' of MB : ( dom b₁ = MA & cod b₁ = a ) } is set
t19 is Morphism of MA,a
t19 (*) a is Element of the carrier' of MB
Hom (t19,MA) is Element of bool the carrier' of MB
{ b₁ where b₁ is Element of the carrier' of MB : ( dom b₁ = t19 & cod b₁ = MA ) } is set
F1 is Morphism of t19,MA
a (*) F1 is Element of the carrier' of MB
A is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
the carrier' of A is non empty set
B is non empty non void V55() strict Category-like transitive associative reflexive with_identities Subcategory of A
the carrier of B is non empty set
the carrier' of B is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
proj1 the Target of A is set
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
proj1 the Source of A is set
the Target of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is Relation-like non empty set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Target of A | the carrier' of B is Relation-like the carrier' of B -defined the carrier' of A -defined the carrier of A -valued set
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
proj1 the Comp of A is 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:] is Relation-like non empty set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is Relation-like non empty set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Comp of A || the carrier' of B is Relation-like Function-like set
the Comp of A | [: the carrier' of B, the carrier' of B:] is Relation-like [: the carrier' of B, the carrier' of B:] -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
the Source of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Source of A | the carrier' of B is Relation-like the carrier' of B -defined the carrier' of A -defined the carrier of A -valued set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of OA is non empty set
the carrier of OA is non empty set
AB is Relation-like the carrier' of OA -defined the carrier' of A -valued Function-like quasi_total Functor of OA,A
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA * AB is Relation-like the carrier' of OA -defined the carrier' of OA -defined the carrier' of B -valued the carrier' of B -valued Function-like quasi_total Functor of OA,B
MB is Element of the carrier of OA
OB is Element of the carrier of OA
Hom (MB,OB) is Element of bool the carrier' of OA
bool the carrier' of OA is non empty set
{ b₁ where b₁ is Element of the carrier' of OA : ( dom b₁ = MB & cod b₁ = OB ) } is set
AB . MB is Element of the carrier of A
the carrier of A is non empty set
Obj AB is Relation-like the carrier of OA -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of OA, the carrier of A:]
[: the carrier of OA, the carrier of A:] is Relation-like non empty set
bool [: the carrier of OA, the carrier of A:] is non empty set
(Obj AB) . MB is Element of the carrier of A
AB . OB is Element of the carrier of A
(Obj AB) . OB is Element of the carrier of A
Hom ((AB . MB),(AB . OB)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = AB . MB & cod b₁ = AB . OB ) } is set
MB is Morphism of MB,OB
(MA * AB) /. MB is Morphism of (MA * AB) . MB,(MA * AB) . OB
(MA * AB) . MB is Element of the carrier of B
the carrier of B is non empty set
Obj (MA * AB) is Relation-like the carrier of OA -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of OA, the carrier of B:]
[: the carrier of OA, the carrier of B:] is Relation-like non empty set
bool [: the carrier of OA, the carrier of B:] is non empty set
(Obj (MA * AB)) . MB is Element of the carrier of B
(MA * AB) . OB is Element of the carrier of B
(Obj (MA * AB)) . OB is Element of the carrier of B
AB /. MB is Morphism of AB . MB,AB . OB
MA /. (AB /. MB) is Morphism of MA . (AB . MB),MA . (AB . OB)
MA . (AB . MB) is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj MA) . (AB . MB) is Element of the carrier of B
MA . (AB . OB) is Element of the carrier of B
(Obj MA) . (AB . OB) is Element of the carrier of B
(MA * AB) . MB is Element of the carrier' of B
AB . MB is Element of the carrier' of A
MA . (AB . MB) is Element of the carrier' of B
MA . (AB /. MB) is Element of the carrier' of B
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Element of the carrier' of A
dom MA is Element of the carrier of A
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of A . MA is Element of the carrier of A
cod MA is Element of the carrier of A
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of A . MA is Element of the carrier of A
Hom ((dom MA),(cod MA)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom MA & cod b₁ = cod MA ) } is set
OA . MA is Element of the carrier' of B
MB is Morphism of dom MA, cod MA
AB . MB is Element of the carrier' of B
AB . MA is Element of the carrier' of B
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
AB is Element of the carrier of B
MA is Element of the carrier of B
Hom (AB,MA) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB & cod b₁ = MA ) } is set
MB is Element of the carrier of B
Hom (MA,MB) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = MA & cod b₁ = MB ) } is set
OA . AB is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . AB is Element of the carrier of A
OA . MA is Element of the carrier of A
(Obj OA) . MA is Element of the carrier of A
OA . MB is Element of the carrier of A
(Obj OA) . MB is Element of the carrier of A
OB is Morphism of AB,MA
OA /. OB is Morphism of OA . AB,OA . MA
MB is Morphism of MA,MB
MB * OB is Morphism of AB,MB
OA /. (MB * OB) is Morphism of OA . AB,OA . MB
OA /. MB is Morphism of OA . MA,OA . MB
(OA /. MB) * (OA /. OB) is Morphism of OA . AB,OA . MB
dom MB 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 quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is Relation-like non empty set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of B . MB is Element of the carrier of B
cod OB 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 quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of B . OB is Element of the carrier of B
OA . MB is Element of the carrier' of A
Hom ((OA . AB),(OA . MA)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = OA . AB & cod b₁ = OA . MA ) } is set
OA . OB is Element of the carrier' of A
Hom ((OA . MA),(OA . MB)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = OA . MA & cod b₁ = OA . MB ) } is set
Hom (AB,MB) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB & cod b₁ = MB ) } is set
OA . (MB * OB) is Element of the carrier' of A
MB (*) OB is Element of the carrier' of B
OA . (MB (*) OB) is Element of the carrier' of A
(OA . MB) (*) (OA . OB) is Element of the carrier' of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Element of the carrier of A
id AB is Morphism of AB,AB
OA /. (id AB) is Morphism of OA . AB,OA . AB
OA . AB is Element of the carrier of B
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . AB is Element of the carrier of B
MA is Element of the carrier of B
id MA is Morphism of MA,MA
Hom (AB,AB) is non empty Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = AB & cod b₁ = AB ) } is set
OA . (id AB) is Element of the carrier' of B
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
AB is Element of the carrier of B
id AB is Morphism of AB,AB
OA /. (id AB) is Morphism of OA . AB,OA . AB
OA . AB is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . AB is Element of the carrier of A
id (OA . AB) is Morphism of OA . AB,OA . AB
Hom (AB,AB) is non empty Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB & cod b₁ = AB ) } is set
OA . (id AB) is Element of the carrier' of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
id A is Relation-like the carrier' of A -defined the carrier' of A -valued Function-like quasi_total Functor of A,A
the carrier' of A is non empty set
id the carrier' of A is Relation-like the carrier' of A -defined the carrier' of A -valued non empty total Element of bool [: the carrier' of A, the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier' of A:] is non empty set
B is Element of the carrier of A
OA is Element of the carrier of A
Hom (B,OA) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = B & cod b₁ = OA ) } is set
AB is Morphism of B,OA
(id A) /. AB is Morphism of (id A) . B,(id A) . OA
(id A) . B is Element of the carrier of A
Obj (id A) is Relation-like the carrier of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of A:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier of A, the carrier of A:] is non empty set
(Obj (id A)) . B is Element of the carrier of A
(id A) . OA is Element of the carrier of A
(Obj (id A)) . OA is Element of the carrier of A
(id A) . AB is Element of the carrier' of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
B is Element of the carrier of A
OA is Element of the carrier of A
Hom (B,OA) is Element of bool the carrier' of A
the carrier' of A is non empty set
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = B & cod b₁ = OA ) } is set
AB is Element of the carrier of A
MA is Element of the carrier of A
Hom (AB,MA) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = AB & cod b₁ = MA ) } is set
MB is set
OB is Element of the carrier' of A
cod OB is Element of the carrier of A
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Target of A . OB is Element of the carrier of A
dom OB is Element of the carrier of A
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Source of A . OB is Element of the carrier of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of A is non empty set
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Element of the carrier of A
MA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj MA) . MB is Element of the carrier of B
Hom ((MA . MB),(MA . MB)) is non empty Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = MA . MB & cod b₁ = MA . MB ) } is set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
MB is Element of the carrier of A
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
MA . MB is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . MB is Element of the carrier of B
Hom ((OA . MB),(MA . MB)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MB & cod b₁ = MA . MB ) } is set
AB . MB is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MB is Element of the carrier of B
Hom ((AB . MB),(MA . MB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB . MB & cod b₁ = MA . MB ) } is set
Hom ((OA . MB),(AB . MB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MB & cod b₁ = AB . MB ) } is set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
[: the carrier of A, the carrier' of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier' of B:] is non empty set
bool the carrier' of B is non empty set
MA is Element of the carrier of A
OA . MA is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MA is Element of the carrier of B
AB . MA is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MA is Element of the carrier of B
Hom ((OA . MA),(AB . MA)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MA & cod b₁ = AB . MA ) } is set
the Element of Hom ((OA . MA),(AB . MA)) is Element of Hom ((OA . MA),(AB . MA))
OB is Element of Hom ((OA . MA),(AB . MA))
OB is Element of Hom ((OA . MA),(AB . MA))
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier' of B:]
MB is Element of the carrier of A
MA . MB is Element of the carrier' of B
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
AB . MB is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MB is Element of the carrier of B
Hom ((OA . MB),(AB . MB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MB & cod b₁ = AB . MB ) } is set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of A is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[: the carrier of A, the carrier' of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier' of B:] is non empty set
AB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier' of B:]
MA is Element of the carrier of A
AB . MA is Element of the carrier' of B
OA . MA is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MA is Element of the carrier of B
id (OA . MA) is Morphism of OA . MA,OA . MA
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,OA)
MB is Element of the carrier of A
MA . MB is Element of the carrier' of B
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
id (OA . MB) is Morphism of OA . MB,OA . MB
AB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,OA)
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,OA)
MB is Element of the carrier of A
AB . MB is Element of the carrier' of B
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
id (OA . MB) is Morphism of OA . MB,OA . MB
MA . MB is Element of the carrier' of B
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
MB is Element of the carrier of A
MA . MB is Element of the carrier' of B
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
AB . MB is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MB is Element of the carrier of B
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MA)
[: the carrier of A, the carrier' of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier' of B:] is non empty set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier' of B:]
MA is Element of the carrier of A
MB . MA is Element of the carrier' of B
OA . MA is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MA is Element of the carrier of B
MA . MA is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . MA is Element of the carrier of B
AB . MA is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MA is Element of the carrier of B
(A,B,OA,AB,MB,MA) is Morphism of OA . MA,AB . MA
(A,B,AB,MA,OB,MA) is Morphism of AB . MA,MA . MA
(A,B,AB,MA,OB,MA) * (A,B,OA,AB,MB,MA) is Morphism of OA . MA,MA . MA
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
a is Element of the carrier of A
(A,B,OA,MA,MA,a) is Morphism of OA . a,MA . a
OA . a is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . a is Element of the carrier of B
MA . a is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . a is Element of the carrier of B
AB . a is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . a is Element of the carrier of B
(A,B,OA,AB,MB,a) is Morphism of OA . a,AB . a
(A,B,AB,MA,OB,a) is Morphism of AB . a,MA . a
(A,B,AB,MA,OB,a) * (A,B,OA,AB,MB,a) is Morphism of OA . a,MA . a
MB . a is Element of the carrier' of B
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
a is Element of the carrier of A
MB . a is Element of the carrier' of B
(A,B,OA,MA,MB,a) is Morphism of OA . a,MA . a
OA . a is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . a is Element of the carrier of B
MA . a is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . a is Element of the carrier of B
AB . a is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . a is Element of the carrier of B
(A,B,OA,AB,MB,a) is Morphism of OA . a,AB . a
(A,B,AB,MA,OB,a) is Morphism of AB . a,MA . a
(A,B,AB,MA,OB,a) * (A,B,OA,AB,MB,a) is Morphism of OA . a,MA . a
(A,B,OA,MA,MA,a) is Morphism of OA . a,MA . a
MA . a is Element of the carrier' of B
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
AB is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
MA is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,AB)
MB is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,AB)
OB is Element of the carrier of B
MA . OB is Element of the carrier' of A
(B,A,OA,AB,MA,OB) is Morphism of OA . OB,AB . OB
OA . OB is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . OB is Element of the carrier of A
AB . OB is Element of the carrier of A
Obj AB is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
(Obj AB) . OB is Element of the carrier of A
(B,A,OA,AB,MB,OB) is Morphism of OA . OB,AB . OB
MB . OB is Element of the carrier' of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
(B,A,OA) is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,OA)
AB is Element of the carrier of B
(B,A,OA,OA,(B,A,OA),AB) is Morphism of OA . AB,OA . AB
OA . AB is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . AB is Element of the carrier of A
id (OA . AB) is Morphism of OA . AB,OA . AB
(B,A,OA) . AB is Element of the carrier' of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
(A,B,OA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,OA)
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
(A,B,AB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,AB)
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,AB,AB,MA,(A,B,AB)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,OA,AB,(A,B,OA),MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
MB is Element of the carrier of A
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
AB . MB is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MB is Element of the carrier of B
Hom ((OA . MB),(AB . MB)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MB & cod b₁ = AB . MB ) } is set
(A,B,OA,AB,(A,B,OA,AB,AB,MA,(A,B,AB)),MB) is Morphism of OA . MB,AB . MB
(A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
(A,B,AB,AB,(A,B,AB),MB) is Morphism of AB . MB,AB . MB
(A,B,AB,AB,(A,B,AB),MB) * (A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
id (AB . MB) is Morphism of AB . MB,AB . MB
(id (AB . MB)) * (A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
MB is Element of the carrier of A
OA . MB is Element of the carrier of B
(Obj OA) . MB is Element of the carrier of B
AB . MB is Element of the carrier of B
(Obj AB) . MB is Element of the carrier of B
Hom ((OA . MB),(AB . MB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MB & cod b₁ = AB . MB ) } is set
(A,B,OA,AB,(A,B,OA,OA,AB,(A,B,OA),MA),MB) is Morphism of OA . MB,AB . MB
(A,B,OA,OA,(A,B,OA),MB) is Morphism of OA . MB,OA . MB
(A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
(A,B,OA,AB,MA,MB) * (A,B,OA,OA,(A,B,OA),MB) is Morphism of OA . MB,AB . MB
id (OA . MB) is Morphism of OA . MB,OA . MB
(A,B,OA,AB,MA,MB) * (id (OA . MB)) is Morphism of OA . MB,AB . MB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MA)
(A,B,OA,AB,MA,OB,MB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MB)
(A,B,AB,MA,MB,MB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MB)
(A,B,OA,AB,MB,OB,(A,B,AB,MA,MB,MB,MA)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MB)
(A,B,OA,MA,MB,(A,B,OA,AB,MA,OB,MB),MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MB)
a is Element of the carrier of A
OA . a is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . a is Element of the carrier of B
AB . a is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . a is Element of the carrier of B
Hom ((OA . a),(AB . a)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . a & cod b₁ = AB . a ) } is set
MA . a is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . a is Element of the carrier of B
Hom ((AB . a),(MA . a)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB . a & cod b₁ = MA . a ) } is set
MB . a is Element of the carrier of B
Obj MB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MB) . a is Element of the carrier of B
Hom ((MA . a),(MB . a)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = MA . a & cod b₁ = MB . a ) } is set
(A,B,OA,MB,(A,B,OA,AB,MB,OB,(A,B,AB,MA,MB,MB,MA)),a) is Morphism of OA . a,MB . a
(A,B,OA,AB,OB,a) is Morphism of OA . a,AB . a
(A,B,AB,MB,(A,B,AB,MA,MB,MB,MA),a) is Morphism of AB . a,MB . a
(A,B,AB,MB,(A,B,AB,MA,MB,MB,MA),a) * (A,B,OA,AB,OB,a) is Morphism of OA . a,MB . a
(A,B,AB,MA,MB,a) is Morphism of AB . a,MA . a
(A,B,MA,MB,MA,a) is Morphism of MA . a,MB . a
(A,B,MA,MB,MA,a) * (A,B,AB,MA,MB,a) is Morphism of AB . a,MB . a
((A,B,MA,MB,MA,a) * (A,B,AB,MA,MB,a)) * (A,B,OA,AB,OB,a) is Morphism of OA . a,MB . a
(A,B,AB,MA,MB,a) * (A,B,OA,AB,OB,a) is Morphism of OA . a,MA . a
(A,B,MA,MB,MA,a) * ((A,B,AB,MA,MB,a) * (A,B,OA,AB,OB,a)) is Morphism of OA . a,MB . a
(A,B,OA,MA,(A,B,OA,AB,MA,OB,MB),a) is Morphism of OA . a,MA . a
(A,B,MA,MB,MA,a) * (A,B,OA,MA,(A,B,OA,AB,MA,OB,MB),a) is Morphism of OA . a,MB . a
(A,B,OA,MB,(A,B,OA,MA,MB,(A,B,OA,AB,MA,OB,MB),MA),a) is Morphism of OA . a,MB . a
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
(B,A,OA) is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,OA)
AB is Element of the carrier of B
MA is Element of the carrier of B
Hom (AB,MA) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB & cod b₁ = MA ) } is set
OA . AB is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . AB is Element of the carrier of A
OA . MA is Element of the carrier of A
(Obj OA) . MA is Element of the carrier of A
(B,A,OA,OA,(B,A,OA),MA) is Morphism of OA . MA,OA . MA
(B,A,OA,OA,(B,A,OA),AB) is Morphism of OA . AB,OA . AB
MB is Morphism of AB,MA
OA /. MB is Morphism of OA . AB,OA . MA
(B,A,OA,OA,(B,A,OA),MA) * (OA /. MB) is Morphism of OA . AB,OA . MA
(OA /. MB) * (B,A,OA,OA,(B,A,OA),AB) is Morphism of OA . AB,OA . MA
Hom (AB,AB) is non empty Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB & cod b₁ = AB ) } is set
Hom (MA,MA) is non empty Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = MA & cod b₁ = MA ) } is set
id (OA . MA) is Morphism of OA . MA,OA . MA
(id (OA . MA)) * (OA /. MB) is Morphism of OA . AB,OA . MA
id MA is Morphism of MA,MA
OA /. (id MA) is Morphism of OA . MA,OA . MA
(OA /. (id MA)) * (OA /. MB) is Morphism of OA . AB,OA . MA
(id MA) * MB is Morphism of AB,MA
OA /. ((id MA) * MB) is Morphism of OA . AB,OA . MA
id AB is Morphism of AB,AB
MB * (id AB) is Morphism of AB,MA
OA /. (MB * (id AB)) is Morphism of OA . AB,OA . MA
OA /. (id AB) is Morphism of OA . AB,OA . AB
(OA /. MB) * (OA /. (id AB)) is Morphism of OA . AB,OA . MA
id (OA . AB) is Morphism of OA . AB,OA . AB
(OA /. MB) * (id (OA . AB)) is Morphism of OA . AB,OA . MA
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of A is non empty set
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
(A,B,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MA)
MB is Element of the carrier of A
OB is Element of the carrier of A
Hom (MB,OB) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = OB ) } is set
MA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj MA) . MB is Element of the carrier of B
MA . OB is Element of the carrier of B
(Obj MA) . OB is Element of the carrier of B
MB is Morphism of MB,OB
MA /. MB is Morphism of MA . MB,MA . OB
(A,B,MA,MA,(A,B,MA),OB) is Morphism of MA . OB,MA . OB
(A,B,MA,MA,(A,B,MA),OB) * (MA /. MB) is Morphism of MA . MB,MA . OB
(A,B,MA,MA,(A,B,MA),MB) is Morphism of MA . MB,MA . MB
(MA /. MB) * (A,B,MA,MA,(A,B,MA),MB) is Morphism of MA . MB,MA . OB
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MA)
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
AB is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
MA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
MB is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,AB)
OB is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,AB,MA)
(B,A,OA,AB,MA,MB,OB) is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,MA)
MB is Element of the carrier of B
MA is Element of the carrier of B
Hom (MB,MA) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = MB & cod b₁ = MA ) } is set
OA . MB is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . MB is Element of the carrier of A
OA . MA is Element of the carrier of A
(Obj OA) . MA is Element of the carrier of A
MA . MA is Element of the carrier of A
Obj MA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
(Obj MA) . MA is Element of the carrier of A
(B,A,OA,MA,(B,A,OA,AB,MA,MB,OB),MA) is Morphism of OA . MA,MA . MA
MA . MB is Element of the carrier of A
(Obj MA) . MB is Element of the carrier of A
(B,A,OA,MA,(B,A,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MB
AB . MA is Element of the carrier of A
Obj AB is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
(Obj AB) . MA is Element of the carrier of A
Hom ((OA . MA),(AB . MA)) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = OA . MA & cod b₁ = AB . MA ) } is set
AB . MB is Element of the carrier of A
(Obj AB) . MB is Element of the carrier of A
Hom ((OA . MB),(AB . MB)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = OA . MB & cod b₁ = AB . MB ) } is set
Hom ((AB . MA),(MA . MA)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = AB . MA & cod b₁ = MA . MA ) } is set
Hom ((AB . MB),(MA . MB)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = AB . MB & cod b₁ = MA . MB ) } is set
Hom ((OA . MB),(OA . MA)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = OA . MB & cod b₁ = OA . MA ) } is set
a is Morphism of MB,MA
OA /. a is Morphism of OA . MB,OA . MA
(B,A,OA,MA,(B,A,OA,AB,MA,MB,OB),MA) * (OA /. a) is Morphism of OA . MB,MA . MA
MA /. a is Morphism of MA . MB,MA . MA
(MA /. a) * (B,A,OA,MA,(B,A,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MA
Hom ((MA . MB),(MA . MA)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MA . MB & cod b₁ = MA . MA ) } is set
Hom ((AB . MB),(AB . MA)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = AB . MB & cod b₁ = AB . MA ) } is set
(B,A,OA,AB,MB,MA) is Morphism of OA . MA,AB . MA
(B,A,AB,MA,OB,MA) is Morphism of AB . MA,MA . MA
(B,A,AB,MA,OB,MA) * (B,A,OA,AB,MB,MA) is Morphism of OA . MA,MA . MA
((B,A,AB,MA,OB,MA) * (B,A,OA,AB,MB,MA)) * (OA /. a) is Morphism of OA . MB,MA . MA
(B,A,OA,AB,MB,MA) * (OA /. a) is Morphism of OA . MB,AB . MA
(B,A,AB,MA,OB,MA) * ((B,A,OA,AB,MB,MA) * (OA /. a)) is Morphism of OA . MB,MA . MA
(B,A,OA,AB,MB,MB) is Morphism of OA . MB,AB . MB
AB /. a is Morphism of AB . MB,AB . MA
(AB /. a) * (B,A,OA,AB,MB,MB) is Morphism of OA . MB,AB . MA
(B,A,AB,MA,OB,MA) * ((AB /. a) * (B,A,OA,AB,MB,MB)) is Morphism of OA . MB,MA . MA
(B,A,AB,MA,OB,MA) * (AB /. a) is Morphism of AB . MB,MA . MA
((B,A,AB,MA,OB,MA) * (AB /. a)) * (B,A,OA,AB,MB,MB) is Morphism of OA . MB,MA . MA
(B,A,AB,MA,OB,MB) is Morphism of AB . MB,MA . MB
(MA /. a) * (B,A,AB,MA,OB,MB) is Morphism of AB . MB,MA . MA
((MA /. a) * (B,A,AB,MA,OB,MB)) * (B,A,OA,AB,MB,MB) is Morphism of OA . MB,MA . MA
(B,A,AB,MA,OB,MB) * (B,A,OA,AB,MB,MB) is Morphism of OA . MB,MA . MB
(MA /. a) * ((B,A,AB,MA,OB,MB) * (B,A,OA,AB,MB,MB)) is Morphism of OA . MB,MA . MA
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MA)
(A,B,OA,AB,MA,MB,OB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
MB is Element of the carrier of A
MA is Element of the carrier of A
Hom (MB,MA) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = MA ) } is set
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
OA . MA is Element of the carrier of B
(Obj OA) . MA is Element of the carrier of B
MA . MA is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . MA is Element of the carrier of B
a is Morphism of MB,MA
OA /. a is Morphism of OA . MB,OA . MA
(A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MA) is Morphism of OA . MA,MA . MA
(A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MA) * (OA /. a) is Morphism of OA . MB,MA . MA
MA . MB is Element of the carrier of B
(Obj MA) . MB is Element of the carrier of B
(A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MB
MA /. a is Morphism of MA . MB,MA . MA
(MA /. a) * (A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MA
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
(A,B,OA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,OA)
the carrier of A is non empty set
AB is Element of the carrier of A
MA is Element of the carrier of A
Hom (AB,MA) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = AB & cod b₁ = MA ) } is set
OA . AB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . AB is Element of the carrier of B
OA . MA is Element of the carrier of B
(Obj OA) . MA is Element of the carrier of B
MB is Morphism of AB,MA
OA /. MB is Morphism of OA . AB,OA . MA
(A,B,OA,OA,(A,B,OA),MA) is Morphism of OA . MA,OA . MA
(A,B,OA,OA,(A,B,OA),MA) * (OA /. MB) is Morphism of OA . AB,OA . MA
(A,B,OA,OA,(A,B,OA),AB) is Morphism of OA . AB,OA . AB
(OA /. MB) * (A,B,OA,OA,(A,B,OA),AB) is Morphism of OA . AB,OA . MA
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MA)
(A,B,OA,AB,MA,MB,OB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
MB is Element of the carrier of A
MA is Element of the carrier of A
Hom (MB,MA) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = MA ) } is set
AB . MB is Element of the carrier of B
the carrier of B is non empty set
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj AB) . MB is Element of the carrier of B
AB . MA is Element of the carrier of B
(Obj AB) . MA is Element of the carrier of B
MA . MA is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . MA is Element of the carrier of B
a is Morphism of MB,MA
AB /. a is Morphism of AB . MB,AB . MA
(A,B,AB,MA,OB,MA) is Morphism of AB . MA,MA . MA
(A,B,AB,MA,OB,MA) * (AB /. a) is Morphism of AB . MB,MA . MA
MA . MB is Element of the carrier of B
(Obj MA) . MB is Element of the carrier of B
(A,B,AB,MA,OB,MB) is Morphism of AB . MB,MA . MB
MA /. a is Morphism of MA . MB,MA . MA
(MA /. a) * (A,B,AB,MA,OB,MB) is Morphism of AB . MB,MA . MA
MB is Element of the carrier of A
MA is Element of the carrier of A
Hom (MB,MA) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = MA ) } is set
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
OA . MA is Element of the carrier of B
(Obj OA) . MA is Element of the carrier of B
AB . MA is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MA is Element of the carrier of B
a is Morphism of MB,MA
OA /. a is Morphism of OA . MB,OA . MA
(A,B,OA,AB,MB,MA) is Morphism of OA . MA,AB . MA
(A,B,OA,AB,MB,MA) * (OA /. a) is Morphism of OA . MB,AB . MA
AB . MB is Element of the carrier of B
(Obj AB) . MB is Element of the carrier of B
(A,B,OA,AB,MB,MB) is Morphism of OA . MB,AB . MB
AB /. a is Morphism of AB . MB,AB . MA
(AB /. a) * (A,B,OA,AB,MB,MB) is Morphism of OA . MB,AB . MA
MB is Element of the carrier of A
MA is Element of the carrier of A
Hom (MB,MA) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = MA ) } is set
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
OA . MA is Element of the carrier of B
(Obj OA) . MA is Element of the carrier of B
MA . MA is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . MA is Element of the carrier of B
a is Morphism of MB,MA
OA /. a is Morphism of OA . MB,OA . MA
(A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MA) is Morphism of OA . MA,MA . MA
(A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MA) * (OA /. a) is Morphism of OA . MB,MA . MA
MA . MB is Element of the carrier of B
(Obj MA) . MB is Element of the carrier of B
(A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MB
MA /. a is Morphism of MA . MB,MA . MA
(MA /. a) * (A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MA
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
(A,B,OA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,OA)
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
(A,B,AB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,AB)
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,AB,AB,MA,(A,B,AB)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,OA,AB,(A,B,OA),MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,AB,AB,MA,(A,B,AB)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,OA,AB,(A,B,OA),MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
AB is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
MA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
MB is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,AB)
OB is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,AB,MA)
(B,A,OA,AB,MA,MB,OB) is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,MA)
MB is Element of the carrier of B
(B,A,OA,MA,(B,A,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MB
OA . MB is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . MB is Element of the carrier of A
MA . MB is Element of the carrier of A
Obj MA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
(Obj MA) . MB is Element of the carrier of A
AB . MB is Element of the carrier of A
Obj AB is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
(Obj AB) . MB is Element of the carrier of A
(B,A,OA,AB,MB,MB) is Morphism of OA . MB,AB . MB
(B,A,AB,MA,OB,MB) is Morphism of AB . MB,MA . MB
(B,A,AB,MA,OB,MB) * (B,A,OA,AB,MB,MB) is Morphism of OA . MB,MA . MB
MA is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,AB)
a is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,AB,MA)
(B,A,OA,AB,MA,MA,a) is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,MA)
(B,A,OA,MA,(B,A,OA,AB,MA,MA,a),MB) is Morphism of OA . MB,MA . MB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MA)
(A,B,OA,AB,MA,OB,MB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MB)
(A,B,AB,MA,MB,MB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MB)
(A,B,OA,AB,MB,OB,(A,B,AB,MA,MB,MB,MA)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MB)
(A,B,OA,MA,MB,(A,B,OA,AB,MA,OB,MB),MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MB)
(A,B,OA,AB,MB,OB,(A,B,AB,MA,MB,MB,MA)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MB)
(A,B,AB,MA,MB,MB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MB)
(A,B,OA,AB,MB,OB,(A,B,AB,MA,MB,MB,MA)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MB)
(A,B,OA,AB,MA,OB,MB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
(A,B,OA,MA,MB,(A,B,OA,AB,MA,OB,MB),MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MB)
(A,B,OA,MA,MB,(A,B,OA,AB,MA,OB,MB),MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MB)
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of A is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of A is non empty set
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
(A,B,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MA)
MB is Element of the carrier of A
MA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj MA) . MB is Element of the carrier of B
(A,B,MA,MA,(A,B,MA),MB) is Morphism of MA . MB,MA . MB
id (MA . MB) is Morphism of MA . MB,MA . MB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
MB is Element of the carrier of A
AB . MB is Element of the carrier of B
the carrier of B is non empty set
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj AB) . MB is Element of the carrier of B
OA . MB is Element of the carrier of B
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj OA) . MB is Element of the carrier of B
Hom ((AB . MB),(OA . MB)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB . MB & cod b₁ = OA . MB ) } is set
(A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
Hom ((OA . MB),(AB . MB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MB & cod b₁ = AB . MB ) } is set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
[: the carrier of A, the carrier' of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier' of B:] is non empty set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier' of B:]
OB is Element of the carrier of A
MB . OB is Element of the carrier' of B
OA . OB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . OB is Element of the carrier of B
AB . OB is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . OB is Element of the carrier of B
(A,B,OA,AB,MA,OB) is Morphism of OA . OB,AB . OB
(A,B,OA,AB,MA,OB) " is Morphism of AB . OB,OA . OB
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
MB is Element of the carrier of A
(A,B,AB,OA,OB,MB) is Morphism of AB . MB,OA . MB
AB . MB is Element of the carrier of B
(Obj AB) . MB is Element of the carrier of B
OA . MB is Element of the carrier of B
(Obj OA) . MB is Element of the carrier of B
(A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
(A,B,OA,AB,MA,MB) " is Morphism of AB . MB,OA . MB
OB . MB is Element of the carrier' of B
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
MB is Element of the carrier of A
(A,B,AB,OA,MB,MB) is Morphism of AB . MB,OA . MB
AB . MB is Element of the carrier of B
the carrier of B is non empty set
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj AB) . MB is Element of the carrier of B
OA . MB is Element of the carrier of B
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj OA) . MB is Element of the carrier of B
(A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
(A,B,OA,AB,MA,MB) " is Morphism of AB . MB,OA . MB
(A,B,AB,OA,OB,MB) is Morphism of AB . MB,OA . MB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of A is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
MB is Element of the carrier of A
OB is Element of the carrier of A
Hom (MB,OB) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = OB ) } is set
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
OA . OB is Element of the carrier of B
(Obj OA) . OB is Element of the carrier of B
Hom ((OA . MB),(OA . OB)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MB & cod b₁ = OA . OB ) } is set
AB . MB is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MB is Element of the carrier of B
AB . OB is Element of the carrier of B
(Obj AB) . OB is Element of the carrier of B
Hom ((AB . MB),(AB . OB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB . MB & cod b₁ = AB . OB ) } is set
Hom ((OA . OB),(AB . OB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . OB & cod b₁ = AB . OB ) } is set
(A,B,OA,AB,MA,OB) is Morphism of OA . OB,AB . OB
Hom ((AB . OB),(OA . OB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB . OB & cod b₁ = OA . OB ) } is set
Hom ((OA . MB),(AB . MB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = OA . MB & cod b₁ = AB . MB ) } is set
(A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
MB is Morphism of MB,OB
AB /. MB is Morphism of AB . MB,AB . OB
(AB /. MB) * (A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . OB
OA /. MB is Morphism of OA . MB,OA . OB
(A,B,OA,AB,MA,OB) * (OA /. MB) is Morphism of OA . MB,AB . OB
(A,B,OA,AB,MA,OB) " is Morphism of AB . OB,OA . OB
((A,B,OA,AB,MA,OB) ") * (AB /. MB) is Morphism of AB . MB,OA . OB
(((A,B,OA,AB,MA,OB) ") * (AB /. MB)) * (A,B,OA,AB,MA,MB) is Morphism of OA . MB,OA . OB
((A,B,OA,AB,MA,OB) ") * ((A,B,OA,AB,MA,OB) * (OA /. MB)) is Morphism of OA . MB,OA . OB
((A,B,OA,AB,MA,OB) ") * (A,B,OA,AB,MA,OB) is Morphism of OA . OB,OA . OB
(((A,B,OA,AB,MA,OB) ") * (A,B,OA,AB,MA,OB)) * (OA /. MB) is Morphism of OA . MB,OA . OB
id (OA . OB) is Morphism of OA . OB,OA . OB
(id (OA . OB)) * (OA /. MB) is Morphism of OA . MB,OA . OB
Hom ((AB . MB),(OA . MB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB . MB & cod b₁ = OA . MB ) } is set
Hom ((AB . MB),(OA . OB)) is Element of bool the carrier' of B
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = AB . MB & cod b₁ = OA . OB ) } is set
id (AB . MB) is Morphism of AB . MB,AB . MB
(((A,B,OA,AB,MA,OB) ") * (AB /. MB)) * (id (AB . MB)) is Morphism of AB . MB,OA . OB
(A,B,OA,AB,MA,MB) " is Morphism of AB . MB,OA . MB
(A,B,OA,AB,MA,MB) * ((A,B,OA,AB,MA,MB) ") is Morphism of AB . MB,AB . MB
(((A,B,OA,AB,MA,OB) ") * (AB /. MB)) * ((A,B,OA,AB,MA,MB) * ((A,B,OA,AB,MA,MB) ")) is Morphism of AB . MB,OA . OB
(OA /. MB) * ((A,B,OA,AB,MA,MB) ") is Morphism of AB . MB,OA . OB
(A,B,OA,AB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
(A,B,AB,OA,(A,B,OA,AB,MA),OB) is Morphism of AB . OB,OA . OB
(A,B,AB,OA,(A,B,OA,AB,MA),OB) * (AB /. MB) is Morphism of AB . MB,OA . OB
(A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . MB
(OA /. MB) * (A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . OB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,AB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
MB is Element of the carrier of A
OB is Element of the carrier of A
Hom (MB,OB) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = OB ) } is set
AB . MB is Element of the carrier of B
the carrier of B is non empty set
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj AB) . MB is Element of the carrier of B
AB . OB is Element of the carrier of B
(Obj AB) . OB is Element of the carrier of B
OA . OB is Element of the carrier of B
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj OA) . OB is Element of the carrier of B
MB is Morphism of MB,OB
AB /. MB is Morphism of AB . MB,AB . OB
(A,B,AB,OA,(A,B,OA,AB,MA),OB) is Morphism of AB . OB,OA . OB
(A,B,AB,OA,(A,B,OA,AB,MA),OB) * (AB /. MB) is Morphism of AB . MB,OA . OB
OA . MB is Element of the carrier of B
(Obj OA) . MB is Element of the carrier of B
(A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . MB
OA /. MB is Morphism of OA . MB,OA . OB
(OA /. MB) * (A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . OB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of A is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,AB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
MB is Element of the carrier of A
OB is Element of the carrier of A
Hom (MB,OB) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = OB ) } is set
AB . MB is Element of the carrier of B
the carrier of B is non empty set
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj AB) . MB is Element of the carrier of B
AB . OB is Element of the carrier of B
(Obj AB) . OB is Element of the carrier of B
OA . OB is Element of the carrier of B
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj OA) . OB is Element of the carrier of B
MB is Morphism of MB,OB
AB /. MB is Morphism of AB . MB,AB . OB
(A,B,AB,OA,(A,B,OA,AB,MA),OB) is Morphism of AB . OB,OA . OB
(A,B,AB,OA,(A,B,OA,AB,MA),OB) * (AB /. MB) is Morphism of AB . MB,OA . OB
OA . MB is Element of the carrier of B
(Obj OA) . MB is Element of the carrier of B
(A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . MB
OA /. MB is Morphism of OA . MB,OA . OB
(OA /. MB) * (A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . OB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,AB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
MB is Element of the carrier of A
(A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . MB
AB . MB is Element of the carrier of B
the carrier of B is non empty set
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj AB) . MB is Element of the carrier of B
OA . MB is Element of the carrier of B
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj OA) . MB is Element of the carrier of B
(A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
(A,B,OA,AB,MA,MB) " is Morphism of AB . MB,OA . MB
(A,B,OA,AB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
(A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . MB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
(A,B,OA,AB,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,OA)
MB is Element of the carrier of A
AB . MB is Element of the carrier of B
the carrier of B is non empty set
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj AB) . MB is Element of the carrier of B
OA . MB is Element of the carrier of B
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj OA) . MB is Element of the carrier of B
(A,B,AB,OA,(A,B,OA,AB,MA),MB) is Morphism of AB . MB,OA . MB
(A,B,OA,AB,MA,MB) is Morphism of OA . MB,AB . MB
(A,B,OA,AB,MA,MB) " is Morphism of AB . MB,OA . MB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MA)
(A,B,OA,AB,MA,MB,OB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
MB is Element of the carrier of A
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
MA . MB is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . MB is Element of the carrier of B
(A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MB
AB . MB is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MB is Element of the carrier of B
(A,B,AB,MA,OB,MB) is Morphism of AB . MB,MA . MB
(A,B,OA,AB,MB,MB) is Morphism of OA . MB,AB . MB
(A,B,AB,MA,OB,MB) * (A,B,OA,AB,MB,MB) is Morphism of OA . MB,MA . MB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
the carrier of A is non empty set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
(A,B,OA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,OA)
AB is Element of the carrier of A
OA . AB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . AB is Element of the carrier of B
(A,B,OA,OA,(A,B,OA),AB) is Morphism of OA . AB,OA . AB
id (OA . AB) is Morphism of OA . AB,OA . AB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MA)
(A,B,OA,AB,MA,MB,OB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
MB is Element of the carrier of A
OA . MB is Element of the carrier of B
the carrier of B is non empty set
Obj OA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
[: the carrier of A, the carrier of B:] is Relation-like non empty set
bool [: the carrier of A, the carrier of B:] is non empty set
(Obj OA) . MB is Element of the carrier of B
MA . MB is Element of the carrier of B
Obj MA is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj MA) . MB is Element of the carrier of B
(A,B,OA,MA,(A,B,OA,AB,MA,MB,OB),MB) is Morphism of OA . MB,MA . MB
AB . MB is Element of the carrier of B
Obj AB is Relation-like the carrier of A -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier of A, the carrier of B:]
(Obj AB) . MB is Element of the carrier of B
(A,B,AB,MA,OB,MB) is Morphism of AB . MB,MA . MB
(A,B,OA,AB,MB,MB) is Morphism of OA . MB,AB . MB
(A,B,AB,MA,OB,MB) * (A,B,OA,AB,MB,MB) is Morphism of OA . MB,MA . MB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of A is non empty set
the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B] is non empty V15() set
{ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B} is non empty finite set
{ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B} is non empty trivial finite set
{{ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B},{ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B}} is non empty finite V35() set
(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)
[[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B],(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)] is non empty V15() set
{[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B],(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)} is non empty finite set
{[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B]} is Relation-like non empty trivial finite set
{{[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B],(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)},{[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B]}} is non empty finite V35() set
{[[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B],(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)]} is Relation-like non empty trivial finite set
AB is set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier' of B is non empty set
the carrier of A is non empty set
the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
Funct (A,B) is non empty FUNCTOR-DOMAIN of A,B
[:(Funct (A,B)),(Funct (A,B)):] is Relation-like non empty set
Funcs ( the carrier of A, the carrier' of B) is non empty FUNCTION_DOMAIN of the carrier of A, the carrier' of B
[:[:(Funct (A,B)),(Funct (A,B)):],(Funcs ( the carrier of A, the carrier' of B)):] is Relation-like non empty set
AB is set
[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B] is non empty V15() set
{ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B} is non empty finite set
{ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B} is non empty trivial finite set
{{ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B},{ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B}} is non empty finite V35() set
(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)
[[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B],(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)] is non empty V15() set
{[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B],(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)} is non empty finite set
{[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B]} is Relation-like non empty trivial finite set
{{[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B],(A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B)},{[ the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B, the Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B]}} is non empty finite V35() set
MA is non empty set
MB is set
MB is non empty (A,B)
OB is set
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,MA] is non empty V15() set
{MB,MA} is non empty finite set
{MB} is non empty trivial finite set
{{MB,MA},{MB}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,MA)
[[MB,MA],a] is non empty V15() set
{[MB,MA],a} is non empty finite set
{[MB,MA]} is Relation-like non empty trivial finite set
{{[MB,MA],a},{[MB,MA]}} is non empty finite V35() set
OA is non empty (A,B)
AB is non empty (A,B)
MA is set
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,OB] is non empty V15() set
{MB,OB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,OB},{MB}} is non empty finite V35() set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,OB)
[[MB,OB],MB] is non empty V15() set
{[MB,OB],MB} is non empty finite set
{[MB,OB]} is Relation-like non empty trivial finite set
{{[MB,OB],MB},{[MB,OB]}} is non empty finite V35() set
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,OB] is non empty V15() set
{MB,OB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,OB},{MB}} is non empty finite V35() set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,OB)
[[MB,OB],MB] is non empty V15() set
{[MB,OB],MB} is non empty finite set
{[MB,OB]} is Relation-like non empty trivial finite set
{{[MB,OB],MB},{[MB,OB]}} is non empty finite V35() set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
(A,B) is non empty (A,B)
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[OA,AB] is non empty V15() set
{OA,AB} is non empty finite set
{OA} is non empty trivial finite set
{{OA,AB},{OA}} is non empty finite V35() set
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
[[OA,AB],MA] is non empty V15() set
{[OA,AB],MA} is non empty finite set
{[OA,AB]} is Relation-like non empty trivial finite set
{{[OA,AB],MA},{[OA,AB]}} is non empty finite V35() set
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,OB] is non empty V15() set
{MB,OB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,OB},{MB}} is non empty finite V35() set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,OB)
[[MB,OB],MB] is non empty V15() set
{[MB,OB],MB} is non empty finite set
{[MB,OB]} is Relation-like non empty trivial finite set
{{[MB,OB],MB},{[MB,OB]}} is non empty finite V35() set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
Funct (A,B) is non empty FUNCTOR-DOMAIN of A,B
(A,B) is non empty (A,B)
the carrier' of A is non empty set
the carrier' of B is non empty set
the carrier of A is non empty set
OA is set
AB is set
MA is set
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[OB,MB] is non empty V15() set
{OB,MB} is non empty finite set
{OB} is non empty trivial finite set
{{OB,MB},{OB}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OB,MB)
[[OB,MB],a] is non empty V15() set
{[OB,MB],a} is non empty finite set
{[OB,MB]} is Relation-like non empty trivial finite set
{{[OB,MB],a},{[OB,MB]}} is non empty finite V35() set
[MB,MA] is non empty V15() set
{MB,MA} is non empty finite set
{MB} is non empty trivial finite set
{{MB,MA},{MB}} is non empty finite V35() set
b is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,MA)
[[MB,MA],b] is non empty V15() set
{[MB,MA],b} is non empty finite set
{[MB,MA]} is Relation-like non empty trivial finite set
{{[MB,MA],b},{[MB,MA]}} is non empty finite V35() set
[OB,MA] is non empty V15() set
{OB,MA} is non empty finite set
{{OB,MA},{OB}} is non empty finite V35() set
(A,B,OB,MB,MA,a,b) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OB,MA)
[[OB,MA],(A,B,OB,MB,MA,a,b)] is non empty V15() set
{[OB,MA],(A,B,OB,MB,MA,a,b)} is non empty finite set
{[OB,MA]} is Relation-like non empty trivial finite set
{{[OB,MA],(A,B,OB,MB,MA,a,b)},{[OB,MA]}} is non empty finite V35() set
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[OB,MB] is non empty V15() set
{OB,MB} is non empty finite set
{OB} is non empty trivial finite set
{{OB,MB},{OB}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OB,MB)
[[OB,MB],a] is non empty V15() set
{[OB,MB],a} is non empty finite set
{[OB,MB]} is Relation-like non empty trivial finite set
{{[OB,MB],a},{[OB,MB]}} is non empty finite V35() set
[MB,MA] is non empty V15() set
{MB,MA} is non empty finite set
{MB} is non empty trivial finite set
{{MB,MA},{MB}} is non empty finite V35() set
b is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,MA)
[[MB,MA],b] is non empty V15() set
{[MB,MA],b} is non empty finite set
{[MB,MA]} is Relation-like non empty trivial finite set
{{[MB,MA],b},{[MB,MA]}} is non empty finite V35() set
[OB,MA] is non empty V15() set
{OB,MA} is non empty finite set
{{OB,MA},{OB}} is non empty finite V35() set
(A,B,OB,MB,MA,a,b) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OB,MA)
[[OB,MA],(A,B,OB,MB,MA,a,b)] is non empty V15() set
{[OB,MA],(A,B,OB,MB,MA,a,b)} is non empty finite set
{[OB,MA]} is Relation-like non empty trivial finite set
{{[OB,MA],(A,B,OB,MB,MA,a,b)},{[OB,MA]}} is non empty finite V35() set
MB is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],t19] is non empty V15() set
{[a,a],t19} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],t19},{[a,a]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],F1] is non empty V15() set
{[a,t19],F1} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],F1},{[a,t19]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,a,a,t19,t19,F1) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,a,t19,t19,F1)] is non empty V15() set
{[a,t19],(A,B,a,a,t19,t19,F1)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,a,t19,t19,F1)},{[a,t19]}} is non empty finite V35() set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],t19] is non empty V15() set
{[a,a],t19} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],t19},{[a,a]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],F1] is non empty V15() set
{[a,t19],F1} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],F1},{[a,t19]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,a,a,t19,t19,F1) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,a,t19,t19,F1)] is non empty V15() set
{[a,t19],(A,B,a,a,t19,t19,F1)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,a,t19,t19,F1)},{[a,t19]}} is non empty finite V35() set
OA is set
AB is set
MA is set
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,OB] is non empty V15() set
{MB,OB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,OB},{MB}} is non empty finite V35() set
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,OB)
[[MB,OB],MA] is non empty V15() set
{[MB,OB],MA} is non empty finite set
{[MB,OB]} is Relation-like non empty trivial finite set
{{[MB,OB],MA},{[MB,OB]}} is non empty finite V35() set
[OB,MB] is non empty V15() set
{OB,MB} is non empty finite set
{OB} is non empty trivial finite set
{{OB,MB},{OB}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OB,MB)
[[OB,MB],a] is non empty V15() set
{[OB,MB],a} is non empty finite set
{[OB,MB]} is Relation-like non empty trivial finite set
{{[OB,MB],a},{[OB,MB]}} is non empty finite V35() set
[MB,MB] is non empty V15() set
{MB,MB} is non empty finite set
{{MB,MB},{MB}} is non empty finite V35() set
(A,B,MB,OB,MB,MA,a) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,MB)
[[MB,MB],(A,B,MB,OB,MB,MA,a)] is non empty V15() set
{[MB,MB],(A,B,MB,OB,MB,MA,a)} is non empty finite set
{[MB,MB]} is Relation-like non empty trivial finite set
{{[MB,MB],(A,B,MB,OB,MB,MA,a)},{[MB,MB]}} is non empty finite V35() set
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,OB] is non empty V15() set
{MB,OB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,OB},{MB}} is non empty finite V35() set
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,OB)
[[MB,OB],MA] is non empty V15() set
{[MB,OB],MA} is non empty finite set
{[MB,OB]} is Relation-like non empty trivial finite set
{{[MB,OB],MA},{[MB,OB]}} is non empty finite V35() set
[OB,MB] is non empty V15() set
{OB,MB} is non empty finite set
{OB} is non empty trivial finite set
{{OB,MB},{OB}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OB,MB)
[[OB,MB],a] is non empty V15() set
{[OB,MB],a} is non empty finite set
{[OB,MB]} is Relation-like non empty trivial finite set
{{[OB,MB],a},{[OB,MB]}} is non empty finite V35() set
[MB,MB] is non empty V15() set
{MB,MB} is non empty finite set
{{MB,MB},{MB}} is non empty finite V35() set
(A,B,MB,OB,MB,MA,a) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,MB)
[[MB,MB],(A,B,MB,OB,MB,MA,a)] is non empty V15() set
{[MB,MB],(A,B,MB,OB,MB,MA,a)} is non empty finite set
{[MB,MB]} is Relation-like non empty trivial finite set
{{[MB,MB],(A,B,MB,OB,MB,MA,a)},{[MB,MB]}} is non empty finite V35() set
[:(A,B),(A,B):] is Relation-like non empty set
[:[:(A,B),(A,B):],(A,B):] is Relation-like non empty set
bool [:[:(A,B),(A,B):],(A,B):] is non empty set
OA is Relation-like [:(A,B),(A,B):] -defined (A,B) -valued Function-like Element of bool [:[:(A,B),(A,B):],(A,B):]
proj1 OA is Relation-like set
AB is Element of (A,B)
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MB)
[[MA,MB],OB] is non empty V15() set
{[MA,MB],OB} is non empty finite set
{[MA,MB]} is Relation-like non empty trivial finite set
{{[MA,MB],OB},{[MA,MB]}} is non empty finite V35() set
AB `1 is set
(AB `1) `1 is set
[MA,MB] `1 is set
[:(A,B),(Funct (A,B)):] is Relation-like non empty set
bool [:(A,B),(Funct (A,B)):] is non empty set
AB is Relation-like (A,B) -defined Funct (A,B) -valued Function-like quasi_total Element of bool [:(A,B),(Funct (A,B)):]
MA is Element of (A,B)
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,OB] is non empty V15() set
{MB,OB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,OB},{MB}} is non empty finite V35() set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,OB)
[[MB,OB],MB] is non empty V15() set
{[MB,OB],MB} is non empty finite set
{[MB,OB]} is Relation-like non empty trivial finite set
{{[MB,OB],MB},{[MB,OB]}} is non empty finite V35() set
MA `1 is set
(MA `1) `2 is set
[MB,OB] `2 is set
MA is Relation-like (A,B) -defined Funct (A,B) -valued Function-like quasi_total Element of bool [:(A,B),(Funct (A,B)):]
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Element of Funct (A,B)
[MB,MB] is non empty V15() set
{MB,MB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,MB},{MB}} is non empty finite V35() set
(A,B,MB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,MB)
[[MB,MB],(A,B,MB)] is non empty V15() set
{[MB,MB],(A,B,MB)} is non empty finite set
{[MB,MB]} is Relation-like non empty trivial finite set
{{[MB,MB],(A,B,MB)},{[MB,MB]}} is non empty finite V35() set
[:(Funct (A,B)),(A,B):] is Relation-like non empty set
bool [:(Funct (A,B)),(A,B):] is non empty set
MB is Relation-like Funct (A,B) -defined (A,B) -valued Function-like quasi_total Element of bool [:(Funct (A,B)),(A,B):]
CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty non void V55() strict CatStr
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,MA] is non empty V15() set
{MB,MA} is non empty finite set
{MB} is non empty trivial finite set
{{MB,MA},{MB}} is non empty finite V35() set
b is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,MA)
[[MB,MA],b] is non empty V15() set
{[MB,MA],b} is non empty finite set
{[MB,MA]} is Relation-like non empty trivial finite set
{{[MB,MA],b},{[MB,MA]}} is non empty finite V35() set
[MA,a] is non empty V15() set
{MA,a} is non empty finite set
{MA} is non empty trivial finite set
{{MA,a},{MA}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,a)
[[MA,a],a] is non empty V15() set
{[MA,a],a} is non empty finite set
{[MA,a]} is Relation-like non empty trivial finite set
{{[MA,a],a},{[MA,a]}} is non empty finite V35() set
[MB,a] is non empty V15() set
{MB,a} is non empty finite set
{{MB,a},{MB}} is non empty finite V35() set
(A,B,MB,MA,a,b,a) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,a)
[[MB,a],(A,B,MB,MA,a,b,a)] is non empty V15() set
{[MB,a],(A,B,MB,MA,a,b,a)} is non empty finite set
{[MB,a]} is Relation-like non empty trivial finite set
{{[MB,a],(A,B,MB,MA,a,b,a)},{[MB,a]}} is non empty finite V35() set
OA . ([[MA,a],a],[[MB,MA],b]) is set
[[[MA,a],a],[[MB,MA],b]] is non empty V15() set
{[[MA,a],a],[[MB,MA],b]} is Relation-like non empty finite set
{[[MA,a],a]} is Relation-like non empty trivial finite set
{{[[MA,a],a],[[MB,MA],b]},{[[MA,a],a]}} is non empty finite V35() set
OA . [[[MA,a],a],[[MB,MA],b]] is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],F1] is non empty V15() set
{[a,t19],F1} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],F1},{[a,t19]}} is non empty finite V35() set
[t19,t19] is non empty V15() set
{t19,t19} is non empty finite set
{t19} is non empty trivial finite set
{{t19,t19},{t19}} is non empty finite V35() set
F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,t19)
[[t19,t19],F2] is non empty V15() set
{[t19,t19],F2} is non empty finite set
{[t19,t19]} is Relation-like non empty trivial finite set
{{[t19,t19],F2},{[t19,t19]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,a,t19,t19,F1,F2) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,t19,t19,F1,F2)] is non empty V15() set
{[a,t19],(A,B,a,t19,t19,F1,F2)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,t19,t19,F1,F2)},{[a,t19]}} is non empty finite V35() set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],F1] is non empty V15() set
{[a,t19],F1} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],F1},{[a,t19]}} is non empty finite V35() set
[t19,t19] is non empty V15() set
{t19,t19} is non empty finite set
{t19} is non empty trivial finite set
{{t19,t19},{t19}} is non empty finite V35() set
F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,t19)
[[t19,t19],F2] is non empty V15() set
{[t19,t19],F2} is non empty finite set
{[t19,t19]} is Relation-like non empty trivial finite set
{{[t19,t19],F2},{[t19,t19]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,a,t19,t19,F1,F2) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,t19,t19,F1,F2)] is non empty V15() set
{[a,t19],(A,B,a,t19,t19,F1,F2)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,t19,t19,F1,F2)},{[a,t19]}} is non empty finite V35() set
the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
MA is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MB is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] -defined the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
[:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
proj1 the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like set
dom MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
b is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,b)
[[a,b],a] is non empty V15() set
{[a,b],a} is non empty finite set
{[a,b]} is Relation-like non empty trivial finite set
{{[a,b],a},{[a,b]}} is non empty finite V35() set
OA . (MA,MB) is set
OA . [MA,MB] is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],F1] is non empty V15() set
{[a,t19],F1} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],F1},{[a,t19]}} is non empty finite V35() set
[t19,t19] is non empty V15() set
{t19,t19} is non empty finite set
{t19} is non empty trivial finite set
{{t19,t19},{t19}} is non empty finite V35() set
F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,t19)
[[t19,t19],F2] is non empty V15() set
{[t19,t19],F2} is non empty finite set
{[t19,t19]} is Relation-like non empty trivial finite set
{{[t19,t19],F2},{[t19,t19]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,a,t19,t19,F1,F2) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,t19,t19,F1,F2)] is non empty V15() set
{[a,t19],(A,B,a,t19,t19,F1,F2)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,t19,t19,F1,F2)},{[a,t19]}} is non empty finite V35() set
MA `1 is set
(MA `1) `1 is set
[t19,t19] `1 is set
[a,t19] `2 is set
MB `1 is set
(MB `1) `2 is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],t19] is non empty V15() set
{[a,t19],t19} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],t19},{[a,t19]}} is non empty finite V35() set
[a,t19] `1 is set
MA `1 is set
(MA `1) `1 is set
MA . MB is set
MB `1 is set
(MB `1) `2 is set
[a,b] `2 is set
OA . [MA,MB] is set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,b,t19)
(A,B,a,b,t19,a,F1) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,b,t19,a,F1)] is non empty V15() set
{[a,t19],(A,B,a,b,t19,a,F1)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,b,t19,a,F1)},{[a,t19]}} is non empty finite V35() set
the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
MA is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MB is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MA (*) MB is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom (MA (*) MB) is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA (*) MB) is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod (MA (*) MB) is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA (*) MB) is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
b is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,b)
[[a,b],a] is non empty V15() set
{[a,b],a} is non empty finite set
{[a,b]} is Relation-like non empty trivial finite set
{{[a,b],a},{[a,b]}} is non empty finite V35() set
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
OA . (MA,MB) is set
OA . [MA,MB] is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],F1] is non empty V15() set
{[a,t19],F1} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],F1},{[a,t19]}} is non empty finite V35() set
[t19,t19] is non empty V15() set
{t19,t19} is non empty finite set
{t19} is non empty trivial finite set
{{t19,t19},{t19}} is non empty finite V35() set
F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,t19)
[[t19,t19],F2] is non empty V15() set
{[t19,t19],F2} is non empty finite set
{[t19,t19]} is Relation-like non empty trivial finite set
{{[t19,t19],F2},{[t19,t19]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,a,t19,t19,F1,F2) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,t19,t19,F1,F2)] is non empty V15() set
{[a,t19],(A,B,a,t19,t19,F1,F2)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,t19,t19,F1,F2)},{[a,t19]}} is non empty finite V35() set
t is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t,t1] is non empty V15() set
{t,t1} is non empty finite set
{t} is non empty trivial finite set
{{t,t1},{t}} is non empty finite V35() set
F19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t,t1)
[[t,t1],F19] is non empty V15() set
{[t,t1],F19} is non empty finite set
{[t,t1]} is Relation-like non empty trivial finite set
{{[t,t1],F19},{[t,t1]}} is non empty finite V35() set
F29 is Element of (A,B)
F29 `1 is set
(F29 `1) `1 is set
[a,t19] `1 is set
[[a,t19],F1] `1 is set
([[a,t19],F1] `1) `1 is set
(F29 `1) `2 is set
[a,t19] `2 is set
[[t19,t19],F2] `1 is set
([[t19,t19],F2] `1) `2 is set
the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] -defined the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
[:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
proj1 the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like set
MA is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MB is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
dom MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
b is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
a is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
a is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MA is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MA is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MB is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MA (*) MB is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
a (*) (MA (*) MB) is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
a (*) MA is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
(a (*) MA) (*) MB is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
a is Element of (A,B)
b is Element of (A,B)
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
OA . (a,b) is set
OA . [a,b] is set
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t19,t19] is non empty V15() set
{t19,t19} is non empty finite set
{t19} is non empty trivial finite set
{{t19,t19},{t19}} is non empty finite V35() set
F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,t19)
[[t19,t19],F2] is non empty V15() set
{[t19,t19],F2} is non empty finite set
{[t19,t19]} is Relation-like non empty trivial finite set
{{[t19,t19],F2},{[t19,t19]}} is non empty finite V35() set
[t19,F1] is non empty V15() set
{t19,F1} is non empty finite set
{t19} is non empty trivial finite set
{{t19,F1},{t19}} is non empty finite V35() set
t is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F1)
[[t19,F1],t] is non empty V15() set
{[t19,F1],t} is non empty finite set
{[t19,F1]} is Relation-like non empty trivial finite set
{{[t19,F1],t},{[t19,F1]}} is non empty finite V35() set
[t19,F1] is non empty V15() set
{t19,F1} is non empty finite set
{{t19,F1},{t19}} is non empty finite V35() set
(A,B,t19,t19,F1,F2,t) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F1)
[[t19,F1],(A,B,t19,t19,F1,F2,t)] is non empty V15() set
{[t19,F1],(A,B,t19,t19,F1,F2,t)} is non empty finite set
{[t19,F1]} is Relation-like non empty trivial finite set
{{[t19,F1],(A,B,t19,t19,F1,F2,t)},{[t19,F1]}} is non empty finite V35() set
a is Element of (A,B)
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
OA . (a,a) is set
OA . [a,a] is set
t1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F29 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t1,F19] is non empty V15() set
{t1,F19} is non empty finite set
{t1} is non empty trivial finite set
{{t1,F19},{t1}} is non empty finite V35() set
t9 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F19)
[[t1,F19],t9] is non empty V15() set
{[t1,F19],t9} is non empty finite set
{[t1,F19]} is Relation-like non empty trivial finite set
{{[t1,F19],t9},{[t1,F19]}} is non empty finite V35() set
[F19,F29] is non empty V15() set
{F19,F29} is non empty finite set
{F19} is non empty trivial finite set
{{F19,F29},{F19}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F19,F29)
[[F19,F29],t19] is non empty V15() set
{[F19,F29],t19} is non empty finite set
{[F19,F29]} is Relation-like non empty trivial finite set
{{[F19,F29],t19},{[F19,F29]}} is non empty finite V35() set
[t1,F29] is non empty V15() set
{t1,F29} is non empty finite set
{{t1,F29},{t1}} is non empty finite V35() set
(A,B,t1,F19,F29,t9,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F29)
[[t1,F29],(A,B,t1,F19,F29,t9,t19)] is non empty V15() set
{[t1,F29],(A,B,t1,F19,F29,t9,t19)} is non empty finite set
{[t1,F29]} is Relation-like non empty trivial finite set
{{[t1,F29],(A,B,t1,F19,F29,t9,t19)},{[t1,F29]}} is non empty finite V35() set
[t19,F19] is non empty V15() set
{t19,F19} is non empty finite set
{{t19,F19},{t19}} is non empty finite V35() set
[[t19,F19],t] is non empty V15() set
{[t19,F19],t} is non empty finite set
{[t19,F19]} is Relation-like non empty trivial finite set
{{[t19,F19],t},{[t19,F19]}} is non empty finite V35() set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,MA) is set
[a,MA] is non empty V15() set
{a,MA} is non empty finite set
{a} is non empty trivial finite set
{{a,MA},{a}} is non empty finite V35() set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . [a,MA] is set
dom (a (*) MA) is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a (*) MA) is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA,MB) is set
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . [MA,MB] is set
cod (MA (*) MB) is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA (*) MB) is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA,MB))) is set
[a,( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA,MB))] is non empty V15() set
{a,( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA,MB))} is non empty finite set
{{a,( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA,MB))},{a}} is non empty finite V35() set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . [a,( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (MA,MB))] is set
[t19,F29] is non empty V15() set
{t19,F29} is non empty finite set
{{t19,F29},{t19}} is non empty finite V35() set
t2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F19)
(A,B,t19,t19,F19,F2,t2) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F19)
(A,B,t19,F19,F29,(A,B,t19,t19,F19,F2,t2),t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F29)
[[t19,F29],(A,B,t19,F19,F29,(A,B,t19,t19,F19,F2,t2),t19)] is non empty V15() set
{[t19,F29],(A,B,t19,F19,F29,(A,B,t19,t19,F19,F2,t2),t19)} is non empty finite set
{[t19,F29]} is Relation-like non empty trivial finite set
{{[t19,F29],(A,B,t19,F19,F29,(A,B,t19,t19,F19,F2,t2),t19)},{[t19,F29]}} is non empty finite V35() set
(A,B,t19,F19,F29,t2,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F29)
(A,B,t19,t19,F29,F2,(A,B,t19,F19,F29,t2,t19)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F29)
[[t19,F29],(A,B,t19,t19,F29,F2,(A,B,t19,F19,F29,t2,t19))] is non empty V15() set
{[t19,F29],(A,B,t19,t19,F29,F2,(A,B,t19,F19,F29,t2,t19))} is non empty finite set
{{[t19,F29],(A,B,t19,t19,F29,F2,(A,B,t19,F19,F29,t2,t19))},{[t19,F29]}} is non empty finite V35() set
[t19,F29] is non empty V15() set
{t19,F29} is non empty finite set
{{t19,F29},{t19}} is non empty finite V35() set
[[t19,F29],(A,B,t19,F19,F29,t2,t19)] is non empty V15() set
{[t19,F29],(A,B,t19,F19,F29,t2,t19)} is non empty finite set
{[t19,F29]} is Relation-like non empty trivial finite set
{{[t19,F29],(A,B,t19,F19,F29,t2,t19)},{[t19,F29]}} is non empty finite V35() set
[[[t19,F29],(A,B,t19,F19,F29,t2,t19)],b] is non empty V15() set
{[[t19,F29],(A,B,t19,F19,F29,t2,t19)],b} is non empty finite set
{[[t19,F29],(A,B,t19,F19,F29,t2,t19)]} is Relation-like non empty trivial finite set
{{[[t19,F29],(A,B,t19,F19,F29,t2,t19)],b},{[[t19,F29],(A,B,t19,F19,F29,t2,t19)]}} is non empty finite V35() set
OA . [[[t19,F29],(A,B,t19,F19,F29,t2,t19)],b] is set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,MA)),MB) is set
[( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,MA)),MB] is non empty V15() set
{( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,MA)),MB} is non empty finite set
{( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,MA))} is non empty trivial finite set
{{( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,MA)),MB},{( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,MA))}} is non empty finite V35() set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . [( the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . (a,MA)),MB] is set
the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
Hom (MB,MB) is Element of bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) : ( dom b<sub>1</sub> = MB & cod b<sub>1</sub> = MB ) } is set
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MA,MA] is non empty V15() set
{MA,MA} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MA},{MA}} is non empty finite V35() set
(A,B,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MA)
[[MA,MA],(A,B,MA)] is non empty V15() set
{[MA,MA],(A,B,MA)} is non empty finite set
{[MA,MA]} is Relation-like non empty trivial finite set
{{[MA,MA],(A,B,MA)},{[MA,MA]}} is non empty finite V35() set
a is Element of (A,B)
b is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
[[MA,MA],(A,B,MA)] `1 is set
([[MA,MA],(A,B,MA)] `1) `1 is set
cod b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
([[MA,MA],(A,B,MA)] `1) `2 is set
the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MA,MA] is non empty V15() set
{MA,MA} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MA},{MA}} is non empty finite V35() set
(A,B,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MA)
[[MA,MA],(A,B,MA)] is non empty V15() set
{[MA,MA],(A,B,MA)} is non empty finite set
{[MA,MA]} is Relation-like non empty trivial finite set
{{[MA,MA],(A,B,MA)},{[MA,MA]}} is non empty finite V35() set
a is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
Hom (MB,b) is Element of bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
{ b₁ where b₁ is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) : ( dom b₁ = MB & cod b₁ = b ) } is set
Hom (b,MB) is Element of bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
{ b₁ where b₁ is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) : ( dom b₁ = b & cod b₁ = MB ) } is set
MB . MA is set
a is Morphism of MB,b
a (*) a is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
t19 is Element of (A,B)
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t19,F1] is non empty V15() set
{t19,F1} is non empty finite set
{t19} is non empty trivial finite set
{{t19,F1},{t19}} is non empty finite V35() set
F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F1)
[[t19,F1],F2] is non empty V15() set
{[t19,F1],F2} is non empty finite set
{[t19,F1]} is Relation-like non empty trivial finite set
{{[t19,F1],F2},{[t19,F1]}} is non empty finite V35() set
[t19,F1] `1 is set
t19 `1 is set
(t19 `1) `1 is set
a is Element of (A,B)
[MA,F1] is non empty V15() set
{MA,F1} is non empty finite set
{{MA,F1},{MA}} is non empty finite V35() set
t is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,F1)
(A,B,MA,MA,F1,(A,B,MA),t) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,F1)
[[MA,F1],(A,B,MA,MA,F1,(A,B,MA),t)] is non empty V15() set
{[MA,F1],(A,B,MA,MA,F1,(A,B,MA),t)} is non empty finite set
{[MA,F1]} is Relation-like non empty trivial finite set
{{[MA,F1],(A,B,MA,MA,F1,(A,B,MA),t)},{[MA,F1]}} is non empty finite V35() set
OA . (t19,(MB . MA)) is set
[t19,(MB . MA)] is non empty V15() set
{t19,(MB . MA)} is non empty finite set
{t19} is non empty trivial finite set
{{t19,(MB . MA)},{t19}} is non empty finite V35() set
OA . [t19,(MB . MA)] is set
t1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F29 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t1,F19] is non empty V15() set
{t1,F19} is non empty finite set
{t1} is non empty trivial finite set
{{t1,F19},{t1}} is non empty finite V35() set
t9 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F19)
[[t1,F19],t9] is non empty V15() set
{[t1,F19],t9} is non empty finite set
{[t1,F19]} is Relation-like non empty trivial finite set
{{[t1,F19],t9},{[t1,F19]}} is non empty finite V35() set
[F19,F29] is non empty V15() set
{F19,F29} is non empty finite set
{F19} is non empty trivial finite set
{{F19,F29},{F19}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F19,F29)
[[F19,F29],t19] is non empty V15() set
{[F19,F29],t19} is non empty finite set
{[F19,F29]} is Relation-like non empty trivial finite set
{{[F19,F29],t19},{[F19,F29]}} is non empty finite V35() set
[t1,F29] is non empty V15() set
{t1,F29} is non empty finite set
{{t1,F29},{t1}} is non empty finite V35() set
(A,B,t1,F19,F29,t9,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F29)
[[t1,F29],(A,B,t1,F19,F29,t9,t19)] is non empty V15() set
{[t1,F29],(A,B,t1,F19,F29,t9,t19)} is non empty finite set
{[t1,F29]} is Relation-like non empty trivial finite set
{{[t1,F29],(A,B,t1,F19,F29,t9,t19)},{[t1,F29]}} is non empty finite V35() set
t1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F29 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t1,F19] is non empty V15() set
{t1,F19} is non empty finite set
{t1} is non empty trivial finite set
{{t1,F19},{t1}} is non empty finite V35() set
t9 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F19)
[[t1,F19],t9] is non empty V15() set
{[t1,F19],t9} is non empty finite set
{[t1,F19]} is Relation-like non empty trivial finite set
{{[t1,F19],t9},{[t1,F19]}} is non empty finite V35() set
[F19,F29] is non empty V15() set
{F19,F29} is non empty finite set
{F19} is non empty trivial finite set
{{F19,F29},{F19}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F19,F29)
[[F19,F29],t19] is non empty V15() set
{[F19,F29],t19} is non empty finite set
{[F19,F29]} is Relation-like non empty trivial finite set
{{[F19,F29],t19},{[F19,F29]}} is non empty finite V35() set
[t1,F29] is non empty V15() set
{t1,F29} is non empty finite set
{{t1,F29},{t1}} is non empty finite V35() set
(A,B,t1,F19,F29,t9,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F29)
[[t1,F29],(A,B,t1,F19,F29,t9,t19)] is non empty V15() set
{[t1,F29],(A,B,t1,F19,F29,t9,t19)} is non empty finite set
{[t1,F29]} is Relation-like non empty trivial finite set
{{[t1,F29],(A,B,t1,F19,F29,t9,t19)},{[t1,F29]}} is non empty finite V35() set
[[F19,F29],t19] `1 is set
([[F19,F29],t19] `1) `2 is set
[[t19,F1],t] is non empty V15() set
{[t19,F1],t} is non empty finite set
{{[t19,F1],t},{[t19,F1]}} is non empty finite V35() set
[[t19,F1],t] `1 is set
([[t19,F1],t] `1) `2 is set
[[F19,F29],t19] `2 is set
[[t19,F1],t] `2 is set
(A,B,F19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F19,F19)
(A,B,F19,F19,F29,(A,B,F19),t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F19,F29)
cod a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
[[MA,MA],(A,B,MA)] `1 is set
([[MA,MA],(A,B,MA)] `1) `2 is set
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] -defined the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
[:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
proj1 the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like set
OA . (a,a) is set
OA . [a,a] is set
a is Morphism of b,MB
a (*) a is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
cod a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
t19 is Element of (A,B)
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t19,F1] is non empty V15() set
{t19,F1} is non empty finite set
{t19} is non empty trivial finite set
{{t19,F1},{t19}} is non empty finite V35() set
F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F1)
[[t19,F1],F2] is non empty V15() set
{[t19,F1],F2} is non empty finite set
{[t19,F1]} is Relation-like non empty trivial finite set
{{[t19,F1],F2},{[t19,F1]}} is non empty finite V35() set
[t19,F1] `2 is set
t19 `1 is set
(t19 `1) `2 is set
a is Element of (A,B)
[t19,MA] is non empty V15() set
{t19,MA} is non empty finite set
{{t19,MA},{t19}} is non empty finite V35() set
t is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,MA)
(A,B,t19,MA,MA,t,(A,B,MA)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,MA)
[[t19,MA],(A,B,t19,MA,MA,t,(A,B,MA))] is non empty V15() set
{[t19,MA],(A,B,t19,MA,MA,t,(A,B,MA))} is non empty finite set
{[t19,MA]} is Relation-like non empty trivial finite set
{{[t19,MA],(A,B,t19,MA,MA,t,(A,B,MA))},{[t19,MA]}} is non empty finite V35() set
OA . ((MB . MA),t19) is set
[(MB . MA),t19] is non empty V15() set
{(MB . MA),t19} is non empty finite set
{(MB . MA)} is non empty trivial finite set
{{(MB . MA),t19},{(MB . MA)}} is non empty finite V35() set
OA . [(MB . MA),t19] is set
t1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F29 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t1,F19] is non empty V15() set
{t1,F19} is non empty finite set
{t1} is non empty trivial finite set
{{t1,F19},{t1}} is non empty finite V35() set
t9 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F19)
[[t1,F19],t9] is non empty V15() set
{[t1,F19],t9} is non empty finite set
{[t1,F19]} is Relation-like non empty trivial finite set
{{[t1,F19],t9},{[t1,F19]}} is non empty finite V35() set
[F19,F29] is non empty V15() set
{F19,F29} is non empty finite set
{F19} is non empty trivial finite set
{{F19,F29},{F19}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F19,F29)
[[F19,F29],t19] is non empty V15() set
{[F19,F29],t19} is non empty finite set
{[F19,F29]} is Relation-like non empty trivial finite set
{{[F19,F29],t19},{[F19,F29]}} is non empty finite V35() set
[t1,F29] is non empty V15() set
{t1,F29} is non empty finite set
{{t1,F29},{t1}} is non empty finite V35() set
(A,B,t1,F19,F29,t9,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F29)
[[t1,F29],(A,B,t1,F19,F29,t9,t19)] is non empty V15() set
{[t1,F29],(A,B,t1,F19,F29,t9,t19)} is non empty finite set
{[t1,F29]} is Relation-like non empty trivial finite set
{{[t1,F29],(A,B,t1,F19,F29,t9,t19)},{[t1,F29]}} is non empty finite V35() set
t1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F29 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t1,F19] is non empty V15() set
{t1,F19} is non empty finite set
{t1} is non empty trivial finite set
{{t1,F19},{t1}} is non empty finite V35() set
t9 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F19)
[[t1,F19],t9] is non empty V15() set
{[t1,F19],t9} is non empty finite set
{[t1,F19]} is Relation-like non empty trivial finite set
{{[t1,F19],t9},{[t1,F19]}} is non empty finite V35() set
[F19,F29] is non empty V15() set
{F19,F29} is non empty finite set
{F19} is non empty trivial finite set
{{F19,F29},{F19}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F19,F29)
[[F19,F29],t19] is non empty V15() set
{[F19,F29],t19} is non empty finite set
{[F19,F29]} is Relation-like non empty trivial finite set
{{[F19,F29],t19},{[F19,F29]}} is non empty finite V35() set
[t1,F29] is non empty V15() set
{t1,F29} is non empty finite set
{{t1,F29},{t1}} is non empty finite V35() set
(A,B,t1,F19,F29,t9,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F29)
[[t1,F29],(A,B,t1,F19,F29,t9,t19)] is non empty V15() set
{[t1,F29],(A,B,t1,F19,F29,t9,t19)} is non empty finite set
{[t1,F29]} is Relation-like non empty trivial finite set
{{[t1,F29],(A,B,t1,F19,F29,t9,t19)},{[t1,F29]}} is non empty finite V35() set
[[t1,F19],t9] `1 is set
([[t1,F19],t9] `1) `1 is set
[[t19,F1],t] is non empty V15() set
{[t19,F1],t} is non empty finite set
{{[t19,F1],t},{[t19,F1]}} is non empty finite V35() set
[[t19,F1],t] `1 is set
([[t19,F1],t] `1) `1 is set
[[t1,F19],t9] `2 is set
[[t19,F1],t] `2 is set
(A,B,F19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F19,F19)
(A,B,t1,F19,F19,t9,(A,B,F19)) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F19)
dom a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
[[MA,MA],(A,B,MA)] `1 is set
([[MA,MA],(A,B,MA)] `1) `1 is set
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] -defined the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like Element of bool [:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
[:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [:[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):], the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
proj1 the Comp of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like set
OA . (a,a) is set
OA . [a,a] is set
[[t1,F29],(A,B,t1,F19,F19,t9,(A,B,F19))] is non empty V15() set
{[t1,F29],(A,B,t1,F19,F19,t9,(A,B,F19))} is non empty finite set
{{[t1,F29],(A,B,t1,F19,F19,t9,(A,B,F19))},{[t1,F29]}} is non empty finite V35() set
MB is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MA,MA] is non empty V15() set
{MA,MA} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MA},{MA}} is non empty finite V35() set
(A,B,MA) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MA)
[[MA,MA],(A,B,MA)] is non empty V15() set
{[MA,MA],(A,B,MA)} is non empty finite set
{[MA,MA]} is Relation-like non empty trivial finite set
{{[MA,MA],(A,B,MA)},{[MA,MA]}} is non empty finite V35() set
a is Element of (A,B)
b is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
dom b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
[: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is Relation-like non empty set
bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):] is non empty set
the Source of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
[[MA,MA],(A,B,MA)] `1 is set
([[MA,MA],(A,B,MA)] `1) `1 is set
cod b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is Relation-like the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -defined the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) -valued Function-like quasi_total Element of bool [: the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #), the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #):]
the Target of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) . b is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
([[MA,MA],(A,B,MA)] `1) `2 is set
Hom (MB,MB) is Element of bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) : ( dom b<sub>1</sub> = MB & cod b<sub>1</sub> = MB ) } is set
a is Morphism of MB,MB
a is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
t19 is Element of the carrier of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
Hom (MB,a) is Element of bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) : ( dom b<sub>1</sub> = MB & cod b<sub>1</sub> = a ) } is set
t19 is Morphism of MB,a
t19 (*) a is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
Hom (t19,MB) is Element of bool the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #) : ( dom b<sub>1</sub> = t19 & cod b<sub>1</sub> = MB ) } is set
F1 is Morphism of t19,MB
a (*) F1 is Element of the carrier' of CatStr(# (Funct (A,B)),(A,B),AB,MA,OA #)
MB is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of MB is non empty set
the carrier' of MB is non empty set
the Comp of MB is Relation-like [: the carrier' of MB, the carrier' of MB:] -defined the carrier' of MB -valued Function-like Element of bool [:[: the carrier' of MB, the carrier' of MB:], the carrier' of MB:]
[: the carrier' of MB, the carrier' of MB:] is Relation-like non empty set
[:[: the carrier' of MB, the carrier' of MB:], the carrier' of MB:] is Relation-like non empty set
bool [:[: the carrier' of MB, the carrier' of MB:], the carrier' of MB:] is non empty set
proj1 the Comp of MB is Relation-like set
MA is Element of the carrier' of MB
dom MA is Element of the carrier of MB
the Source of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
[: the carrier' of MB, the carrier of MB:] is Relation-like non empty set
bool [: the carrier' of MB, the carrier of MB:] is non empty set
the Source of MB . MA is Element of the carrier of MB
MA `1 is set
(MA `1) `1 is set
a is Element of the carrier' of MB
cod a is Element of the carrier of MB
the Target of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
the Target of MB . a is Element of the carrier of MB
a `1 is set
(a `1) `2 is set
a is Element of the carrier' of MB
dom a is Element of the carrier of MB
the Source of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
[: the carrier' of MB, the carrier of MB:] is Relation-like non empty set
bool [: the carrier' of MB, the carrier of MB:] is non empty set
the Source of MB . a is Element of the carrier of MB
MA is Element of the carrier' of MB
cod MA is Element of the carrier of MB
the Target of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
the Target of MB . MA is Element of the carrier of MB
[a,MA] is non empty V15() Element of the carrier' of [:MB,MB:]
[:MB,MB:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of MB, the carrier of MB:] is Relation-like non empty set
[: the Source of MB, the Source of MB:] is Relation-like [: the carrier' of MB, the carrier' of MB:] -defined [: the carrier of MB, the carrier of MB:] -valued Function-like quasi_total Element of bool [:[: the carrier' of MB, the carrier' of MB:],[: the carrier of MB, the carrier of MB:]:]
[:[: the carrier' of MB, the carrier' of MB:],[: the carrier of MB, the carrier of MB:]:] is Relation-like non empty set
bool [:[: the carrier' of MB, the carrier' of MB:],[: the carrier of MB, the carrier of MB:]:] is non empty set
[: the Target of MB, the Target of MB:] is Relation-like [: the carrier' of MB, the carrier' of MB:] -defined [: the carrier of MB, the carrier of MB:] -valued Function-like quasi_total Element of bool [:[: the carrier' of MB, the carrier' of MB:],[: the carrier of MB, the carrier of MB:]:]
|: the Comp of MB, the Comp of MB:| is Relation-like [:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:] -defined [: the carrier' of MB, the carrier' of MB:] -valued Function-like Element of bool [:[:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:],[: the carrier' of MB, the carrier' of MB:]:]
[:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:] is Relation-like non empty set
[:[:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:],[: the carrier' of MB, the carrier' of MB:]:] is Relation-like non empty set
bool [:[:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:],[: the carrier' of MB, the carrier' of MB:]:] is non empty set
CatStr(# [: the carrier of MB, the carrier of MB:],[: the carrier' of MB, the carrier' of MB:],[: the Source of MB, the Source of MB:],[: the Target of MB, the Target of MB:],|: the Comp of MB, the Comp of MB:| #) is non empty non void V55() strict CatStr
the carrier' of [:MB,MB:] is non empty set
{a,MA} is non empty finite set
{a} is non empty trivial finite set
{{a,MA},{a}} is non empty finite V35() set
b is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,b,a)
[[b,a],a] is non empty V15() set
{[b,a],a} is non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],a},{[b,a]}} is non empty finite V35() set
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t19,t19] is non empty V15() set
{t19,t19} is non empty finite set
{t19} is non empty trivial finite set
{{t19,t19},{t19}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,t19)
[[t19,t19],F1] is non empty V15() set
{[t19,t19],F1} is non empty finite set
{[t19,t19]} is Relation-like non empty trivial finite set
{{[t19,t19],F1},{[t19,t19]}} is non empty finite V35() set
[[t19,t19],F1] `1 is set
([[t19,t19],F1] `1) `2 is set
[[b,a],a] `1 is set
([[b,a],a] `1) `1 is set
[t19,a] is non empty V15() set
{t19,a} is non empty finite set
{{t19,a},{t19}} is non empty finite V35() set
F2 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,a)
(A,B,t19,t19,a,F1,F2) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,a)
[[t19,a],(A,B,t19,t19,a,F1,F2)] is non empty V15() set
{[t19,a],(A,B,t19,t19,a,F1,F2)} is non empty finite set
{[t19,a]} is Relation-like non empty trivial finite set
{{[t19,a],(A,B,t19,t19,a,F1,F2)},{[t19,a]}} is non empty finite V35() set
t is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t,t1] is non empty V15() set
{t,t1} is non empty finite set
{t} is non empty trivial finite set
{{t,t1},{t}} is non empty finite V35() set
F29 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t,t1)
[[t,t1],F29] is non empty V15() set
{[t,t1],F29} is non empty finite set
{[t,t1]} is Relation-like non empty trivial finite set
{{[t,t1],F29},{[t,t1]}} is non empty finite V35() set
[t1,F19] is non empty V15() set
{t1,F19} is non empty finite set
{t1} is non empty trivial finite set
{{t1,F19},{t1}} is non empty finite V35() set
t9 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t1,F19)
[[t1,F19],t9] is non empty V15() set
{[t1,F19],t9} is non empty finite set
{[t1,F19]} is Relation-like non empty trivial finite set
{{[t1,F19],t9},{[t1,F19]}} is non empty finite V35() set
[t,F19] is non empty V15() set
{t,F19} is non empty finite set
{{t,F19},{t}} is non empty finite V35() set
(A,B,t,t1,F19,F29,t9) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t,F19)
[[t,F19],(A,B,t,t1,F19,F29,t9)] is non empty V15() set
{[t,F19],(A,B,t,t1,F19,F29,t9)} is non empty finite set
{[t,F19]} is Relation-like non empty trivial finite set
{{[t,F19],(A,B,t,t1,F19,F29,t9)},{[t,F19]}} is non empty finite V35() set
a is Element of the carrier' of MB
MA is Element of the carrier' of MB
[a,MA] is non empty V15() Element of the carrier' of [:MB,MB:]
[:MB,MB:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of MB, the carrier of MB:] is Relation-like non empty set
the Source of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
[: the carrier' of MB, the carrier of MB:] is Relation-like non empty set
bool [: the carrier' of MB, the carrier of MB:] is non empty set
[: the Source of MB, the Source of MB:] is Relation-like [: the carrier' of MB, the carrier' of MB:] -defined [: the carrier of MB, the carrier of MB:] -valued Function-like quasi_total Element of bool [:[: the carrier' of MB, the carrier' of MB:],[: the carrier of MB, the carrier of MB:]:]
[:[: the carrier' of MB, the carrier' of MB:],[: the carrier of MB, the carrier of MB:]:] is Relation-like non empty set
bool [:[: the carrier' of MB, the carrier' of MB:],[: the carrier of MB, the carrier of MB:]:] is non empty set
the Target of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
[: the Target of MB, the Target of MB:] is Relation-like [: the carrier' of MB, the carrier' of MB:] -defined [: the carrier of MB, the carrier of MB:] -valued Function-like quasi_total Element of bool [:[: the carrier' of MB, the carrier' of MB:],[: the carrier of MB, the carrier of MB:]:]
|: the Comp of MB, the Comp of MB:| is Relation-like [:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:] -defined [: the carrier' of MB, the carrier' of MB:] -valued Function-like Element of bool [:[:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:],[: the carrier' of MB, the carrier' of MB:]:]
[:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:] is Relation-like non empty set
[:[:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:],[: the carrier' of MB, the carrier' of MB:]:] is Relation-like non empty set
bool [:[:[: the carrier' of MB, the carrier' of MB:],[: the carrier' of MB, the carrier' of MB:]:],[: the carrier' of MB, the carrier' of MB:]:] is non empty set
CatStr(# [: the carrier of MB, the carrier of MB:],[: the carrier' of MB, the carrier' of MB:],[: the Source of MB, the Source of MB:],[: the Target of MB, the Target of MB:],|: the Comp of MB, the Comp of MB:| #) is non empty non void V55() strict CatStr
the carrier' of [:MB,MB:] is non empty set
{a,MA} is non empty finite set
{a} is non empty trivial finite set
{{a,MA},{a}} is non empty finite V35() set
the Comp of MB . [a,MA] is set
the Comp of MB . (a,MA) is set
[a,MA] is non empty V15() set
the Comp of MB . [a,MA] is set
b is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,b,a)
[[b,a],t19] is non empty V15() set
{[b,a],t19} is non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],t19},{[b,a]}} is non empty finite V35() set
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],t19] is non empty V15() set
{[a,a],t19} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],t19},{[a,a]}} is non empty finite V35() set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{{b,a},{b}} is non empty finite V35() set
(A,B,b,a,a,t19,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,b,a)
[[b,a],(A,B,b,a,a,t19,t19)] is non empty V15() set
{[b,a],(A,B,b,a,a,t19,t19)} is non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],(A,B,b,a,a,t19,t19)},{[b,a]}} is non empty finite V35() set
MA is Element of the carrier of MB
id MA is Morphism of MA,MA
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
(A,B,a) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],(A,B,a)] is non empty V15() set
{[a,a],(A,B,a)} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],(A,B,a)},{[a,a]}} is non empty finite V35() set
b is Element of (A,B)
a is Element of the carrier' of MB
dom a is Element of the carrier of MB
the Source of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
[: the carrier' of MB, the carrier of MB:] is Relation-like non empty set
bool [: the carrier' of MB, the carrier of MB:] is non empty set
the Source of MB . a is Element of the carrier of MB
[[a,a],(A,B,a)] `1 is set
([[a,a],(A,B,a)] `1) `1 is set
cod a is Element of the carrier of MB
the Target of MB is Relation-like the carrier' of MB -defined the carrier of MB -valued Function-like quasi_total Element of bool [: the carrier' of MB, the carrier of MB:]
the Target of MB . a is Element of the carrier of MB
([[a,a],(A,B,a)] `1) `2 is set
Hom (MA,MA) is non empty Element of bool the carrier' of MB
bool the carrier' of MB is non empty set
{ b₁ where b₁ is Element of the carrier' of MB : ( dom b₁ = MA & cod b₁ = MA ) } is set
a is Morphism of MA,MA
t19 is Element of the carrier of MB
F1 is Element of the carrier of MB
Hom (MA,t19) is Element of bool the carrier' of MB
{ b₁ where b₁ is Element of the carrier' of MB : ( dom b₁ = MA & cod b₁ = t19 ) } is set
t19 is Morphism of MA,t19
t19 (*) a is Element of the carrier' of MB
Hom (F1,MA) is Element of bool the carrier' of MB
{ b₁ where b₁ is Element of the carrier' of MB : ( dom b₁ = F1 & cod b₁ = MA ) } is set
F2 is Morphism of F1,MA
a (*) F2 is Element of the carrier' of MB
OA is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of OA is non empty set
the carrier' of OA is non empty set
the Comp of OA is Relation-like [: the carrier' of OA, the carrier' of OA:] -defined the carrier' of OA -valued Function-like Element of bool [:[: the carrier' of OA, the carrier' of OA:], the carrier' of OA:]
[: the carrier' of OA, the carrier' of OA:] is Relation-like non empty set
[:[: the carrier' of OA, the carrier' of OA:], the carrier' of OA:] is Relation-like non empty set
bool [:[: the carrier' of OA, the carrier' of OA:], the carrier' of OA:] is non empty set
proj1 the Comp of OA is Relation-like set
AB is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of AB is non empty set
the carrier' of AB is non empty set
the Comp of AB is Relation-like [: the carrier' of AB, the carrier' of AB:] -defined the carrier' of AB -valued Function-like Element of bool [:[: the carrier' of AB, the carrier' of AB:], the carrier' of AB:]
[: the carrier' of AB, the carrier' of AB:] is Relation-like non empty set
[:[: the carrier' of AB, the carrier' of AB:], the carrier' of AB:] is Relation-like non empty set
bool [:[: the carrier' of AB, the carrier' of AB:], the carrier' of AB:] is non empty set
proj1 the Comp of AB is Relation-like set
the Target of OA is Relation-like the carrier' of OA -defined the carrier of OA -valued Function-like quasi_total Element of bool [: the carrier' of OA, the carrier of OA:]
[: the carrier' of OA, the carrier of OA:] is Relation-like non empty set
bool [: the carrier' of OA, the carrier of OA:] is non empty set
the Target of AB is Relation-like the carrier' of AB -defined the carrier of AB -valued Function-like quasi_total Element of bool [: the carrier' of AB, the carrier of AB:]
[: the carrier' of AB, the carrier of AB:] is Relation-like non empty set
bool [: the carrier' of AB, the carrier of AB:] is non empty set
MA is Element of the carrier' of OA
the Target of OA . MA is set
the Target of AB . MA is set
the Target of OA . MA is Element of the carrier of OA
cod MA is Element of the carrier of OA
MA `1 is set
(MA `1) `2 is set
MB is Element of the carrier' of AB
cod MB is Element of the carrier of AB
the Target of AB . MB is Element of the carrier of AB
bool [: the carrier' of OA, the carrier' of OA:] is non empty set
OB is Element of [: the carrier' of OA, the carrier' of OA:]
OB `1 is set
OB `2 is set
[(OB `1),(OB `2)] is non empty V15() set
{(OB `1),(OB `2)} is non empty finite set
{(OB `1)} is non empty trivial finite set
{{(OB `1),(OB `2)},{(OB `1)}} is non empty finite V35() set
b is Element of the carrier' of AB
a is Element of the carrier' of AB
[b,a] is non empty V15() Element of the carrier' of [:AB,AB:]
[:AB,AB:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of AB, the carrier of AB:] is Relation-like non empty set
the Source of AB is Relation-like the carrier' of AB -defined the carrier of AB -valued Function-like quasi_total Element of bool [: the carrier' of AB, the carrier of AB:]
[: the Source of AB, the Source of AB:] is Relation-like [: the carrier' of AB, the carrier' of AB:] -defined [: the carrier of AB, the carrier of AB:] -valued Function-like quasi_total Element of bool [:[: the carrier' of AB, the carrier' of AB:],[: the carrier of AB, the carrier of AB:]:]
[:[: the carrier' of AB, the carrier' of AB:],[: the carrier of AB, the carrier of AB:]:] is Relation-like non empty set
bool [:[: the carrier' of AB, the carrier' of AB:],[: the carrier of AB, the carrier of AB:]:] is non empty set
[: the Target of AB, the Target of AB:] is Relation-like [: the carrier' of AB, the carrier' of AB:] -defined [: the carrier of AB, the carrier of AB:] -valued Function-like quasi_total Element of bool [:[: the carrier' of AB, the carrier' of AB:],[: the carrier of AB, the carrier of AB:]:]
|: the Comp of AB, the Comp of AB:| is Relation-like [:[: the carrier' of AB, the carrier' of AB:],[: the carrier' of AB, the carrier' of AB:]:] -defined [: the carrier' of AB, the carrier' of AB:] -valued Function-like Element of bool [:[:[: the carrier' of AB, the carrier' of AB:],[: the carrier' of AB, the carrier' of AB:]:],[: the carrier' of AB, the carrier' of AB:]:]
[:[: the carrier' of AB, the carrier' of AB:],[: the carrier' of AB, the carrier' of AB:]:] is Relation-like non empty set
[:[:[: the carrier' of AB, the carrier' of AB:],[: the carrier' of AB, the carrier' of AB:]:],[: the carrier' of AB, the carrier' of AB:]:] is Relation-like non empty set
bool [:[:[: the carrier' of AB, the carrier' of AB:],[: the carrier' of AB, the carrier' of AB:]:],[: the carrier' of AB, the carrier' of AB:]:] is non empty set
CatStr(# [: the carrier of AB, the carrier of AB:],[: the carrier' of AB, the carrier' of AB:],[: the Source of AB, the Source of AB:],[: the Target of AB, the Target of AB:],|: the Comp of AB, the Comp of AB:| #) is non empty non void V55() strict CatStr
the carrier' of [:AB,AB:] is non empty set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
MB is Relation-like the carrier' of OA -defined the carrier' of OA -valued Element of bool [: the carrier' of OA, the carrier' of OA:]
the Comp of AB . [b,a] is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],t19] is non empty V15() set
{[a,a],t19} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],t19},{[a,a]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],F1] is non empty V15() set
{[a,t19],F1} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],F1},{[a,t19]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,a,a,t19,t19,F1) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,a,t19,t19,F1)] is non empty V15() set
{[a,t19],(A,B,a,a,t19,t19,F1)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,a,t19,t19,F1)},{[a,t19]}} is non empty finite V35() set
MA is Element of the carrier' of OA
dom MA is Element of the carrier of OA
the Source of OA is Relation-like the carrier' of OA -defined the carrier of OA -valued Function-like quasi_total Element of bool [: the carrier' of OA, the carrier of OA:]
the Source of OA . MA is Element of the carrier of OA
MA `1 is set
(MA `1) `1 is set
[a,t19] `1 is set
[a,a] `2 is set
a `1 is set
(a `1) `2 is set
MB is Element of the carrier' of OA
cod MB is Element of the carrier of OA
the Target of OA . MB is Element of the carrier of OA
[MA,MB] is non empty V15() Element of the carrier' of [:OA,OA:]
[:OA,OA:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[: the carrier of OA, the carrier of OA:] is Relation-like non empty set
[: the Source of OA, the Source of OA:] is Relation-like [: the carrier' of OA, the carrier' of OA:] -defined [: the carrier of OA, the carrier of OA:] -valued Function-like quasi_total Element of bool [:[: the carrier' of OA, the carrier' of OA:],[: the carrier of OA, the carrier of OA:]:]
[:[: the carrier' of OA, the carrier' of OA:],[: the carrier of OA, the carrier of OA:]:] is Relation-like non empty set
bool [:[: the carrier' of OA, the carrier' of OA:],[: the carrier of OA, the carrier of OA:]:] is non empty set
[: the Target of OA, the Target of OA:] is Relation-like [: the carrier' of OA, the carrier' of OA:] -defined [: the carrier of OA, the carrier of OA:] -valued Function-like quasi_total Element of bool [:[: the carrier' of OA, the carrier' of OA:],[: the carrier of OA, the carrier of OA:]:]
|: the Comp of OA, the Comp of OA:| is Relation-like [:[: the carrier' of OA, the carrier' of OA:],[: the carrier' of OA, the carrier' of OA:]:] -defined [: the carrier' of OA, the carrier' of OA:] -valued Function-like Element of bool [:[:[: the carrier' of OA, the carrier' of OA:],[: the carrier' of OA, the carrier' of OA:]:],[: the carrier' of OA, the carrier' of OA:]:]
[:[: the carrier' of OA, the carrier' of OA:],[: the carrier' of OA, the carrier' of OA:]:] is Relation-like non empty set
[:[:[: the carrier' of OA, the carrier' of OA:],[: the carrier' of OA, the carrier' of OA:]:],[: the carrier' of OA, the carrier' of OA:]:] is Relation-like non empty set
bool [:[:[: the carrier' of OA, the carrier' of OA:],[: the carrier' of OA, the carrier' of OA:]:],[: the carrier' of OA, the carrier' of OA:]:] is non empty set
CatStr(# [: the carrier of OA, the carrier of OA:],[: the carrier' of OA, the carrier' of OA:],[: the Source of OA, the Source of OA:],[: the Target of OA, the Target of OA:],|: the Comp of OA, the Comp of OA:| #) is non empty non void V55() strict CatStr
the carrier' of [:OA,OA:] is non empty set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
MA is Relation-like the carrier' of OA -defined the carrier' of OA -valued Element of bool [: the carrier' of OA, the carrier' of OA:]
the Comp of OA . [MA,MB] is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],t19] is non empty V15() set
{[a,a],t19} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],t19},{[a,a]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{a} is non empty trivial finite set
{{a,t19},{a}} is non empty finite V35() set
F1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],F1] is non empty V15() set
{[a,t19],F1} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],F1},{[a,t19]}} is non empty finite V35() set
[a,t19] is non empty V15() set
{a,t19} is non empty finite set
{{a,t19},{a}} is non empty finite V35() set
(A,B,a,a,t19,t19,F1) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,t19)
[[a,t19],(A,B,a,a,t19,t19,F1)] is non empty V15() set
{[a,t19],(A,B,a,a,t19,t19,F1)} is non empty finite set
{[a,t19]} is Relation-like non empty trivial finite set
{{[a,t19],(A,B,a,a,t19,t19,F1)},{[a,t19]}} is non empty finite V35() set
dom b is Element of the carrier of AB
the Source of AB . b is Element of the carrier of AB
b `1 is set
(b `1) `1 is set
[a,t19] `1 is set
[a,a] `2 is set
MB `1 is set
(MB `1) `2 is set
cod a is Element of the carrier of AB
the Target of AB . a is Element of the carrier of AB
OB is set
OB `2 is set
OB `1 is set
MA is Element of the carrier' of OA
MB is Element of the carrier' of OA
[MA,MB] is non empty V15() Element of the carrier' of [:OA,OA:]
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
the Comp of AB . [MA,MB] is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
b is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,b)
[[a,b],a] is non empty V15() set
{[a,b],a} is non empty finite set
{[a,b]} is Relation-like non empty trivial finite set
{{[a,b],a},{[a,b]}} is non empty finite V35() set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,b,a)
[[b,a],t19] is non empty V15() set
{[b,a],t19} is non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],t19},{[b,a]}} is non empty finite V35() set
[a,a] is non empty V15() set
{a,a} is non empty finite set
{{a,a},{a}} is non empty finite V35() set
(A,B,a,b,a,a,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],(A,B,a,b,a,a,t19)] is non empty V15() set
{[a,a],(A,B,a,b,a,a,t19)} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],(A,B,a,b,a,a,t19)},{[a,a]}} is non empty finite V35() set
the Comp of OA . [MA,MB] is set
t19 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F1 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
F2 is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[t19,F1] is non empty V15() set
{t19,F1} is non empty finite set
{t19} is non empty trivial finite set
{{t19,F1},{t19}} is non empty finite V35() set
t is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F1)
[[t19,F1],t] is non empty V15() set
{[t19,F1],t} is non empty finite set
{[t19,F1]} is Relation-like non empty trivial finite set
{{[t19,F1],t},{[t19,F1]}} is non empty finite V35() set
[F1,F2] is non empty V15() set
{F1,F2} is non empty finite set
{F1} is non empty trivial finite set
{{F1,F2},{F1}} is non empty finite V35() set
t1 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,F1,F2)
[[F1,F2],t1] is non empty V15() set
{[F1,F2],t1} is non empty finite set
{[F1,F2]} is Relation-like non empty trivial finite set
{{[F1,F2],t1},{[F1,F2]}} is non empty finite V35() set
[t19,F2] is non empty V15() set
{t19,F2} is non empty finite set
{{t19,F2},{t19}} is non empty finite V35() set
(A,B,t19,F1,F2,t,t1) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,t19,F2)
[[t19,F2],(A,B,t19,F1,F2,t,t1)] is non empty V15() set
{[t19,F2],(A,B,t19,F1,F2,t,t1)} is non empty finite set
{[t19,F2]} is Relation-like non empty trivial finite set
{{[t19,F2],(A,B,t19,F1,F2,t,t1)},{[t19,F2]}} is non empty finite V35() set
the Comp of OA . OB is set
the Comp of AB . OB is set
MA is Element of the carrier' of OA
the Source of OA . MA is set
the Source of AB . MA is set
the Source of OA . MA is Element of the carrier of OA
dom MA is Element of the carrier of OA
MA `1 is set
(MA `1) `1 is set
MB is Element of the carrier' of AB
dom MB is Element of the carrier of AB
the Source of AB . MB is Element of the carrier of AB
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
(A,B) is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier' of (A,B) is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[OA,AB] is non empty V15() set
{OA,AB} is non empty finite set
{OA} is non empty trivial finite set
{{OA,AB},{OA}} is non empty finite V35() set
MA is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
[[OA,AB],MA] is non empty V15() set
{[OA,AB],MA} is non empty finite set
{[OA,AB]} is Relation-like non empty trivial finite set
{{[OA,AB],MA},{[OA,AB]}} is non empty finite V35() set
MB is Element of the carrier' of (A,B)
dom MB is Element of the carrier of (A,B)
the carrier of (A,B) is non empty set
the Source of (A,B) is Relation-like the carrier' of (A,B) -defined the carrier of (A,B) -valued Function-like quasi_total Element of bool [: the carrier' of (A,B), the carrier of (A,B):]
[: the carrier' of (A,B), the carrier of (A,B):] is Relation-like non empty set
bool [: the carrier' of (A,B), the carrier of (A,B):] is non empty set
the Source of (A,B) . MB is Element of the carrier of (A,B)
cod MB is Element of the carrier of (A,B)
the Target of (A,B) is Relation-like the carrier' of (A,B) -defined the carrier of (A,B) -valued Function-like quasi_total Element of bool [: the carrier' of (A,B), the carrier of (A,B):]
the Target of (A,B) . MB is Element of the carrier of (A,B)
MB `1 is set
(MB `1) `1 is set
[OA,AB] `1 is set
(MB `1) `2 is set
[OA,AB] `2 is set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
(A,B) is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier of (A,B) is non empty set
the carrier' of B is non empty set
OA is Element of the carrier of (A,B)
AB is Element of the carrier of (A,B)
Hom (OA,AB) is Element of bool the carrier' of (A,B)
the carrier' of (A,B) is non empty set
bool the carrier' of (A,B) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of (A,B) : ( dom b<sub>1</sub> = OA & cod b<sub>1</sub> = AB ) } is set
MA is Morphism of OA,AB
(A,B) is non empty (A,B)
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
OB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MB,OB] is non empty V15() set
{MB,OB} is non empty finite set
{MB} is non empty trivial finite set
{{MB,OB},{MB}} is non empty finite V35() set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MB,OB)
[[MB,OB],MB] is non empty V15() set
{[MB,OB],MB} is non empty finite set
{[MB,OB]} is Relation-like non empty trivial finite set
{{[MB,OB],MB},{[MB,OB]}} is non empty finite V35() set
dom MA is Element of the carrier of (A,B)
the Source of (A,B) is Relation-like the carrier' of (A,B) -defined the carrier of (A,B) -valued Function-like quasi_total Element of bool [: the carrier' of (A,B), the carrier of (A,B):]
[: the carrier' of (A,B), the carrier of (A,B):] is Relation-like non empty set
bool [: the carrier' of (A,B), the carrier of (A,B):] is non empty set
the Source of (A,B) . MA is Element of the carrier of (A,B)
cod MA is Element of the carrier of (A,B)
the Target of (A,B) is Relation-like the carrier' of (A,B) -defined the carrier of (A,B) -valued Function-like quasi_total Element of bool [: the carrier' of (A,B), the carrier of (A,B):]
the Target of (A,B) . MA is Element of the carrier of (A,B)
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
(A,B) is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier' of (A,B) is non empty set
the Comp of (A,B) is Relation-like [: the carrier' of (A,B), the carrier' of (A,B):] -defined the carrier' of (A,B) -valued Function-like Element of bool [:[: the carrier' of (A,B), the carrier' of (A,B):], the carrier' of (A,B):]
[: the carrier' of (A,B), the carrier' of (A,B):] is Relation-like non empty set
[:[: the carrier' of (A,B), the carrier' of (A,B):], the carrier' of (A,B):] is Relation-like non empty set
bool [:[: the carrier' of (A,B), the carrier' of (A,B):], the carrier' of (A,B):] is non empty set
proj1 the Comp of (A,B) is Relation-like set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[OA,AB] is non empty V15() set
{OA,AB} is non empty finite set
{OA} is non empty trivial finite set
{{OA,AB},{OA}} is non empty finite V35() set
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
MB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[MA,MB] is non empty V15() set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,MA,MB)
[[MA,MB],OB] is non empty V15() set
{[MA,MB],OB} is non empty finite set
{[MA,MB]} is Relation-like non empty trivial finite set
{{[MA,MB],OB},{[MA,MB]}} is non empty finite V35() set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
[[OA,AB],MB] is non empty V15() set
{[OA,AB],MB} is non empty finite set
{[OA,AB]} is Relation-like non empty trivial finite set
{{[OA,AB],MB},{[OA,AB]}} is non empty finite V35() set
MA is Element of the carrier' of (A,B)
a is Element of the carrier' of (A,B)
[a,MA] is non empty V15() Element of the carrier' of [:(A,B),(A,B):]
[:(A,B),(A,B):] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of (A,B) is non empty set
[: the carrier of (A,B), the carrier of (A,B):] is Relation-like non empty set
the Source of (A,B) is Relation-like the carrier' of (A,B) -defined the carrier of (A,B) -valued Function-like quasi_total Element of bool [: the carrier' of (A,B), the carrier of (A,B):]
[: the carrier' of (A,B), the carrier of (A,B):] is Relation-like non empty set
bool [: the carrier' of (A,B), the carrier of (A,B):] is non empty set
[: the Source of (A,B), the Source of (A,B):] is Relation-like [: the carrier' of (A,B), the carrier' of (A,B):] -defined [: the carrier of (A,B), the carrier of (A,B):] -valued Function-like quasi_total Element of bool [:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier of (A,B), the carrier of (A,B):]:]
[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier of (A,B), the carrier of (A,B):]:] is Relation-like non empty set
bool [:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier of (A,B), the carrier of (A,B):]:] is non empty set
the Target of (A,B) is Relation-like the carrier' of (A,B) -defined the carrier of (A,B) -valued Function-like quasi_total Element of bool [: the carrier' of (A,B), the carrier of (A,B):]
[: the Target of (A,B), the Target of (A,B):] is Relation-like [: the carrier' of (A,B), the carrier' of (A,B):] -defined [: the carrier of (A,B), the carrier of (A,B):] -valued Function-like quasi_total Element of bool [:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier of (A,B), the carrier of (A,B):]:]
|: the Comp of (A,B), the Comp of (A,B):| is Relation-like [:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:] -defined [: the carrier' of (A,B), the carrier' of (A,B):] -valued Function-like Element of bool [:[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:],[: the carrier' of (A,B), the carrier' of (A,B):]:]
[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:] is Relation-like non empty set
[:[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:],[: the carrier' of (A,B), the carrier' of (A,B):]:] is Relation-like non empty set
bool [:[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:],[: the carrier' of (A,B), the carrier' of (A,B):]:] is non empty set
CatStr(# [: the carrier of (A,B), the carrier of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):],[: the Source of (A,B), the Source of (A,B):],[: the Target of (A,B), the Target of (A,B):],|: the Comp of (A,B), the Comp of (A,B):| #) is non empty non void V55() strict CatStr
the carrier' of [:(A,B),(A,B):] is non empty set
{a,MA} is non empty finite set
{a} is non empty trivial finite set
{{a,MA},{a}} is non empty finite V35() set
the Comp of (A,B) . [a,MA] is set
b is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,b,a)
[[b,a],t19] is non empty V15() set
{[b,a],t19} is non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],t19},{[b,a]}} is non empty finite V35() set
[a,a] is non empty V15() set
{a,a} is non empty finite set
{a} is non empty trivial finite set
{{a,a},{a}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],t19] is non empty V15() set
{[a,a],t19} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],t19},{[a,a]}} is non empty finite V35() set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{{b,a},{b}} is non empty finite V35() set
(A,B,b,a,a,t19,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,b,a)
[[b,a],(A,B,b,a,a,t19,t19)] is non empty V15() set
{[b,a],(A,B,b,a,a,t19,t19)} is non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],(A,B,b,a,a,t19,t19)},{[b,a]}} is non empty finite V35() set
[[MA,MB],OB] `1 is set
([[MA,MB],OB] `1) `2 is set
[b,a] `2 is set
[[a,a],t19] `1 is set
([[a,a],t19] `1) `1 is set
[OA,AB] `1 is set
cod MA is Element of the carrier of (A,B)
the Target of (A,B) . MA is Element of the carrier of (A,B)
dom a is Element of the carrier of (A,B)
the Source of (A,B) . a is Element of the carrier of (A,B)
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of A is non empty set
the carrier of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
(A,B) is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier' of (A,B) is non empty set
OA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
AB is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[OA,AB] is non empty V15() set
{OA,AB} is non empty finite set
{OA} is non empty trivial finite set
{{OA,AB},{OA}} is non empty finite V35() set
MA is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[AB,MA] is non empty V15() set
{AB,MA} is non empty finite set
{AB} is non empty trivial finite set
{{AB,MA},{AB}} is non empty finite V35() set
[OA,MA] is non empty V15() set
{OA,MA} is non empty finite set
{{OA,MA},{OA}} is non empty finite V35() set
MB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,AB)
[[OA,AB],MB] is non empty V15() set
{[OA,AB],MB} is non empty finite set
{[OA,AB]} is Relation-like non empty trivial finite set
{{[OA,AB],MB},{[OA,AB]}} is non empty finite V35() set
OB is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,AB,MA)
[[AB,MA],OB] is non empty V15() set
{[AB,MA],OB} is non empty finite set
{[AB,MA]} is Relation-like non empty trivial finite set
{{[AB,MA],OB},{[AB,MA]}} is non empty finite V35() set
(A,B,OA,AB,MA,MB,OB) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,OA,MA)
[[OA,MA],(A,B,OA,AB,MA,MB,OB)] is non empty V15() set
{[OA,MA],(A,B,OA,AB,MA,MB,OB)} is non empty finite set
{[OA,MA]} is Relation-like non empty trivial finite set
{{[OA,MA],(A,B,OA,AB,MA,MB,OB)},{[OA,MA]}} is non empty finite V35() set
MB is Element of the carrier' of (A,B)
MA is Element of the carrier' of (A,B)
MA (*) MB is Element of the carrier' of (A,B)
[MA,MB] is non empty V15() Element of the carrier' of [:(A,B),(A,B):]
[:(A,B),(A,B):] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of (A,B) is non empty set
[: the carrier of (A,B), the carrier of (A,B):] is Relation-like non empty set
[: the carrier' of (A,B), the carrier' of (A,B):] is Relation-like non empty set
the Source of (A,B) is Relation-like the carrier' of (A,B) -defined the carrier of (A,B) -valued Function-like quasi_total Element of bool [: the carrier' of (A,B), the carrier of (A,B):]
[: the carrier' of (A,B), the carrier of (A,B):] is Relation-like non empty set
bool [: the carrier' of (A,B), the carrier of (A,B):] is non empty set
[: the Source of (A,B), the Source of (A,B):] is Relation-like [: the carrier' of (A,B), the carrier' of (A,B):] -defined [: the carrier of (A,B), the carrier of (A,B):] -valued Function-like quasi_total Element of bool [:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier of (A,B), the carrier of (A,B):]:]
[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier of (A,B), the carrier of (A,B):]:] is Relation-like non empty set
bool [:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier of (A,B), the carrier of (A,B):]:] is non empty set
the Target of (A,B) is Relation-like the carrier' of (A,B) -defined the carrier of (A,B) -valued Function-like quasi_total Element of bool [: the carrier' of (A,B), the carrier of (A,B):]
[: the Target of (A,B), the Target of (A,B):] is Relation-like [: the carrier' of (A,B), the carrier' of (A,B):] -defined [: the carrier of (A,B), the carrier of (A,B):] -valued Function-like quasi_total Element of bool [:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier of (A,B), the carrier of (A,B):]:]
the Comp of (A,B) is Relation-like [: the carrier' of (A,B), the carrier' of (A,B):] -defined the carrier' of (A,B) -valued Function-like Element of bool [:[: the carrier' of (A,B), the carrier' of (A,B):], the carrier' of (A,B):]
[:[: the carrier' of (A,B), the carrier' of (A,B):], the carrier' of (A,B):] is Relation-like non empty set
bool [:[: the carrier' of (A,B), the carrier' of (A,B):], the carrier' of (A,B):] is non empty set
|: the Comp of (A,B), the Comp of (A,B):| is Relation-like [:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:] -defined [: the carrier' of (A,B), the carrier' of (A,B):] -valued Function-like Element of bool [:[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:],[: the carrier' of (A,B), the carrier' of (A,B):]:]
[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:] is Relation-like non empty set
[:[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:],[: the carrier' of (A,B), the carrier' of (A,B):]:] is Relation-like non empty set
bool [:[:[: the carrier' of (A,B), the carrier' of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):]:],[: the carrier' of (A,B), the carrier' of (A,B):]:] is non empty set
CatStr(# [: the carrier of (A,B), the carrier of (A,B):],[: the carrier' of (A,B), the carrier' of (A,B):],[: the Source of (A,B), the Source of (A,B):],[: the Target of (A,B), the Target of (A,B):],|: the Comp of (A,B), the Comp of (A,B):| #) is non empty non void V55() strict CatStr
the carrier' of [:(A,B),(A,B):] is non empty set
{MA,MB} is non empty finite set
{MA} is non empty trivial finite set
{{MA,MB},{MA}} is non empty finite V35() set
proj1 the Comp of (A,B) is Relation-like set
the Comp of (A,B) . (MA,MB) is set
[MA,MB] is non empty V15() set
the Comp of (A,B) . [MA,MB] is set
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
b is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
a is Relation-like the carrier' of A -defined the carrier' of B -valued Function-like quasi_total Functor of A,B
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
a is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,b)
[[a,b],a] is non empty V15() set
{[a,b],a} is non empty finite set
{[a,b]} is Relation-like non empty trivial finite set
{{[a,b],a},{[a,b]}} is non empty finite V35() set
[b,a] is non empty V15() set
{b,a} is non empty finite set
{b} is non empty trivial finite set
{{b,a},{b}} is non empty finite V35() set
t19 is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,b,a)
[[b,a],t19] is non empty V15() set
{[b,a],t19} is non empty finite set
{[b,a]} is Relation-like non empty trivial finite set
{{[b,a],t19},{[b,a]}} is non empty finite V35() set
[a,a] is non empty V15() set
{a,a} is non empty finite set
{{a,a},{a}} is non empty finite V35() set
(A,B,a,b,a,a,t19) is Relation-like the carrier of A -defined the carrier' of B -valued Function-like quasi_total (A,B,a,a)
[[a,a],(A,B,a,b,a,a,t19)] is non empty V15() set
{[a,a],(A,B,a,b,a,a,t19)} is non empty finite set
{[a,a]} is Relation-like non empty trivial finite set
{{[a,a],(A,B,a,b,a,a,t19)},{[a,a]}} is non empty finite V35() set
the set is set
1Cat ( the set , the set ) is non empty trivial finite non void 1 -element V55() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{ the set } is non empty trivial finite set
K241( the set , the set ) is Relation-like { the set } -defined { the set } -valued Function-like quasi_total finite Element of bool [:{ the set },{ the set }:]
[:{ the set },{ the set }:] is Relation-like non empty finite set
bool [:{ the set },{ the set }:] is non empty finite V35() set
K240( the set , the set , the set ) is Relation-like [:{ the set },{ the set }:] -defined { the set } -valued Function-like quasi_total finite Element of bool [:[:{ the set },{ the set }:],{ the set }:]
[:[:{ the set },{ the set }:],{ the set }:] is Relation-like non empty finite set
bool [:[:{ the set },{ the set }:],{ the set }:] is non empty finite V35() set
CatStr(# { the set },{ the set },K241( the set , the set ),K241( the set , the set ),K240( the set , the set , the set ) #) is non empty non void V55() strict CatStr
the carrier' of (1Cat ( the set , the set )) is non empty trivial finite set
the carrier of (1Cat ( the set , the set )) is non empty trivial finite set
B is Element of the carrier' of (1Cat ( the set , the set ))
the Element of the carrier of (1Cat ( the set , the set )) is Element of the carrier of (1Cat ( the set , the set ))
id the Element of the carrier of (1Cat ( the set , the set )) is Morphism of the Element of the carrier of (1Cat ( the set , the set )), the Element of the carrier of (1Cat ( the set , the set ))
A is non empty non void V55() Category-like transitive associative reflexive with_identities () CatStr
the carrier of A is non empty set
B is Element of the carrier of A
Hom (B,B) is non empty Element of bool the carrier' of A
the carrier' of A is non empty set
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = B & cod b₁ = B ) } is set
id B is Morphism of B,B
{(id B)} is non empty trivial finite set
OA is Morphism of B,B
AB is Element of the carrier of A
id AB is Morphism of AB,AB
dom OA is Element of the carrier of A
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of A . OA is Element of the carrier of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
B is Element of the carrier of A
Hom (B,B) is non empty Element of bool the carrier' of A
the carrier' of A is non empty set
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = B & cod b₁ = B ) } is set
id B is Morphism of B,B
{(id B)} is non empty trivial finite set
OA is finite set
AB is finite set
card AB is Element of K144()
B is Element of the carrier of A
OA is Element of the carrier of A
Hom (B,OA) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = B & cod b₁ = OA ) } is set
the Element of Hom (B,OA) is Element of Hom (B,OA)
MA is Element of the carrier' of A
MB is Element of the carrier of A
id MB is Morphism of MB,MB
Hom (MB,MB) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = MB & cod b₁ = MB ) } is set
the carrier' of A is non empty set
B is Element of the carrier' of A
dom B is Element of the carrier of A
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of A . B is Element of the carrier of A
Hom ((dom B),(dom B)) is non empty Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom B & cod b₁ = dom B ) } is set
OA is finite set
card OA is Element of K144()
OA is set
{OA} is non empty trivial finite set
id (dom B) is Morphism of dom B, dom B
cod B is Element of the carrier of A
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of A . B is Element of the carrier of A
Hom ((dom B),(cod B)) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = dom B & cod b₁ = cod B ) } is set
A is set
B is set
1Cat (A,B) is non empty trivial finite non void 1 -element V55() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{A} is non empty trivial finite set
{B} is non empty trivial finite set
K241(B,A) is Relation-like {B} -defined {A} -valued Function-like quasi_total finite Element of bool [:{B},{A}:]
[:{B},{A}:] is Relation-like non empty finite set
bool [:{B},{A}:] is non empty finite V35() set
K240(B,B,B) is Relation-like [:{B},{B}:] -defined {B} -valued Function-like quasi_total finite Element of bool [:[:{B},{B}:],{B}:]
[:{B},{B}:] is Relation-like non empty finite set
[:[:{B},{B}:],{B}:] is Relation-like non empty finite set
bool [:[:{B},{B}:],{B}:] is non empty finite V35() set
CatStr(# {A},{B},K241(B,A),K241(B,A),K240(B,B,B) #) is non empty non void V55() strict CatStr
the carrier' of (1Cat (A,B)) is non empty trivial finite set
the carrier of (1Cat (A,B)) is non empty trivial finite set
OA is Element of the carrier' of (1Cat (A,B))
the Element of the carrier of (1Cat (A,B)) is Element of the carrier of (1Cat (A,B))
id the Element of the carrier of (1Cat (A,B)) is Morphism of the Element of the carrier of (1Cat (A,B)), the Element of the carrier of (1Cat (A,B))
A is non empty non void V55() Category-like transitive associative reflexive with_identities () CatStr
B is non empty non void V55() Category-like transitive associative reflexive with_identities Subcategory of A
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Element of the carrier' of B
the carrier' of A is non empty set
dom OA 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 quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is Relation-like non empty set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of B . OA is Element of the carrier of B
id (dom OA) is Morphism of dom OA, dom OA
the carrier of A is non empty set
AB is Element of the carrier' of A
MA is Element of the carrier of A
id MA is Morphism of MA,MA
dom AB is Element of the carrier of A
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of A . AB is Element of the carrier of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[:A,B:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is Relation-like non empty set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is Relation-like non empty set
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is Relation-like non empty set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is Relation-like non empty set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is Relation-like non empty set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
|: the Comp of A, the Comp of B:| is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is Relation-like non empty set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is Relation-like non empty set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],|: the Comp of A, the Comp of B:| #) is non empty non void V55() strict CatStr
the carrier' of [:A,B:] is non empty set
the carrier of [:A,B:] is non empty set
OA is Element of the carrier' of [:A,B:]
AB is Element of the carrier' of A
MA is Element of the carrier' of B
[AB,MA] is non empty V15() Element of the carrier' of [:A,B:]
{AB,MA} is non empty finite set
{AB} is non empty trivial finite set
{{AB,MA},{AB}} is non empty finite V35() set
MB is Element of the carrier of B
id MB is Morphism of MB,MB
OB is Element of the carrier of A
id OB is Morphism of OB,OB
[OB,MB] is non empty V15() Element of the carrier of [:A,B:]
{OB,MB} is non empty finite set
{OB} is non empty trivial finite set
{{OB,MB},{OB}} is non empty finite V35() set
id [OB,MB] is Morphism of [OB,MB],[OB,MB]
A is non empty non void V55() Category-like transitive associative reflexive with_identities () CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
AB is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
MA is Element of the carrier' of B
dom MA is Element of the carrier of B
the carrier of B is non empty set
the Source of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is Relation-like non empty set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of B . MA is Element of the carrier of B
OA . (dom MA) is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . (dom MA) is Element of the carrier of A
AB . (dom MA) is Element of the carrier of A
Obj AB is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
(Obj AB) . (dom MA) is Element of the carrier of A
Hom ((OA . (dom MA)),(AB . (dom MA))) is Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = OA . (dom MA) & cod b₁ = AB . (dom MA) ) } is set
cod MA 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 quasi_total Element of bool [: the carrier' of B, the carrier of B:]
the Target of B . MA is Element of the carrier of B
Hom ((dom MA),(cod MA)) is Element of bool the carrier' of B
bool the carrier' of B is non empty set
{ b₁ where b₁ is Element of the carrier' of B : ( dom b₁ = dom MA & cod b₁ = cod MA ) } is set
OA . (cod MA) is Element of the carrier of A
(Obj OA) . (cod MA) is Element of the carrier of A
Hom ((OA . (dom MA)),(OA . (cod MA))) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = OA . (dom MA) & cod b₁ = OA . (cod MA) ) } is set
id (OA . (dom MA)) is Morphism of OA . (dom MA),OA . (dom MA)
{(id (OA . (dom MA)))} is non empty trivial finite set
AB . (cod MA) is Element of the carrier of A
(Obj AB) . (cod MA) is Element of the carrier of A
Hom ((AB . (dom MA)),(AB . (cod MA))) is Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = AB . (dom MA) & cod b₁ = AB . (cod MA) ) } is set
id (AB . (dom MA)) is Morphism of AB . (dom MA),AB . (dom MA)
{(id (AB . (dom MA)))} is non empty trivial finite set
OA . MA is Element of the carrier' of A
AB . MA is Element of the carrier' of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities () CatStr
the carrier' of A is non empty set
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier' of B is non empty set
the carrier of B is non empty set
OA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
(B,A,OA) is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,OA)
AB is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,OA,OA)
MA is Element of the carrier of B
OA . MA is Element of the carrier of A
the carrier of A is non empty set
Obj OA is Relation-like the carrier of B -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of B, the carrier of A:]
[: the carrier of B, the carrier of A:] is Relation-like non empty set
bool [: the carrier of B, the carrier of A:] is non empty set
(Obj OA) . MA is Element of the carrier of A
Hom ((OA . MA),(OA . MA)) is non empty Element of bool the carrier' of A
bool the carrier' of A is non empty set
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = OA . MA & cod b₁ = OA . MA ) } is set
id (OA . MA) is Morphism of OA . MA,OA . MA
{(id (OA . MA))} is non empty trivial finite set
(B,A,OA,OA,AB,MA) is Morphism of OA . MA,OA . MA
(B,A,OA,OA,(B,A,OA),MA) is Morphism of OA . MA,OA . MA
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
(B,A) is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
the carrier' of (B,A) is non empty set
the carrier of (B,A) is non empty set
OA is Element of the carrier' of (B,A)
(B,A) is non empty (B,A)
the carrier' of B is non empty set
the carrier' of A is non empty set
the carrier of B is non empty set
AB is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
MA is Relation-like the carrier' of B -defined the carrier' of A -valued Function-like quasi_total Functor of B,A
[AB,MA] is non empty V15() set
{AB,MA} is non empty finite set
{AB} is non empty trivial finite set
{{AB,MA},{AB}} is non empty finite V35() set
MB is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,AB,MA)
[[AB,MA],MB] is non empty V15() set
{[AB,MA],MB} is non empty finite set
{[AB,MA]} is Relation-like non empty trivial finite set
{{[AB,MA],MB},{[AB,MA]}} is non empty finite V35() set
Funct (B,A) is non empty FUNCTOR-DOMAIN of B,A
OB is Element of the carrier of (B,A)
id OB is Morphism of OB,OB
(B,A,AB) is Relation-like the carrier of B -defined the carrier' of A -valued Function-like quasi_total (B,A,AB,AB)
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
the Element of the carrier of A is Element of the carrier of A
id the Element of the carrier of A is Morphism of the Element of the carrier of A, the Element of the carrier of A
1Cat ( the Element of the carrier of A,(id the Element of the carrier of A)) is non empty trivial finite non void 1 -element V55() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{ the Element of the carrier of A} is non empty trivial finite set
{(id the Element of the carrier of A)} is non empty trivial finite set
K241((id the Element of the carrier of A), the Element of the carrier of A) is Relation-like {(id the Element of the carrier of A)} -defined { the Element of the carrier of A} -valued Function-like quasi_total finite Element of bool [:{(id the Element of the carrier of A)},{ the Element of the carrier of A}:]
[:{(id the Element of the carrier of A)},{ the Element of the carrier of A}:] is Relation-like non empty finite set
bool [:{(id the Element of the carrier of A)},{ the Element of the carrier of A}:] is non empty finite V35() set
K240((id the Element of the carrier of A),(id the Element of the carrier of A),(id the Element of the carrier of A)) is Relation-like [:{(id the Element of the carrier of A)},{(id the Element of the carrier of A)}:] -defined {(id the Element of the carrier of A)} -valued Function-like quasi_total finite Element of bool [:[:{(id the Element of the carrier of A)},{(id the Element of the carrier of A)}:],{(id the Element of the carrier of A)}:]
[:{(id the Element of the carrier of A)},{(id the Element of the carrier of A)}:] is Relation-like non empty finite set
[:[:{(id the Element of the carrier of A)},{(id the Element of the carrier of A)}:],{(id the Element of the carrier of A)}:] is Relation-like non empty finite set
bool [:[:{(id the Element of the carrier of A)},{(id the Element of the carrier of A)}:],{(id the Element of the carrier of A)}:] is non empty finite V35() set
CatStr(# { the Element of the carrier of A},{(id the Element of the carrier of A)},K241((id the Element of the carrier of A), the Element of the carrier of A),K241((id the Element of the carrier of A), the Element of the carrier of A),K240((id the Element of the carrier of A),(id the Element of the carrier of A),(id the Element of the carrier of A)) #) is non empty non void V55() strict CatStr
OA is non empty non void V55() Category-like transitive associative reflexive with_identities Subcategory of A
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
{ (id b₁) where b₁ is Element of the carrier of A : verum } is set
the carrier' of A is non empty set
{ H₁(b₁) where b₁ is Element of the carrier of A : S₁[b₁] } is set
{ H₁(b₁) where b₁ is Element of the carrier of A : S₂[b₁] } is set
{ H₁(b₁) where b₁ is Element of the carrier of A : ( H₁(b₁) in the carrier' of A & S₁[b₁] ) } is set
{ H₁(b₁) where b₁ is Element of the carrier of A : S₃[b₁] } is set
the Element of the carrier of A is Element of the carrier of A
id the Element of the carrier of A is Morphism of the Element of the carrier of A, the Element of the carrier of A
OB is Element of the carrier of A
id OB is Morphism of OB,OB
MB is Element of the carrier of A
id MB is Morphism of MB,MB
OB is Element of the carrier of A
id OB is Morphism of OB,OB
MB is Element of the carrier of A
id MB is Morphism of MB,MB
bool the carrier' of A is non empty set
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
OB is non empty Element of bool the carrier' of A
the Comp of A || OB is Relation-like Function-like set
[:OB,OB:] is Relation-like non empty set
the Comp of A | [:OB,OB:] is Relation-like [:OB,OB:] -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
proj2 ( the Comp of A || OB) is set
MB is set
proj1 ( the Comp of A || OB) is set
MA is set
( the Comp of A || OB) . MA is set
proj1 the Comp of A is Relation-like set
[:OB,OB:] is Relation-like the carrier' of A -defined the carrier' of A -valued non empty Element of bool [: the carrier' of A, the carrier' of A:]
bool [: the carrier' of A, the carrier' of A:] is non empty set
(proj1 the Comp of A) /\ [:OB,OB:] is Relation-like the carrier' of A -defined the carrier' of A -valued Element of bool [: the carrier' of A, the carrier' of A:]
a is set
b is set
[a,b] is non empty V15() set
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
a is Element of the carrier of A
id a is Morphism of a,a
Hom (a,a) is non empty Element of bool the carrier' of A
{ b₁ where b₁ is Element of the carrier' of A : ( dom b₁ = a & cod b₁ = a ) } is set
a is Element of the carrier of A
id a is Morphism of a,a
dom (id a) is Element of the carrier of A
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of A . (id a) is Element of the carrier of A
cod (id a) is Element of the carrier of A
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of A . (id a) is Element of the carrier of A
(id a) * (id a) is Morphism of a,a
(id a) (*) (id a) is Element of the carrier' of A
the Comp of A . ((id a),(id a)) is set
[(id a),(id a)] is non empty V15() set
{(id a),(id a)} is non empty finite set
{(id a)} is non empty trivial finite set
{{(id a),(id a)},{(id a)}} is non empty finite V35() set
the Comp of A . [(id a),(id a)] is set
[:[:OB,OB:], the carrier' of A:] is Relation-like non empty set
bool [:[:OB,OB:], the carrier' of A:] is non empty set
[:[:OB,OB:],OB:] is Relation-like non empty set
bool [:[:OB,OB:],OB:] is non empty set
MA is Element of the carrier of A
id MA is Morphism of MA,MA
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
( the carrier' of A, the carrier of A, the Source of A,OB) is Relation-like OB -defined the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [:OB, the carrier of A:]
[:OB, the carrier of A:] is Relation-like non empty set
bool [:OB, the carrier of A:] is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
( the carrier' of A, the carrier of A, the Target of A,OB) is Relation-like OB -defined the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [:OB, the carrier of A:]
MB is Relation-like [:OB,OB:] -defined OB -valued Function-like Element of bool [:[:OB,OB:],OB:]
CatStr(# the carrier of A,OB,( the carrier' of A, the carrier of A, the Source of A,OB),( the carrier' of A, the carrier of A, the Target of A,OB),MB #) is non empty non void V55() strict CatStr
MA is non empty non void V55() Category-like transitive associative reflexive with_identities Subcategory of A
the carrier' of MA is non empty set
a is Element of the carrier' of MA
b is Element of the carrier of A
id b is Morphism of b,b
the carrier of MA is non empty set
a is Element of the carrier of MA
a is Element of the carrier of MA
id a is Morphism of a,a
a is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of A
the carrier of a is non empty set
the carrier' of a is non empty set
B is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of A
the carrier of B is non empty set
the carrier' of B is non empty set
OA is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of A
the carrier of OA is non empty set
the carrier' of OA is non empty set
the Target of OA is Relation-like the carrier' of OA -defined the carrier of OA -valued Function-like quasi_total Element of bool [: the carrier' of OA, the carrier of OA:]
[: the carrier' of OA, the carrier of OA:] is Relation-like non empty set
bool [: the carrier' of OA, the carrier of OA:] is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the carrier' of A is non empty set
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Target of A | the carrier' of B is Relation-like the carrier' of B -defined the carrier' of A -defined the carrier of A -valued set
the Comp of OA is Relation-like [: the carrier' of OA, the carrier' of OA:] -defined the carrier' of OA -valued Function-like Element of bool [:[: the carrier' of OA, the carrier' of OA:], the carrier' of OA:]
[: the carrier' of OA, the carrier' of OA:] is Relation-like non empty set
[:[: the carrier' of OA, the carrier' of OA:], the carrier' of OA:] is Relation-like non empty set
bool [:[: the carrier' of OA, the carrier' of OA:], the carrier' of OA:] is non empty set
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of A || the carrier' of B is Relation-like Function-like set
[: the carrier' of B, the carrier' of B:] is Relation-like non empty set
the Comp of A | [: the carrier' of B, the carrier' of B:] is Relation-like [: the carrier' of B, the carrier' of B:] -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
the Source of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is Relation-like non empty set
bool [: the carrier' of B, the carrier of B:] is non empty set
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Source of A | the carrier' of B is Relation-like the carrier' of B -defined the carrier' of A -defined the carrier of A -valued 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 Relation-like non empty set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
the Target of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
A is non empty non void V55() strict Category-like transitive associative reflexive with_identities CatStr
(A) is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of A
the carrier' of A is non empty set
the carrier of A is non empty set
{ (id b₁) where b₁ is Element of the carrier of A : verum } is set
B is set
OA is Element of the carrier of A
id OA is Morphism of OA,OA
the carrier' of (A) is non empty set
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
(A) is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of A
((A)) is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of (A)
A is set
B is set
1Cat (A,B) is non empty trivial finite non void 1 -element V55() trivial' strict Category-like transitive associative reflexive with_identities CatStr
{A} is non empty trivial finite set
{B} is non empty trivial finite set
K241(B,A) is Relation-like {B} -defined {A} -valued Function-like quasi_total finite Element of bool [:{B},{A}:]
[:{B},{A}:] is Relation-like non empty finite set
bool [:{B},{A}:] is non empty finite V35() set
K240(B,B,B) is Relation-like [:{B},{B}:] -defined {B} -valued Function-like quasi_total finite Element of bool [:[:{B},{B}:],{B}:]
[:{B},{B}:] is Relation-like non empty finite set
[:[:{B},{B}:],{B}:] is Relation-like non empty finite set
bool [:[:{B},{B}:],{B}:] is non empty finite V35() set
CatStr(# {A},{B},K241(B,A),K241(B,A),K240(B,B,B) #) is non empty non void V55() strict CatStr
((1Cat (A,B))) is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of 1Cat (A,B)
A is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
(A) is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of A
B is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
[:A,B:] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of A is non empty set
the carrier of B is non empty set
[: the carrier of A, the carrier of B:] is Relation-like non empty set
the carrier' of A is non empty set
the carrier' of B is non empty set
[: the carrier' of A, the carrier' of B:] is Relation-like non empty set
the Source of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
[: the carrier' of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier' of A, the carrier of A:] is non empty set
the Source of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the carrier' of B, the carrier of B:] is Relation-like non empty set
bool [: the carrier' of B, the carrier of B:] is non empty set
[: the Source of A, the Source of B:] is Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:] is non empty set
the Target of A is Relation-like the carrier' of A -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier' of A, the carrier of A:]
the Target of B is Relation-like the carrier' of B -defined the carrier of B -valued Function-like quasi_total Element of bool [: the carrier' of B, the carrier of B:]
[: the Target of A, the Target of B:] is Relation-like [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:]:]
the Comp of A is Relation-like [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued Function-like Element of bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:]
[: the carrier' of A, the carrier' of A:] is Relation-like non empty set
[:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is Relation-like non empty set
bool [:[: the carrier' of A, the carrier' of A:], the carrier' of A:] is non empty set
the Comp of B is Relation-like [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued Function-like Element of bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:]
[: the carrier' of B, the carrier' of B:] is Relation-like non empty set
[:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is Relation-like non empty set
bool [:[: the carrier' of B, the carrier' of B:], the carrier' of B:] is non empty set
|: the Comp of A, the Comp of B:| is Relation-like [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued Function-like Element of bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:]
[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] is Relation-like non empty set
[:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is Relation-like non empty set
bool [:[:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:],[: the carrier' of A, the carrier' of B:]:] is non empty set
CatStr(# [: the carrier of A, the carrier of B:],[: the carrier' of A, the carrier' of B:],[: the Source of A, the Source of B:],[: the Target of A, the Target of B:],|: the Comp of A, the Comp of B:| #) is non empty non void V55() strict CatStr
([:A,B:]) is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of [:A,B:]
(B) is non empty non void V55() strict Category-like transitive associative reflexive with_identities () Subcategory of B
[:(A),(B):] is non empty non void V55() Category-like transitive associative reflexive with_identities CatStr
the carrier of (A) is non empty set
the carrier of (B) is non empty set
[: the carrier of (A), the carrier of (B):] is Relation-like non empty set
the carrier' of (A) is non empty set
the carrier' of (B) is non empty set
[: the carrier' of (A), the carrier' of (B):] is Relation-like non empty set
the Source of (A) is Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like quasi_total Element of bool [: the carrier' of (A), the carrier of (A):]
[: the carrier' of (A), the carrier of (A):] is Relation-like non empty set
bool [: the carrier' of (A), the carrier of (A):] is non empty set
the Source of (B) is Relation-like the carrier' of (B) -defined the carrier of (B) -valued Function-like quasi_total Element of bool [: the carrier' of (B), the carrier of (B):]
[: the carrier' of (B), the carrier of (B):] is Relation-like non empty set
bool [: the carrier' of (B), the carrier of (B):] is non empty set
[: the Source of (A), the Source of (B):] is Relation-like [: the carrier' of (A), the carrier' of (B):] -defined [: the carrier of (A), the carrier of (B):] -valued Function-like quasi_total Element of bool [:[: the carrier' of (A), the carrier' of (B):],[: the carrier of (A), the carrier of (B):]:]
[:[: the carrier' of (A), the carrier' of (B):],[: the carrier of (A), the carrier of (B):]:] is Relation-like non empty set
bool [:[: the carrier' of (A), the carrier' of (B):],[: the carrier of (A), the carrier of (B):]:] is non empty set
the Target of (A) is Relation-like the carrier' of (A) -defined the carrier of (A) -valued Function-like quasi_total Element of bool [: the carrier' of (A), the carrier of (A):]
the Target of (B) is Relation-like the carrier' of (B) -defined the carrier of (B) -valued Function-like quasi_total Element of bool [: the carrier' of (B), the carrier of (B):]
[: the Target of (A), the Target of (B):] is Relation-like [: the carrier' of (A), the carrier' of (B):] -defined [: the carrier of (A), the carrier of (B):] -valued Function-like quasi_total Element of bool [:[: the carrier' of (A), the carrier' of (B):],[: the carrier of (A), the carrier of (B):]:]
the Comp of (A) is Relation-like [: the carrier' of (A), the carrier' of (A):] -defined the carrier' of (A) -valued Function-like Element of bool [:[: the carrier' of (A), the carrier' of (A):], the carrier' of (A):]
[: the carrier' of (A), the carrier' of (A):] is Relation-like non empty set
[:[: the carrier' of (A), the carrier' of (A):], the carrier' of (A):] is Relation-like non empty set
bool [:[: the carrier' of (A), the carrier' of (A):], the carrier' of (A):] is non empty set
the Comp of (B) is Relation-like [: the carrier' of (B), the carrier' of (B):] -defined the carrier' of (B) -valued Function-like Element of bool [:[: the carrier' of (B), the carrier' of (B):], the carrier' of (B):]
[: the carrier' of (B), the carrier' of (B):] is Relation-like non empty set
[:[: the carrier' of (B), the carrier' of (B):], the carrier' of (B):] is Relation-like non empty set
bool [:[: the carrier' of (B), the carrier' of (B):], the carrier' of (B):] is non empty set
|: the Comp of (A), the Comp of (B):| is Relation-like [:[: the carrier' of (A), the carrier' of (B):],[: the carrier' of (A), the carrier' of (B):]:] -defined [: the carrier' of (A), the carrier' of (B):] -valued Function-like Element of bool [:[:[: the carrier' of (A), the carrier' of (B):],[: the carrier' of (A), the carrier' of (B):]:],[: the carrier' of (A), the carrier' of (B):]:]
[:[: the carrier' of (A), the carrier' of (B):],[: the carrier' of (A), the carrier' of (B):]:] is Relation-like non empty set
[:[:[: the carrier' of (A), the carrier' of (B):],[: the carrier' of (A), the carrier' of (B):]:],[: the carrier' of (A), the carrier' of (B):]:] is Relation-like non empty set
bool [:[:[: the carrier' of (A), the carrier' of (B):],[: the carrier' of (A), the carrier' of (B):]:],[: the carrier' of (A), the carrier' of (B):]:] is non empty set
CatStr(# [: the carrier of (A), the carrier of (B):],[: the carrier' of (A), the carrier' of (B):],[: the Source of (A), the Source of (B):],[: the Target of (A), the Target of (B):],|: the Comp of (A), the Comp of (B):| #) is non empty non void V55() strict CatStr
bool the carrier of A is non empty set
the carrier of [:A,B:] is non empty set
{ (id b₁) where b₁ is Element of the carrier of [:A,B:] : verum } is set
{ (id b₁) where b₁ is Element of the carrier of A : verum } is set
{ (id b₁) where b₁ is Element of the carrier of B : verum } is set
[: { (id b₁) where b₁ is Element of the carrier of A : verum } , { (id b₁) where b₁ is Element of the carrier of B : verum } :] is Relation-like set
OB is set
MB is Element of the carrier of [:A,B:]
id MB is Morphism of MB,MB
MA is Element of the carrier of A
a is Element of the carrier of B
[MA,a] is non empty V15() Element of the carrier of [:A,B:]
{MA,a} is non empty finite set
{MA} is non empty trivial finite set
{{MA,a},{MA}} is non empty finite V35() set
id a is Morphism of a,a
id MA is Morphism of MA,MA
[(id MA),(id a)] is non empty V15() Element of the carrier' of [:A,B:]
the carrier' of [:A,B:] is non empty set
{(id MA),(id a)} is non empty finite set
{(id MA)} is non empty trivial finite set
{{(id MA),(id a)},{(id MA)}} is non empty finite V35() set
OB is set
MB is set
MA is set
[MB,MA] is non empty V15() set
{MB,MA} is non empty finite set
{MB} is non empty trivial finite set
{{MB,MA},{MB}} is non empty finite V35() set
a is Element of the carrier of A
id a is Morphism of a,a
b is Element of the carrier of B
id b is Morphism of b,b
[a,b] is non empty V15() Element of the carrier of [:A,B:]
{a,b} is non empty finite set
{a} is non empty trivial finite set
{{a,b},{a}} is non empty finite V35() set
id [a,b] is Morphism of [a,b],[a,b]
[(id a),(id b)] is non empty V15() Element of the carrier' of [:A,B:]
the carrier' of [:A,B:] is non empty set
{(id a),(id b)} is non empty finite set
{(id a)} is non empty trivial finite set
{{(id a),(id b)},{(id a)}} is non empty finite V35() set
bool the carrier of B is non empty set
bool the carrier' of B is non empty set
bool the carrier' of A is non empty set
the carrier of ([:A,B:]) is non empty set
the Target of B | the carrier' of (B) is Relation-like the carrier' of (B) -defined the carrier' of B -defined the carrier of B -valued set
the Source of B | the carrier' of (B) is Relation-like the carrier' of (B) -defined the carrier' of B -defined the carrier of B -valued set
the carrier' of ([:A,B:]) is non empty set
the Source of A | the carrier' of (A) is Relation-like the carrier' of (A) -defined the carrier' of A -defined the carrier of A -valued set
MA is non empty Element of bool the carrier' of A
MB is non empty Element of bool the carrier' of B
[:MA,MB:] is Relation-like the carrier' of A -defined the carrier' of B -valued non empty Element of bool [: the carrier' of A, the carrier' of B:]
bool [: the carrier' of A, the carrier' of B:] is non empty set
([: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:],[: the Source of A, the Source of B:],[:MA,MB:]) is Relation-like [:MA,MB:] -defined [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like quasi_total Element of bool [:[:MA,MB:],[: the carrier of A, the carrier of B:]:]
[:[:MA,MB:],[: the carrier of A, the carrier of B:]:] is Relation-like non empty set
bool [:[:MA,MB:],[: the carrier of A, the carrier of B:]:] is non empty set
the Source of ([:A,B:]) is Relation-like the carrier' of ([:A,B:]) -defined the carrier of ([:A,B:]) -valued Function-like quasi_total Element of bool [: the carrier' of ([:A,B:]), the carrier of ([:A,B:]):]
[: the carrier' of ([:A,B:]), the carrier of ([:A,B:]):] is Relation-like non empty set
bool [: the carrier' of ([:A,B:]), the carrier of ([:A,B:]):] is non empty set
the Target of A | the carrier' of (A) is Relation-like the carrier' of (A) -defined the carrier' of A -defined the carrier of A -valued set
([: the carrier' of A, the carrier' of B:],[: the carrier of A, the carrier of B:],[: the Target of A, the Target of B:],[:MA,MB:]) is Relation-like [:MA,MB:] -defined [: the carrier' of A, the carrier' of B:] -defined [: the carrier of A, the carrier of B:] -valued Function-like quasi_total Element of bool [:[:MA,MB:],[: the carrier of A, the carrier of B:]:]
the Target of ([:A,B:]) is Relation-like the carrier' of ([:A,B:]) -defined the carrier of ([:A,B:]) -valued Function-like quasi_total Element of bool [: the carrier' of ([:A,B:]), the carrier of ([:A,B:]):]
the Comp of A || MA is Relation-like Function-like set
[:MA,MA:] is Relation-like non empty set
the Comp of A | [:MA,MA:] is Relation-like [:MA,MA:] -defined [: the carrier' of A, the carrier' of A:] -defined the carrier' of A -valued set
the Comp of B || MB is Relation-like Function-like set
[:MB,MB:] is Relation-like non empty set
the Comp of B | [:MB,MB:] is Relation-like [:MB,MB:] -defined [: the carrier' of B, the carrier' of B:] -defined the carrier' of B -valued set
|: the Comp of A, the Comp of B:| || [:MA,MB:] is Relation-like Function-like set
[:[:MA,MB:],[:MA,MB:]:] is Relation-like non empty set
|: the Comp of A, the Comp of B:| | [:[:MA,MB:],[:MA,MB:]:] is Relation-like [:[:MA,MB:],[:MA,MB:]:] -defined [:[: the carrier' of A, the carrier' of B:],[: the carrier' of A, the carrier' of B:]:] -defined [: the carrier' of A, the carrier' of B:] -valued set
the Comp of ([:A,B:]) is Relation-like [: the carrier' of ([:A,B:]), the carrier' of ([:A,B:]):] -defined the carrier' of ([:A,B:]) -valued Function-like Element of bool [:[: the carrier' of ([:A,B:]), the carrier' of ([:A,B:]):], the carrier' of ([:A,B:]):]
[: the carrier' of ([:A,B:]), the carrier' of ([:A,B:]):] is Relation-like non empty set
[:[: the carrier' of ([:A,B:]), the carrier' of ([:A,B:]):], the carrier' of ([:A,B:]):] is Relation-like non empty set
bool [:[: the carrier' of ([:A,B:]), the carrier' of ([:A,B:]):], the carrier' of ([:A,B:]):] is non empty set