:: FUNCTOR0 semantic presentation

K141() is Element of bool K137()
K137() is set
bool K137() is non empty set
{} is set
the Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
1 is non empty set
{{},1} is set
K103() is set
bool K103() is non empty set
bool K141() is non empty set
F₁() is non empty set
F₂() is Relation-like Function-like set
{ [[b₁,b₂],F₅(b₁,b₂)] where b₁, b₂ is Element of F₁() : P₁[b₁,b₂] } is set
F₃() is Element of F₁()
F₄() is Element of F₁()
F₂() . (F₃(),F₄()) is set
[F₃(),F₄()] is V15() set
{F₃(),F₄()} is set
{F₃()} is set
{{F₃(),F₄()},{F₃()}} is set
F₂() . [F₃(),F₄()] is set
F₅(F₃(),F₄()) is set
[:F₁(),F₁():] is Relation-like non empty set
{ [b₁,H₁(b₁)] where b₁ is Element of [:F₁(),F₁():] : S₁[b₁] } is set
{ [b₁,F₅((b₁ `1),(b<sub>1</sub> `2))] where b₁ is Element of [:F₁(),F₁():] : P₁[b₁ `1 ,b<sub>1</sub> `2 ] } is set
A is set
B is Element of F₁()
A is Element of F₁()
[B,A] is V15() set
{B,A} is set
{B} is set
{{B,A},{B}} is set
F₅(B,A) is set
[[B,A],F₅(B,A)] is V15() set
{[B,A],F₅(B,A)} is set
{[B,A]} is Relation-like Function-like set
{{[B,A],F₅(B,A)},{[B,A]}} is set
B is Element of [:F₁(),F₁():]
B `1 is set
B `2 is set
A is set
B is Element of [:F₁(),F₁():]
B `1 is set
B `2 is set
F₅((B `1),(B `2)) is set
[B,F₅((B `1),(B `2))] is V15() set
{B,F₅((B `1),(B `2))} is set
{B} is set
{{B,F₅((B `1),(B `2))},{B}} is set
A is Element of F₁()
B is Element of F₁()
[A,B] is V15() set
{A,B} is set
{A} is set
{{A,B},{A}} is set
A is Element of [:F₁(),F₁():]
A `1 is set
A `2 is set
F₂() . A is set
F₅((A `1),(A `2)) is set
A is set
[:A,{}:] is Relation-like set
bool [:A,{}:] is non empty set
A is set
id A is Relation-like A -defined A -valued Function-like one-to-one V14(A) quasi_total Element of bool [:A,A:]
[:A,A:] is Relation-like set
bool [:A,A:] is non empty set
B is Relation-like A -defined Function-like V14(A) set
(id A) * B is Relation-like A -defined Function-like set
dom B is Element of bool A
bool A is non empty set
A is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
~ A is Relation-like Function-like Function-yielding V37() set
proj2 A is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty trivial Function-yielding V37() set
proj2 (~ A) is set
B is Relation-like Function-like set
[:A,B:] is Relation-like Function-like set
proj1 A is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
proj1 [:A,B:] is set
proj1 B is set
[:{},(proj1 B):] is Relation-like set
[:B,A:] is Relation-like Function-like set
proj1 A is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
proj1 [:B,A:] is set
proj1 B is set
[:(proj1 B),{}:] is Relation-like set
A is set
id A is Relation-like A -defined A -valued Function-like one-to-one V14(A) quasi_total Element of bool [:A,A:]
[:A,A:] is Relation-like set
bool [:A,A:] is non empty set
B is Relation-like Function-like set
B .: (id A) is set
~ B is Relation-like Function-like set
(~ B) .: (id A) is set
A is set
proj1 B is set
B is set
B . B is set
F is set
G is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
proj1 (~ B) is set
B . (F,G) is set
B . [F,G] is set
(~ B) . (F,G) is set
(~ B) . [F,G] is set
A is set
proj1 (~ B) is set
B is set
(~ B) . B is set
F is set
G is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
proj1 B is set
(~ B) . (F,G) is set
(~ B) . [F,G] is set
B . (F,G) is set
B . [F,G] is set
A is set
B is set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
[:B,B:] is Relation-like set
A is Relation-like A -defined B -valued Function-like quasi_total Element of bool [:A,B:]
[:A,A:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like quasi_total Element of bool [:[:A,A:],[:B,B:]:]
[:A,A:] is Relation-like set
[:[:A,A:],[:B,B:]:] is Relation-like set
bool [:[:A,A:],[:B,B:]:] is non empty set
rng [:A,A:] is Relation-like B -defined B -valued Element of bool [:B,B:]
bool [:B,B:] is non empty set
rng A is Element of bool B
bool B is non empty set
[:(rng A),(rng A):] is Relation-like B -defined B -valued Element of bool [:B,B:]
A is Relation-like Function-like Function-yielding V37() set
~ A is Relation-like Function-like Function-yielding V37() set
A is set
B is set
[:A,B:] is Relation-like set
[:B,A:] is Relation-like set
A is set
[:A,B:] --> A is Relation-like [:A,B:] -defined {A} -valued Function-like constant V14([:A,B:]) quasi_total Element of bool [:[:A,B:],{A}:]
{A} is set
[:[:A,B:],{A}:] is Relation-like set
bool [:[:A,B:],{A}:] is non empty set
~ ([:A,B:] --> A) is Relation-like Function-like set
[:B,A:] --> A is Relation-like [:B,A:] -defined {A} -valued Function-like constant V14([:B,A:]) quasi_total Element of bool [:[:B,A:],{A}:]
[:[:B,A:],{A}:] is Relation-like set
bool [:[:B,A:],{A}:] is non empty set
B is set
dom ([:B,A:] --> A) is Relation-like B -defined A -valued Element of bool [:B,A:]
bool [:B,A:] is non empty set
F is set
G is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
o2 is set
c₇ is set
[o2,c₇] is V15() set
{o2,c₇} is set
{o2} is set
{{o2,c₇},{o2}} is set
[c₇,o2] is V15() set
{c₇,o2} is set
{c₇} is set
{{c₇,o2},{c₇}} is set
dom ([:A,B:] --> A) is Relation-like A -defined B -valued Element of bool [:A,B:]
bool [:A,B:] is non empty set
G is set
F is set
[G,F] is V15() set
{G,F} is set
{G} is set
{{G,F},{G}} is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
B is set
F is set
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
([:B,A:] --> A) . (F,B) is set
[F,B] is V15() set
{F,B} is set
{F} is set
{{F,B},{F}} is set
([:B,A:] --> A) . [F,B] is set
([:A,B:] --> A) . (B,F) is set
([:A,B:] --> A) . [B,F] is set
A is Relation-like Function-like set
B is Relation-like Function-like set
[:A,B:] is Relation-like Function-like set
[:A,B:] " is Relation-like Function-like set
A " is Relation-like Function-like set
B " is Relation-like Function-like set
[:(A "),(B "):] is Relation-like Function-like set
proj1 (A ") is set
proj2 A is set
proj1 (B ") is set
proj2 B is set
proj1 ([:A,B:] ") is set
proj2 [:A,B:] is set
[:(proj1 (A ")),(proj1 (B ")):] is Relation-like set
A is set
B is set
([:A,B:] ") . (A,B) is set
[A,B] is V15() set
{A,B} is set
{A} is set
{{A,B},{A}} is set
([:A,B:] ") . [A,B] is set
(A ") . A is set
(B ") . B is set
[((A ") . A),((B ") . B)] is V15() set
{((A ") . A),((B ") . B)} is set
{((A ") . A)} is set
{{((A ") . A),((B ") . B)},{((A ") . A)}} is set
proj1 [:A,B:] is set
proj1 A is set
proj1 B is set
[:(proj1 A),(proj1 B):] is Relation-like set
proj2 (A ") is set
proj2 (B ") is set
A . ((A ") . A) is set
(A ") * A is Relation-like Function-like set
((A ") * A) . A is set
(A ") " is Relation-like Function-like set
(A ") * ((A ") ") is Relation-like Function-like set
((A ") * ((A ") ")) . A is set
id (proj1 (A ")) is Relation-like proj1 (A ") -defined proj1 (A ") -valued Function-like one-to-one V14( proj1 (A ")) quasi_total Element of bool [:(proj1 (A ")),(proj1 (A ")):]
[:(proj1 (A ")),(proj1 (A ")):] is Relation-like set
bool [:(proj1 (A ")),(proj1 (A ")):] is non empty set
(id (proj1 (A "))) . A is set
B . ((B ") . B) is set
(B ") * B is Relation-like Function-like set
((B ") * B) . B is set
(B ") " is Relation-like Function-like set
(B ") * ((B ") ") is Relation-like Function-like set
((B ") * ((B ") ")) . B is set
id (proj1 (B ")) is Relation-like proj1 (B ") -defined proj1 (B ") -valued Function-like one-to-one V14( proj1 (B ")) quasi_total Element of bool [:(proj1 (B ")),(proj1 (B ")):]
[:(proj1 (B ")),(proj1 (B ")):] is Relation-like set
bool [:(proj1 (B ")),(proj1 (B ")):] is non empty set
(id (proj1 (B "))) . B is set
[:A,B:] . (((A ") . A),((B ") . B)) is set
[:A,B:] . [((A ") . A),((B ") . B)] is set
A is Relation-like Function-like set
[:A,A:] is Relation-like Function-like set
B is set
proj1 A is set
A is set
A . B is set
A . A is set
proj1 [:A,A:] is set
[:(proj1 A),(proj1 A):] is Relation-like set
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
[:A,A:] . (B,B) is set
[:A,A:] . [B,B] is set
[(A . A),(A . A)] is V15() set
{(A . A),(A . A)} is set
{(A . A)} is set
{{(A . A),(A . A)},{(A . A)}} is set
[:A,A:] . (A,A) is set
[:A,A:] . [A,A] is set
A is Relation-like Function-like set
~ A is Relation-like Function-like set
B is set
proj1 (~ A) is set
A is set
(~ A) . B is set
(~ A) . A is set
B is set
F is set
[:B,F:] is Relation-like set
G is set
c₇ is set
[G,c₇] is V15() set
{G,c₇} is set
{G} is set
{{G,c₇},{G}} is set
o2 is set
o3 is set
[o2,o3] is V15() set
{o2,o3} is set
{o2} is set
{{o2,o3},{o2}} is set
[c₇,G] is V15() set
{c₇,G} is set
{c₇} is set
{{c₇,G},{c₇}} is set
proj1 A is set
[o3,o2] is V15() set
{o3,o2} is set
{o3} is set
{{o3,o2},{o3}} is set
A . (c₇,G) is set
A . [c₇,G] is set
(~ A) . (G,c₇) is set
(~ A) . [G,c₇] is set
(~ A) . (o2,o3) is set
(~ A) . [o2,o3] is set
A . (o3,o2) is set
A . [o3,o2] is set
A is Relation-like Function-like set
B is Relation-like Function-like set
[:A,B:] is Relation-like Function-like set
~ [:A,B:] is Relation-like Function-like set
[:B,A:] is Relation-like Function-like set
A is set
proj1 [:B,A:] is set
B is set
[:B,A:] . A is set
[:B,A:] . B is set
proj1 B is set
proj1 A is set
[:(proj1 B),(proj1 A):] is Relation-like set
proj1 [:A,B:] is set
[:(proj1 A),(proj1 B):] is Relation-like set
F is set
G is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
c₇ is set
o2 is set
[c₇,o2] is V15() set
{c₇,o2} is set
{c₇} is set
{{c₇,o2},{c₇}} is set
proj1 (~ [:A,B:]) is set
[:B,A:] . (F,G) is set
[:B,A:] . [F,G] is set
B . F is set
A . G is set
[(B . F),(A . G)] is V15() set
{(B . F),(A . G)} is set
{(B . F)} is set
{{(B . F),(A . G)},{(B . F)}} is set
[:B,A:] . (c₇,o2) is set
[:B,A:] . [c₇,o2] is set
B . c₇ is set
A . o2 is set
[(B . c₇),(A . o2)] is V15() set
{(B . c₇),(A . o2)} is set
{(B . c₇)} is set
{{(B . c₇),(A . o2)},{(B . c₇)}} is set
(~ [:A,B:]) . [F,G] is set
(~ [:A,B:]) . (F,G) is set
[:A,B:] . (G,F) is set
[G,F] is V15() set
{G,F} is set
{G} is set
{{G,F},{G}} is set
[:A,B:] . [G,F] is set
[(A . o2),(B . c₇)] is V15() set
{(A . o2),(B . c₇)} is set
{(A . o2)} is set
{{(A . o2),(B . c₇)},{(A . o2)}} is set
[:A,B:] . (o2,c₇) is set
[o2,c₇] is V15() set
{o2,c₇} is set
{o2} is set
{{o2,c₇},{o2}} is set
[:A,B:] . [o2,c₇] is set
(~ [:A,B:]) . (c₇,o2) is set
(~ [:A,B:]) . [c₇,o2] is set
A is Relation-like Function-like set
B is Relation-like Function-like set
[:A,B:] is Relation-like Function-like set
~ [:A,B:] is Relation-like Function-like set
(~ [:A,B:]) " is Relation-like Function-like set
[:B,A:] is Relation-like Function-like set
[:B,A:] " is Relation-like Function-like set
~ ([:B,A:] ") is Relation-like Function-like set
B " is Relation-like Function-like set
A " is Relation-like Function-like set
[:(B "),(A "):] is Relation-like Function-like set
proj1 ([:B,A:] ") is set
proj1 (B ") is set
proj1 (A ") is set
[:(proj1 (B ")),(proj1 (A ")):] is Relation-like set
proj1 [:A,B:] is set
proj1 A is set
proj1 B is set
[:(proj1 A),(proj1 B):] is Relation-like set
proj1 [:B,A:] is set
[:(proj1 B),(proj1 A):] is Relation-like set
[:A,B:] " is Relation-like Function-like set
[:(A "),(B "):] is Relation-like Function-like set
proj1 (~ ([:B,A:] ")) is set
[:(proj1 (A ")),(proj1 (B ")):] is Relation-like set
proj1 [:(A "),(B "):] is set
proj2 [:A,B:] is set
proj2 (~ [:A,B:]) is set
A is set
B is set
(~ ([:B,A:] ")) . A is set
proj2 A is set
proj2 B is set
[:(proj2 A),(proj2 B):] is Relation-like set
F is set
G is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
(A ") . F is set
(B ") . G is set
[G,F] is V15() set
{G,F} is set
{G} is set
{{G,F},{G}} is set
(~ ([:B,A:] ")) . (F,G) is set
(~ ([:B,A:] ")) . [F,G] is set
[:(B "),(A "):] . (G,F) is set
[:(B "),(A "):] . [G,F] is set
[((B ") . G),((A ") . F)] is V15() set
{((B ") . G),((A ") . F)} is set
{((B ") . G)} is set
{{((B ") . G),((A ") . F)},{((B ") . G)}} is set
proj2 (A ") is set
proj2 (B ") is set
proj1 (~ [:A,B:]) is set
A . ((A ") . F) is set
B . ((B ") . G) is set
(~ [:A,B:]) . B is set
(~ [:A,B:]) . (((B ") . G),((A ") . F)) is set
(~ [:A,B:]) . [((B ") . G),((A ") . F)] is set
[:A,B:] . (((A ") . F),((B ") . G)) is set
[((A ") . F),((B ") . G)] is V15() set
{((A ") . F),((B ") . G)} is set
{((A ") . F)} is set
{{((A ") . F),((B ") . G)},{((A ") . F)}} is set
[:A,B:] . [((A ") . F),((B ") . G)] is set
F is set
G is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
(~ [:A,B:]) . (F,G) is set
(~ [:A,B:]) . [F,G] is set
[:A,B:] . (G,F) is set
[G,F] is V15() set
{G,F} is set
{G} is set
{{G,F},{G}} is set
[:A,B:] . [G,F] is set
A . G is set
B . F is set
[(A . G),(B . F)] is V15() set
{(A . G),(B . F)} is set
{(A . G)} is set
{{(A . G),(B . F)},{(A . G)}} is set
[(B . F),(A . G)] is V15() set
{(B . F),(A . G)} is set
{(B . F)} is set
{{(B . F),(A . G)},{(B . F)}} is set
[:(proj2 B),(proj2 A):] is Relation-like set
proj2 [:B,A:] is set
[:B,A:] . (F,G) is set
[:B,A:] . [F,G] is set
([:B,A:] ") . ([:B,A:] . (F,G)) is set
([:B,A:] ") . ((B . F),(A . G)) is set
([:B,A:] ") . [(B . F),(A . G)] is set
(~ ([:B,A:] ")) . ((A . G),(B . F)) is set
(~ ([:B,A:] ")) . [(A . G),(B . F)] is set
A is set
B is set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
id B is Relation-like B -defined B -valued Function-like one-to-one V14(B) quasi_total Element of bool [:B,B:]
[:B,B:] is Relation-like set
bool [:B,B:] is non empty set
[:A,A:] is Relation-like set
id A is Relation-like A -defined A -valued Function-like one-to-one V14(A) quasi_total Element of bool [:A,A:]
bool [:A,A:] is non empty set
A is Relation-like A -defined B -valued Function-like quasi_total Element of bool [:A,B:]
[:A,A:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like quasi_total Element of bool [:[:A,A:],[:B,B:]:]
[:[:A,A:],[:B,B:]:] is Relation-like set
bool [:[:A,A:],[:B,B:]:] is non empty set
[:A,A:] .: (id A) is Relation-like B -defined B -valued Element of bool [:B,B:]
rng A is Element of bool B
bool B is non empty set
B is set
F is set
G is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
c₇ is set
A . c₇ is set
dom A is Element of bool A
bool A is non empty set
[c₇,c₇] is V15() set
{c₇,c₇} is set
{c₇} is set
{{c₇,c₇},{c₇}} is set
[:A,A:] . (c₇,c₇) is set
[:A,A:] . [c₇,c₇] is set
A is Relation-like Function-like Function-yielding V37() set
B is Relation-like Function-like Function-yielding V37() set
B ** A is Relation-like Function-like Function-yielding V37() set
A is Relation-like Function-like set
A * (B ** A) is Relation-like Function-like Function-yielding V37() set
A * A is Relation-like Function-like Function-yielding V37() set
A * B is Relation-like Function-like Function-yielding V37() set
(A * B) ** (A * A) is Relation-like Function-like Function-yielding V37() set
proj1 (A * (B ** A)) is set
proj1 (B ** A) is set
A " (proj1 (B ** A)) is set
proj1 B is set
proj1 A is set
(proj1 B) /\ (proj1 A) is set
A " ((proj1 B) /\ (proj1 A)) is set
A " (proj1 A) is set
A " (proj1 B) is set
(A " (proj1 A)) /\ (A " (proj1 B)) is set
proj1 (A * B) is set
(A " (proj1 A)) /\ (proj1 (A * B)) is set
proj1 (A * A) is set
(proj1 (A * A)) /\ (proj1 (A * B)) is set
B is set
proj1 A is set
A . B is set
(A * (B ** A)) . B is Relation-like Function-like set
(B ** A) . (A . B) is Relation-like Function-like set
A . (A . B) is Relation-like Function-like set
B . (A . B) is Relation-like Function-like set
(A . (A . B)) * (B . (A . B)) is Relation-like Function-like set
(A * B) . B is Relation-like Function-like set
(A . (A . B)) * ((A * B) . B) is Relation-like Function-like set
(A * A) . B is Relation-like Function-like set
((A * A) . B) * ((A * B) . B) is Relation-like Function-like set
A is set
B is set
[:A,B:] is Relation-like set
A is set
[:[:A,B:],A:] is Relation-like set
bool [:[:A,B:],A:] is non empty set
B is Relation-like [:A,B:] -defined A -valued Function-like quasi_total Element of bool [:[:A,B:],A:]
~ B is Relation-like Function-like set
[:B,A:] is Relation-like set
[:[:B,A:],A:] is Relation-like set
bool [:[:B,A:],A:] is non empty set
F is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
~ F is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
A is set
B is set
[:A,B:] is Relation-like set
A is set
[:[:A,B:],A:] is Relation-like set
bool [:[:A,B:],A:] is non empty set
B is Relation-like [:A,B:] -defined A -valued Function-like quasi_total Element of bool [:[:A,B:],A:]
(A,B,A,B) is Relation-like [:B,A:] -defined A -valued Function-like quasi_total Element of bool [:[:B,A:],A:]
[:B,A:] is Relation-like set
[:[:B,A:],A:] is Relation-like set
bool [:[:B,A:],A:] is non empty set
rng (A,B,A,B) is Element of bool A
bool A is non empty set
rng B is Element of bool A
A is set
[:A,A:] is Relation-like set
id A is Relation-like A -defined A -valued Function-like one-to-one V14(A) quasi_total Element of bool [:A,A:]
bool [:A,A:] is non empty set
B is non empty set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
[:B,B:] is Relation-like non empty set
id B is Relation-like B -defined B -valued Function-like one-to-one non empty V14(B) quasi_total Element of bool [:B,B:]
bool [:B,B:] is non empty set
A is Relation-like A -defined B -valued Function-like V14(A) quasi_total Element of bool [:A,B:]
[:A,A:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
[:[:A,A:],[:B,B:]:] is Relation-like set
bool [:[:A,A:],[:B,B:]:] is non empty set
[:A,A:] .: (id A) is Relation-like B -defined B -valued Element of bool [:B,B:]
B is set
F is set
[:A,A:] . F is set
G is set
c₇ is set
[G,c₇] is V15() set
{G,c₇} is set
{G} is set
{{G,c₇},{G}} is set
o2 is Element of A
A . o2 is set
dom A is Element of bool A
bool A is non empty set
[:A,A:] . (o2,c₇) is set
[o2,c₇] is V15() set
{o2,c₇} is set
{o2} is set
{{o2,c₇},{o2}} is set
[:A,A:] . [o2,c₇] is set
[(A . o2),(A . o2)] is V15() set
{(A . o2),(A . o2)} is set
{(A . o2)} is set
{{(A . o2),(A . o2)},{(A . o2)}} is set
A is set
[:A,A:] is Relation-like set
B is set
[:B,B:] is Relation-like set
[:[:A,A:],[:B,B:]:] is Relation-like set
bool [:[:A,A:],[:B,B:]:] is non empty set
A is set
[:A,A:] is Relation-like set
B is non empty set
[:B,B:] is Relation-like non empty set
[:[:A,A:],[:B,B:]:] is Relation-like set
bool [:[:A,A:],[:B,B:]:] is non empty set
A is Element of B
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
[:A,A:] --> [A,A] is Relation-like [:A,A:] -defined {[A,A]} -valued Function-like constant V14([:A,A:]) quasi_total Element of bool [:[:A,A:],{[A,A]}:]
{[A,A]} is Relation-like Function-like set
[:[:A,A:],{[A,A]}:] is Relation-like set
bool [:[:A,A:],{[A,A]}:] is non empty set
B is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
A --> A is Relation-like A -defined B -valued Function-like constant V14(A) quasi_total Element of bool [:A,B:]
F is Relation-like A -defined B -valued Function-like V14(A) quasi_total Element of bool [:A,B:]
[:F,F:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
F is Relation-like A -defined B -valued Function-like V14(A) quasi_total Element of bool [:A,B:]
[:F,F:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
(A,A,[:B,B:],[:F,F:]) is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
(A,A,{[A,A]},([:A,A:] --> [A,A])) is Relation-like [:A,A:] -defined {[A,A]} -valued Function-like V14([:A,A:]) quasi_total Element of bool [:[:A,A:],{[A,A]}:]
A is set
[:A,A:] is Relation-like set
B is set
[:B,B:] is Relation-like set
[:[:A,A:],[:B,B:]:] is Relation-like set
bool [:[:A,A:],[:B,B:]:] is non empty set
A is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like quasi_total Element of bool [:[:A,A:],[:B,B:]:]
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
B is Relation-like A -defined B -valued Function-like quasi_total Element of bool [:A,B:]
[:B,B:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like quasi_total Element of bool [:[:A,A:],[:B,B:]:]
F is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
[:F,F:] is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
[:B,B:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like quasi_total Element of bool [:[:A,A:],[:B,B:]:]
(A,A,[:B,B:],[:B,B:]) is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like quasi_total Element of bool [:[:A,A:],[:B,B:]:]
F is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
[:F,F:] is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
~ [:F,F:] is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
the Element of B is Element of B
[ the Element of B, the Element of B] is V15() set
{ the Element of B, the Element of B} is set
{ the Element of B} is set
{{ the Element of B, the Element of B},{ the Element of B}} is set
[:A,A:] --> [ the Element of B, the Element of B] is Relation-like [:A,A:] -defined {[ the Element of B, the Element of B]} -valued Function-like constant V14([:A,A:]) quasi_total Element of bool [:[:A,A:],{[ the Element of B, the Element of B]}:]
{[ the Element of B, the Element of B]} is Relation-like Function-like set
[:[:A,A:],{[ the Element of B, the Element of B]}:] is Relation-like set
bool [:[:A,A:],{[ the Element of B, the Element of B]}:] is non empty set
F is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like quasi_total Element of bool [:[:A,A:],[:B,B:]:]
A is non empty set
[:A,A:] is Relation-like non empty set
B is non empty set
[:B,B:] is Relation-like non empty set
[:[:A,A:],[:B,B:]:] is Relation-like non empty set
bool [:[:A,A:],[:B,B:]:] is non empty set
A is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like non empty V14([:A,A:]) quasi_total (A,B) (A,B) Element of bool [:[:A,A:],[:B,B:]:]
[:A,B:] is Relation-like non empty set
bool [:A,B:] is non empty set
B is Relation-like A -defined B -valued Function-like non empty V14(A) quasi_total Element of bool [:A,B:]
[:B,B:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like non empty V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
F is Relation-like A -defined B -valued Function-like non empty V14(A) quasi_total Element of bool [:A,B:]
[:F,F:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like non empty V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
(A,A,[:B,B:],[:F,F:]) is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like non empty V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
the Element of A is Element of A
B . the Element of A is Element of B
c₇ is Element of B
[c₇,c₇] is V15() set
{c₇,c₇} is set
{c₇} is set
{{c₇,c₇},{c₇}} is set
[:A,A:] --> [c₇,c₇] is Relation-like [:A,A:] -defined {[c₇,c₇]} -valued Function-like constant non empty V14([:A,A:]) quasi_total Element of bool [:[:A,A:],{[c₇,c₇]}:]
{[c₇,c₇]} is Relation-like Function-like set
[:[:A,A:],{[c₇,c₇]}:] is Relation-like set
bool [:[:A,A:],{[c₇,c₇]}:] is non empty set
dom A is Relation-like A -defined A -valued non empty Element of bool [:A,A:]
bool [:A,A:] is non empty set
o2 is set
o3 is Element of A
f is Element of A
[o3,f] is V15() set
{o3,f} is set
{o3} is set
{{o3,f},{o3}} is set
dom F is non empty Element of bool A
bool A is non empty set
dom B is non empty Element of bool A
dom [:F,F:] is Relation-like A -defined A -valued non empty Element of bool [:A,A:]
[:(dom F),(dom F):] is Relation-like A -defined A -valued non empty Element of bool [:A,A:]
[o3, the Element of A] is V15() set
{o3, the Element of A} is set
{{o3, the Element of A},{o3}} is set
B . o3 is Element of B
[c₇,(B . o3)] is V15() set
{c₇,(B . o3)} is set
{{c₇,(B . o3)},{c₇}} is set
A . ( the Element of A,o3) is Element of [:B,B:]
[ the Element of A,o3] is V15() set
{ the Element of A,o3} is set
{ the Element of A} is set
{{ the Element of A,o3},{ the Element of A}} is set
A . [ the Element of A,o3] is set
[:F,F:] . (o3, the Element of A) is Element of [:B,B:]
[:F,F:] . [o3, the Element of A] is set
F . o3 is Element of B
F . the Element of A is Element of B
[(F . o3),(F . the Element of A)] is V15() set
{(F . o3),(F . the Element of A)} is set
{(F . o3)} is set
{{(F . o3),(F . the Element of A)},{(F . o3)}} is set
[f, the Element of A] is V15() set
{f, the Element of A} is set
{f} is set
{{f, the Element of A},{f}} is set
B . f is Element of B
[c₇,(B . f)] is V15() set
{c₇,(B . f)} is set
{{c₇,(B . f)},{c₇}} is set
A . ( the Element of A,f) is Element of [:B,B:]
[ the Element of A,f] is V15() set
{ the Element of A,f} is set
{{ the Element of A,f},{ the Element of A}} is set
A . [ the Element of A,f] is set
[:F,F:] . (f, the Element of A) is Element of [:B,B:]
[:F,F:] . [f, the Element of A] is set
F . f is Element of B
[(F . f),(F . the Element of A)] is V15() set
{(F . f),(F . the Element of A)} is set
{(F . f)} is set
{{(F . f),(F . the Element of A)},{(F . f)}} is set
[f,o3] is V15() set
{f,o3} is set
{{f,o3},{f}} is set
A . o2 is set
[:B,B:] . (o3,f) is Element of [:B,B:]
[:B,B:] . [o3,f] is set
[:F,F:] . (f,o3) is Element of [:B,B:]
[:F,F:] . [f,o3] is set
A is set
B is set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
A is Relation-like A -defined B -valued Function-like quasi_total Element of bool [:A,B:]
F is Relation-like B -defined Function-like V14(B) set
B is Relation-like A -defined Function-like V14(A) set
[[0]] A is Relation-like empty-yielding A -defined Function-like V14(A) Function-yielding V37() set
A --> {} is Relation-like A -defined {{}} -valued Function-like constant V14(A) quasi_total Element of bool [:A,{{}}:]
{{}} is set
[:A,{{}}:] is Relation-like set
bool [:A,{{}}:] is non empty set
G is non empty set
[:A,G:] is Relation-like set
bool [:A,G:] is non empty set
c₇ is Relation-like A -defined G -valued Function-like V14(A) quasi_total Element of bool [:A,G:]
o2 is Relation-like G -defined Function-like non empty V14(G) set
c₇ * o2 is Relation-like A -defined Function-like V14(A) set
the Relation-like A -defined Function-like V14(A) Function-yielding V37() ManySortedFunction of B,c₇ * o2 is Relation-like A -defined Function-like V14(A) Function-yielding V37() ManySortedFunction of B,c₇ * o2
f is Relation-like A -defined Function-like V14(A) set
K is non empty set
[:A,K:] is Relation-like set
bool [:A,K:] is non empty set
g9 is Relation-like K -defined Function-like non empty V14(K) set
f9 is Relation-like A -defined K -valued Function-like V14(A) quasi_total Element of bool [:A,K:]
f99 is Relation-like A -defined K -valued Function-like V14(A) quasi_total Element of bool [:A,K:]
g99 is Relation-like K -defined Function-like non empty V14(K) set
g is Relation-like A -defined Function-like V14(A) set
f99 * g99 is Relation-like A -defined Function-like V14(A) set
A is set
B is non empty set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
A is Relation-like A -defined B -valued Function-like V14(A) quasi_total Element of bool [:A,B:]
B is Relation-like A -defined Function-like V14(A) set
F is Relation-like B -defined Function-like non empty V14(B) set
A * F is Relation-like A -defined Function-like V14(A) set
G is Relation-like A -defined Function-like V14(A) set
c₇ is non empty set
[:A,c₇:] is Relation-like set
bool [:A,c₇:] is non empty set
o3 is Relation-like A -defined c₇ -valued Function-like V14(A) quasi_total Element of bool [:A,c₇:]
o2 is Relation-like c₇ -defined Function-like non empty V14(c₇) set
o3 * o2 is Relation-like A -defined Function-like V14(A) set
A is set
B is set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
A is Relation-like A -defined B -valued Function-like quasi_total Element of bool [:A,B:]
B is Relation-like A -defined Function-like V14(A) set
F is Relation-like B -defined Function-like V14(B) set
G is Relation-like A -defined Function-like V14(A) (A,B,A,B,F)
c₇ is non empty set
[:A,c₇:] is Relation-like set
bool [:A,c₇:] is non empty set
o3 is Relation-like A -defined c₇ -valued Function-like V14(A) quasi_total Element of bool [:A,c₇:]
o2 is Relation-like c₇ -defined Function-like non empty V14(c₇) set
o3 * o2 is Relation-like A -defined Function-like V14(A) set
[[0]] A is Relation-like empty-yielding A -defined Function-like V14(A) Function-yielding V37() set
A --> {} is Relation-like A -defined {{}} -valued Function-like constant V14(A) quasi_total Element of bool [:A,{{}}:]
[:A,{{}}:] is Relation-like set
bool [:A,{{}}:] 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
A is non empty set
[:B,A:] is Relation-like non empty set
bool [:B,A:] is non empty set
B is Relation-like A -defined B -valued Function-like V14(A) quasi_total Element of bool [:A,B:]
F is Relation-like B -defined A -valued Function-like non empty V14(B) quasi_total Element of bool [:B,A:]
F * B is Relation-like A -defined A -valued Function-like V14(A) quasi_total Element of bool [:A,A:]
[:A,A:] is Relation-like set
bool [:A,A:] is non empty set
G is Relation-like B -defined Function-like non empty V14(B) set
B * G is Relation-like A -defined Function-like V14(A) set
c₇ is Relation-like A -defined Function-like non empty V14(A) set
o2 is Relation-like B -defined Function-like non empty V14(B) Function-yielding V37() (B,A,F,G,c₇)
B * o2 is Relation-like A -defined Function-like V14(A) Function-yielding V37() set
(F * B) * c₇ is Relation-like A -defined Function-like V14(A) set
F * c₇ is Relation-like B -defined Function-like non empty V14(B) set
B * (F * c₇) is Relation-like A -defined Function-like V14(A) set
A is set
B is non empty set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
[:A,A:] is Relation-like set
[:B,B:] is Relation-like non empty set
A is Relation-like A -defined B -valued Function-like V14(A) quasi_total Element of bool [:A,B:]
[:A,A:] is Relation-like [:A,A:] -defined [:B,B:] -valued Function-like V14([:A,A:]) quasi_total Element of bool [:[:A,A:],[:B,B:]:]
[:[:A,A:],[:B,B:]:] is Relation-like set
bool [:[:A,A:],[:B,B:]:] is non empty set
B is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) set
F is Relation-like [:B,B:] -defined Function-like non empty V14([:B,B:]) set
G is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) Function-yielding V37() ([:A,A:],[:B,B:],[:A,A:],B,F)
~ G is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) Function-yielding V37() set
~ B is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) set
~ F is Relation-like [:B,B:] -defined Function-like non empty V14([:B,B:]) set
[:A,A:] * F is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) set
c₇ is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) Function-yielding V37() ManySortedFunction of B,[:A,A:] * F
~ c₇ is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) Function-yielding V37() ManySortedFunction of ~ B, ~ ([:A,A:] * F)
~ ([:A,A:] * F) is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) set
[:A,A:] * (~ F) is Relation-like [:A,A:] -defined Function-like V14([:A,A:]) set
A is non empty set
B is non empty set
[:A,B:] is Relation-like non empty set
bool [:A,B:] is non empty set
A is Relation-like A -defined Function-like non empty V14(A) set
B is Relation-like B -defined Function-like non empty V14(B) set
F is Element of B
B . F is set
A --> F is Relation-like A -defined B -valued Function-like constant non empty V14(A) quasi_total Element of bool [:A,B:]
G is Element of B . F
{ [b₁,((A . b₁) --> G)] where b₁ is Element of A : verum } is set
c₇ is Relation-like A -defined B -valued Function-like non empty V14(A) quasi_total Element of bool [:A,B:]
{G} is set
{ [b₁,H₁(b₁)] where b₁ is Element of A : S₁[b₁] } is set
o2 is Relation-like Function-like set
proj1 o2 is set
{ b₁ where b₁ is Element of A : S₁[b₁] } is set
o3 is Relation-like A -defined Function-like non empty V14(A) set
{ [b₁,H₂(b₁)] where b₁ is Element of A : S₁[b₁] } is set
f is set
g is Element of A
dom c₇ is non empty Element of bool A
bool A is non empty set
c₇ . f is set
B . (c₇ . f) is set
c₇ * B is Relation-like A -defined Function-like non empty V14(A) set
(c₇ * B) . f is set
o3 . g is set
A . g is set
(A . g) --> G is Relation-like A . g -defined {G} -valued Function-like constant V14(A . g) quasi_total Element of bool [:(A . g),{G}:]
[:(A . g),{G}:] is Relation-like set
bool [:(A . g),{G}:] is non empty set
o3 . f is set
A . f is set
[:(A . f),((c₇ * B) . f):] is Relation-like set
bool [:(A . f),((c₇ * B) . f):] 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
A is non empty set
[:B,A:] is Relation-like non empty set
bool [:B,A:] is non empty set
B is Relation-like A -defined B -valued Function-like V14(A) quasi_total Element of bool [:A,B:]
F is Relation-like B -defined A -valued Function-like non empty V14(B) quasi_total Element of bool [:B,A:]
F * B is Relation-like A -defined A -valued Function-like V14(A) quasi_total Element of bool [:A,A:]
[:A,A:] is Relation-like set
bool [:A,A:] is non empty set
G is Relation-like A -defined Function-like V14(A) set
c₇ is Relation-like B -defined Function-like non empty V14(B) set
B * c₇ is Relation-like A -defined Function-like V14(A) set
o2 is Relation-like A -defined Function-like non empty V14(A) set
(F * B) * o2 is Relation-like A -defined Function-like V14(A) set
o3 is Relation-like A -defined Function-like V14(A) Function-yielding V37() (A,B,B,G,c₇)
f is Relation-like A -defined Function-like V14(A) Function-yielding V37() (A,A,F * B,B * c₇,o2)
f ** o3 is Relation-like A -defined Function-like V14(A) Function-yielding V37() set
g is Relation-like A -defined Function-like V14(A) Function-yielding V37() ManySortedFunction of B * c₇,(F * B) * o2
dom g is Element of bool A
bool A is non empty set
K is Relation-like A -defined Function-like V14(A) Function-yielding V37() ManySortedFunction of G,B * c₇
dom K is Element of bool A
g ** K is Relation-like A -defined Function-like V14(A) Function-yielding V37() set
dom (g ** K) is Element of bool A
(dom g) /\ (dom K) is Element of bool A
f9 is Relation-like A -defined Function-like V14(A) set
g9 is set
f9 . g9 is set
G . g9 is set
((F * B) * o2) . g9 is set
[:(G . g9),(((F * B) * o2) . g9):] is Relation-like set
bool [:(G . g9),(((F * B) * o2) . g9):] is non empty set
(B * c₇) . g9 is set
[:(G . g9),((B * c₇) . g9):] is Relation-like set
bool [:(G . g9),((B * c₇) . g9):] is non empty set
K . g9 is Relation-like Function-like set
[:((B * c₇) . g9),(((F * B) * o2) . g9):] is Relation-like set
bool [:((B * c₇) . g9),(((F * B) * o2) . g9):] is non empty set
g . g9 is Relation-like Function-like set
g99 is Relation-like G . g9 -defined (B * c₇) . g9 -valued Function-like quasi_total Element of bool [:(G . g9),((B * c₇) . g9):]
f99 is Relation-like (B * c₇) . g9 -defined ((F * B) * o2) . g9 -valued Function-like quasi_total Element of bool [:((B * c₇) . g9),(((F * B) * o2) . g9):]
f99 * g99 is Relation-like G . g9 -defined ((F * B) * o2) . g9 -valued Function-like Element of bool [:(G . g9),(((F * B) * o2) . g9):]
A is non empty AltGraph
B is non empty AltGraph
the carrier of A 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
A is (A,B)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
B is Element of the carrier of A
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
A is 1-sorted
B is 1-sorted
A is non empty AltGraph
B is non empty AltGraph
A is (A,B)
the carrier of A 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
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
the of A .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
id the carrier of B is Relation-like the carrier of B -defined the carrier of B -valued Function-like one-to-one non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of B:]
B is Element of the carrier of A
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
the of A . [B,B] is set
F is set
G is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
(A,B,A,B) is Element of the carrier of B
( the of A . (B,B)) `1 is set
[(A,B,A,B),(A,B,A,B)] is V15() set
{(A,B,A,B),(A,B,A,B)} is set
{(A,B,A,B)} is set
{{(A,B,A,B),(A,B,A,B)},{(A,B,A,B)}} is set
B is set
F is set
the of A . F is set
G is Element of the carrier of A
c₇ is Element of the carrier of A
[G,c₇] is V15() set
{G,c₇} is set
{G} is set
{{G,c₇},{G}} is set
o2 is Element of the carrier of A
(A,B,A,o2) is Element of the carrier of B
the of A . (o2,o2) is Element of [: the carrier of B, the carrier of B:]
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the of A . [o2,o2] is set
( the of A . (o2,o2)) `1 is set
[(A,B,A,o2),(A,B,A,o2)] is V15() set
{(A,B,A,o2),(A,B,A,o2)} is set
{(A,B,A,o2)} is set
{{(A,B,A,o2),(A,B,A,o2)},{(A,B,A,o2)}} is set
A is non empty reflexive AltGraph
B is non empty reflexive AltGraph
the carrier of B is non empty set
the carrier of A is non empty set
A is (A,B)
id the carrier of B is Relation-like the carrier of B -defined the carrier of B -valued Function-like one-to-one non empty V14( the carrier of B) 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 carrier of A, the carrier of A:] is Relation-like non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
the of A .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
B is Element of the carrier of B
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
F is Element of [: the carrier of B, the carrier of B:]
G is Element of [: the carrier of A, the carrier of A:]
the of A . G is Element of [: the carrier of B, the carrier of B:]
c<sub>7</sub> is set
o2 is set
[c<sub>7</sub>,o2] is V15() set
{c<sub>7</sub>,o2} is set
{c<sub>7</sub>} is set
{{c<sub>7</sub>,o2},{c<sub>7</sub>}} is set
o3 is Element of the carrier of A
(A,B,A,o3) is Element of the carrier of B
the of A . (o3,o3) is Element of [: the carrier of B, the carrier of B:]
[o3,o3] is V15() set
{o3,o3} is set
{o3} is set
{{o3,o3},{o3}} is set
the of A . [o3,o3] is set
( the of A . (o3,o3)) `1 is set
A is non empty AltGraph
B is non empty AltGraph
A is 1-sorted
B is 1-sorted
A is AltGraph
B is AltGraph
the carrier of A is set
[: the carrier of A, the carrier of A:] is Relation-like set
the carrier of B is set
[: the carrier of B, the carrier of B:] is Relation-like set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) set
the Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:], the Arrows of A, the Arrows of B) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:], the Arrows of A, the Arrows of B)
(A,B, the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:], the Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:], the Arrows of A, the Arrows of B)) is (A,B) (A,B)
F is (A,B) (A,B)
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the carrier of A is set
[: the carrier of A, the carrier of A:] is Relation-like set
the carrier of B is set
[: the carrier of B, the carrier of B:] is Relation-like set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) set
the Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:], the Arrows of A, the Arrows of B) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:], the Arrows of A, the Arrows of B)
(A,B, the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:], the Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total ( the carrier of A, the carrier of B) Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:], the Arrows of A, the Arrows of B)) is (A,B) (A,B)
F is (A,B) (A,B)
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
A is AltGraph
B is AltGraph
the carrier of A is set
A is (A,B)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
[: the carrier of A, the carrier of A:] is Relation-like set
the carrier of B is set
[: the carrier of B, the carrier of B:] is Relation-like set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) set
B is Element of the carrier of A
F is Element of the carrier of A
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
A is AltGraph
B is AltGraph
the carrier of A is set
A is (A,B)
B is Element of the carrier of A
F is Element of the carrier of A
(A,B,A,B,F) is set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
[: the carrier of A, the carrier of A:] is Relation-like set
the carrier of B is set
[: the carrier of B, the carrier of B:] is Relation-like set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
A is non empty AltGraph
B is non empty AltGraph
the carrier of A is non empty set
A is (A,B) (A,B)
B is Element of the carrier of A
F is Element of the carrier of A
(A,B,A,B,F) is Relation-like Function-like set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
[: the carrier of A, the carrier of A:] is Relation-like 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
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
<^B,F^> is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
<^(A,B,A,B),(A,B,A,F)^> is set
[:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:] is Relation-like set
bool [:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:] is non empty set
G is non empty set
[:[: the carrier of A, the carrier of A:],G:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],G:] is non empty set
o2 is Relation-like [: the carrier of A, the carrier of A:] -defined G -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],G:]
c₇ is Relation-like G -defined Function-like non empty V14(G) set
o2 * c₇ is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A . [B,F] is set
the Arrows of A . (B,F) is 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
o3 is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:o3,o3:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
o3 . B is Element of the carrier of B
[(o3 . B),(o3 . B)] is V15() set
{(o3 . B),(o3 . B)} is set
{(o3 . B)} is set
{{(o3 . B),(o3 . B)},{(o3 . B)}} is set
[(o3 . B),(o3 . B)] `1 is set
o3 . F is Element of the carrier of B
[(o3 . F),(o3 . F)] is V15() set
{(o3 . F),(o3 . F)} is set
{(o3 . F)} is set
{{(o3 . F),(o3 . F)},{(o3 . F)}} is set
[(o3 . F),(o3 . F)] `1 is set
dom o2 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
(o2 * c₇) . [B,F] is set
o2 . (B,F) is Element of G
o2 . [B,F] is set
c₇ . (o2 . (B,F)) is set
the Arrows of B . ((A,B,A,B),(A,B,A,F)) is set
[(A,B,A,B),(A,B,A,F)] is V15() set
{(A,B,A,B),(A,B,A,F)} is set
{(A,B,A,B)} is set
{{(A,B,A,B),(A,B,A,F)},{(A,B,A,B)}} is set
the Arrows of B . [(A,B,A,B),(A,B,A,F)] is set
A is non empty AltGraph
B is non empty AltGraph
the carrier of A is non empty set
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
A is (A,B) (A,B)
(A,B,A,B) is Element of the carrier of B
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
<^(A,B,A,B),(A,B,A,F)^> is set
(A,B,A,B,F) is Relation-like <^B,F^> -defined <^(A,B,A,B),(A,B,A,F)^> -valued Function-like quasi_total Element of bool [:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:]
[:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:] is Relation-like set
bool [:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
G is Element of <^B,F^>
(A,B,A,B,F) . G is set
c₇ is non empty set
o2 is non empty set
[:c₇,o2:] is Relation-like non empty set
bool [:c₇,o2:] is non empty set
o3 is Relation-like c₇ -defined o2 -valued Function-like non empty V14(c₇) quasi_total Element of bool [:c₇,o2:]
f is Element of c₇
o3 . f is Element of o2
A is non empty AltGraph
B is non empty AltGraph
the carrier of A is non empty set
A is (A,B) (A,B)
B is Element of the carrier of A
F is Element of the carrier of A
(A,B,A,B,F) is Relation-like Function-like set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
[: the carrier of A, the carrier of A:] is Relation-like 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
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
<^B,F^> is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
<^(A,B,A,F),(A,B,A,B)^> is set
[:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:] is Relation-like set
bool [:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:] is non empty set
G is non empty set
[:[: the carrier of A, the carrier of A:],G:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],G:] is non empty set
o2 is Relation-like [: the carrier of A, the carrier of A:] -defined G -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],G:]
c₇ is Relation-like G -defined Function-like non empty V14(G) set
o2 * c₇ is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A . [B,F] is set
the Arrows of A . (B,F) is 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
o3 is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:o3,o3:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:o3,o3:]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
dom o2 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
dom ( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:o3,o3:]) 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:]
dom [:o3,o3:] 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:]
[:o3,o3:] . (B,B) is Element of [: the carrier of B, the carrier of B:]
[:o3,o3:] . [B,B] is set
([:o3,o3:] . (B,B)) `1 is set
o3 . B is Element of the carrier of B
[(o3 . B),(o3 . B)] is V15() set
{(o3 . B),(o3 . B)} is set
{(o3 . B)} is set
{{(o3 . B),(o3 . B)},{(o3 . B)}} is set
[(o3 . B),(o3 . B)] `1 is set
[:o3,o3:] . (F,F) is Element of [: the carrier of B, the carrier of B:]
[:o3,o3:] . [F,F] is set
([:o3,o3:] . (F,F)) `1 is set
o3 . F is Element of the carrier of B
[(o3 . F),(o3 . F)] is V15() set
{(o3 . F),(o3 . F)} is set
{(o3 . F)} is set
{{(o3 . F),(o3 . F)},{(o3 . F)}} is set
[(o3 . F),(o3 . F)] `1 is set
[F,B] is V15() set
{F,B} is set
{{F,B},{F}} is set
(o2 * c₇) . [B,F] is set
o2 . (B,F) is Element of G
o2 . [B,F] is set
c₇ . (o2 . (B,F)) is set
[:o3,o3:] . (F,B) is Element of [: the carrier of B, the carrier of B:]
[:o3,o3:] . [F,B] is set
c₇ . ([:o3,o3:] . (F,B)) is set
the Arrows of B . ((A,B,A,F),(A,B,A,B)) is set
[(A,B,A,F),(A,B,A,B)] is V15() set
{(A,B,A,F),(A,B,A,B)} is set
{(A,B,A,F)} is set
{{(A,B,A,F),(A,B,A,B)},{(A,B,A,F)}} is set
the Arrows of B . [(A,B,A,F),(A,B,A,B)] is set
A is non empty AltGraph
B is non empty AltGraph
the carrier of A is non empty set
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
A is (A,B) (A,B)
(A,B,A,F) is Element of the carrier of B
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
<^(A,B,A,F),(A,B,A,B)^> is set
(A,B,A,B,F) is Relation-like <^B,F^> -defined <^(A,B,A,F),(A,B,A,B)^> -valued Function-like quasi_total Element of bool [:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:]
[:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:] is Relation-like set
bool [:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
G is Element of <^B,F^>
(A,B,A,B,F) . G is set
c₇ is non empty set
o2 is non empty set
[:c₇,o2:] is Relation-like non empty set
bool [:c₇,o2:] is non empty set
o3 is Relation-like c₇ -defined o2 -valued Function-like non empty V14(c₇) quasi_total Element of bool [:c₇,o2:]
f is Element of c₇
o3 . f is Element of o2
B is non empty AltGraph
the carrier of B is non empty set
A is Element of the carrier of B
<^A,A^> is set
A is non empty AltGraph
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
[: the carrier of A, the carrier of A:] --> [A,A] is Relation-like [: the carrier of A, the carrier of A:] -defined {[A,A]} -valued Function-like constant non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],{[A,A]}:]
{[A,A]} is Relation-like Function-like set
[:[: the carrier of A, the carrier of A:],{[A,A]}:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],{[A,A]}:] is non empty set
B is Element of <^A,A^>
{ [[b₁,b₂],(<^b₁,b₂^> --> B)] where b₁, b₂ is Element of the carrier of A : verum } is set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
o3 is Element of [: the carrier of B, the carrier of B:]
the Arrows of B . o3 is set
the Arrows of B . (A,A) is set
the Arrows of B . [A,A] is set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
[: the carrier of A, the carrier of A:] --> o3 is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like constant non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
g is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
f is Element of the Arrows of B . o3
{ [[b₁,b₂],(<^b₁,b₂^> --> f)] where b₁, b₂ is Element of the carrier of A : verum } is set
{ [b₁,(( the Arrows of A . b₁) --> f)] where b₁ is Element of [: the carrier of A, the carrier of A:] : verum } is set
g9 is set
g99 is Element of the carrier of A
f99 is Element of the carrier of A
[g99,f99] is V15() set
{g99,f99} is set
{g99} is set
{{g99,f99},{g99}} is set
<^g99,f99^> is set
<^g99,f99^> --> f is Relation-like <^g99,f99^> -defined {f} -valued Function-like constant V14(<^g99,f99^>) quasi_total Element of bool [:<^g99,f99^>,{f}:]
{f} is set
[:<^g99,f99^>,{f}:] is Relation-like set
bool [:<^g99,f99^>,{f}:] is non empty set
[[g99,f99],(<^g99,f99^> --> f)] is V15() set
{[g99,f99],(<^g99,f99^> --> f)} is set
{[g99,f99]} is Relation-like Function-like set
{{[g99,f99],(<^g99,f99^> --> f)},{[g99,f99]}} is set
o2 is Element of [: the carrier of A, the carrier of A:]
the Arrows of A . (g99,f99) is set
the Arrows of A . [g99,f99] is set
( the Arrows of A . (g99,f99)) --> f is Relation-like the Arrows of A . (g99,f99) -defined {f} -valued Function-like constant V14( the Arrows of A . (g99,f99)) quasi_total Element of bool [:( the Arrows of A . (g99,f99)),{f}:]
[:( the Arrows of A . (g99,f99)),{f}:] is Relation-like set
bool [:( the Arrows of A . (g99,f99)),{f}:] is non empty set
[o2,(( the Arrows of A . (g99,f99)) --> f)] is V15() set
{o2,(( the Arrows of A . (g99,f99)) --> f)} is set
{o2} is set
{{o2,(( the Arrows of A . (g99,f99)) --> f)},{o2}} is set
the Arrows of A . o2 is set
( the Arrows of A . o2) --> f is Relation-like the Arrows of A . o2 -defined {f} -valued Function-like constant V14( the Arrows of A . o2) quasi_total Element of bool [:( the Arrows of A . o2),{f}:]
[:( the Arrows of A . o2),{f}:] is Relation-like set
bool [:( the Arrows of A . o2),{f}:] is non empty set
[o2,(( the Arrows of A . o2) --> f)] is V15() set
{o2,(( the Arrows of A . o2) --> f)} is set
{{o2,(( the Arrows of A . o2) --> f)},{o2}} is set
g9 is set
g99 is Element of [: the carrier of A, the carrier of A:]
the Arrows of A . g99 is set
( the Arrows of A . g99) --> f is Relation-like the Arrows of A . g99 -defined {f} -valued Function-like constant V14( the Arrows of A . g99) quasi_total Element of bool [:( the Arrows of A . g99),{f}:]
{f} is set
[:( the Arrows of A . g99),{f}:] is Relation-like set
bool [:( the Arrows of A . g99),{f}:] is non empty set
[g99,(( the Arrows of A . g99) --> f)] is V15() set
{g99,(( the Arrows of A . g99) --> f)} is set
{g99} is set
{{g99,(( the Arrows of A . g99) --> f)},{g99}} is set
g99 `1 is set
g99 `2 is set
f99 is Element of the carrier of A
o2 is Element of the carrier of A
o1 is Element of the carrier of A
o2 is Element of the carrier of A
[o1,o2] is V15() set
{o1,o2} is set
{o1} is set
{{o1,o2},{o1}} is set
the Arrows of A . (o1,o2) is set
the Arrows of A . [o1,o2] is set
( the Arrows of A . (o1,o2)) --> f is Relation-like the Arrows of A . (o1,o2) -defined {f} -valued Function-like constant V14( the Arrows of A . (o1,o2)) quasi_total Element of bool [:( the Arrows of A . (o1,o2)),{f}:]
[:( the Arrows of A . (o1,o2)),{f}:] is Relation-like set
bool [:( the Arrows of A . (o1,o2)),{f}:] is non empty set
[[o1,o2],(( the Arrows of A . (o1,o2)) --> f)] is V15() set
{[o1,o2],(( the Arrows of A . (o1,o2)) --> f)} is set
{[o1,o2]} is Relation-like Function-like set
{{[o1,o2],(( the Arrows of A . (o1,o2)) --> f)},{[o1,o2]}} is set
<^o1,o2^> is set
<^o1,o2^> --> f is Relation-like <^o1,o2^> -defined {f} -valued Function-like constant V14(<^o1,o2^>) quasi_total Element of bool [:<^o1,o2^>,{f}:]
[:<^o1,o2^>,{f}:] is Relation-like set
bool [:<^o1,o2^>,{f}:] is non empty set
[[o1,o2],(<^o1,o2^> --> f)] is V15() set
{[o1,o2],(<^o1,o2^> --> f)} is set
{{[o1,o2],(<^o1,o2^> --> f)},{[o1,o2]}} is set
K is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
g9 is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:],K, the Arrows of A, the Arrows of B)
(A,B,K,g9) is (A,B) (A,B)
the of (A,B,K,g9) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the of (A,B,K,g9) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of (A,B,K,g9), the Arrows of A, the Arrows of B)
F is (A,B) (A,B)
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: 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 A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of F, the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
G is (A,B) (A,B)
the of G is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the of G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of G, the Arrows of A, the Arrows of B)
B is non empty AltGraph
the carrier of B is non empty set
A is non empty AltGraph
the carrier of A is non empty set
A is Element of the carrier of B
<^A,A^> is set
B is Element of <^A,A^>
(A,B,A,B) is (A,B) (A,B)
F is Element of the carrier of A
(A,B,(A,B,A,B),F) is Element of the carrier of B
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of (A,B,A,B) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of (A,B,A,B) . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of (A,B,A,B) . [F,F] is set
( the of (A,B,A,B) . (F,F)) `1 is set
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
{[A,A]} is Relation-like Function-like set
[: the carrier of A, the carrier of A:] --> [A,A] is Relation-like [: the carrier of A, the carrier of A:] -defined {[A,A]} -valued Function-like constant non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],{[A,A]}:]
[:[: the carrier of A, the carrier of A:],{[A,A]}:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],{[A,A]}:] is non empty set
([: the carrier of A, the carrier of A:] --> [A,A]) . (F,F) is Element of {[A,A]}
([: the carrier of A, the carrier of A:] --> [A,A]) . [F,F] is set
(([: the carrier of A, the carrier of A:] --> [A,A]) . (F,F)) `1 is set
[A,A] `1 is set
B is non empty reflexive AltGraph
the carrier of B is non empty set
A is Element of the carrier of B
<^A,A^> is set
A is non empty AltGraph
B is Element of <^A,A^>
(A,B,A,B) is (A,B) (A,B)
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the of (A,B,A,B) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: 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 A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
[: the carrier of A, the carrier of A:] --> [A,A] is Relation-like [: the carrier of A, the carrier of A:] -defined {[A,A]} -valued Function-like constant non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],{[A,A]}:]
{[A,A]} is Relation-like Function-like set
[:[: the carrier of A, the carrier of A:],{[A,A]}:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],{[A,A]}:] is non empty set
F is Element of the carrier of A
G is Element of the carrier of A
<^F,G^> is set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of (A,B,A,B) . (F,G) is Element of [: the carrier of B, the carrier of B:]
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
the of (A,B,A,B) . [F,G] is set
the Arrows of B . ( the of (A,B,A,B) . (F,G)) is set
the Arrows of B . (A,A) is set
the Arrows of B . [A,A] is set
A is non empty AltGraph
B is non empty reflexive AltGraph
the carrier of B is non empty set
the Element of the carrier of B is Element of the carrier of B
<^ the Element of the carrier of B, the Element of the carrier of B^> is set
the Element of <^ the Element of the carrier of B, the Element of the carrier of B^> is Element of <^ the Element of the carrier of B, the Element of the carrier of B^>
(A,B, the Element of the carrier of B, the Element of <^ the Element of the carrier of B, the Element of the carrier of B^>) is (A,B) (A,B) (A,B) (A,B) (A,B)
A is non empty AltGraph
B is non empty AltGraph
the carrier of A 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
A is (A,B) (A,B)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
B is Element of the carrier of A
F is Element of the carrier of A
the of A . (B,F) is Element of [: the carrier of B, the carrier of B:]
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
the of A . [B,F] is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
[(A,B,A,B),(A,B,A,F)] is V15() set
{(A,B,A,B),(A,B,A,F)} is set
{(A,B,A,B)} is set
{{(A,B,A,B),(A,B,A,F)},{(A,B,A,B)}} is 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
G is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
G . B is Element of the carrier of B
[(G . B),(G . B)] is V15() set
{(G . B),(G . B)} is set
{(G . B)} is set
{{(G . B),(G . B)},{(G . B)}} is set
[(G . B),(G . B)] `1 is set
G . F is Element of the carrier of B
[(G . F),(G . F)] is V15() set
{(G . F),(G . F)} is set
{(G . F)} is set
{{(G . F),(G . F)},{(G . F)}} is set
[(G . F),(G . F)] `1 is set
A is non empty AltGraph
B is non empty AltGraph
A is (A,B) (A,B)
the carrier of A is non empty set
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
(A,B,A,B) is Element of the carrier of B
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
<^(A,B,A,B),(A,B,A,F)^> is set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the Arrows of B . ((A,B,A,B),(A,B,A,F)) is set
[(A,B,A,B),(A,B,A,F)] is V15() set
{(A,B,A,B),(A,B,A,F)} is set
{(A,B,A,B)} is set
{{(A,B,A,B),(A,B,A,F)},{(A,B,A,B)}} is set
the Arrows of B . [(A,B,A,B),(A,B,A,F)] is set
the of A . (B,F) is Element of [: the carrier of B, the carrier of B:]
[B,F] is V15() set
{B,F} is set
{{B,F},{B}} is set
the of A . [B,F] is set
the Arrows of B . ( the of A . (B,F)) is set
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
the of A . (B,F) is Element of [: the carrier of B, the carrier of B:]
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
the of A . [B,F] is set
the Arrows of B . ( the of A . (B,F)) is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
<^(A,B,A,B),(A,B,A,F)^> is set
the Arrows of B . ((A,B,A,B),(A,B,A,F)) is set
[(A,B,A,B),(A,B,A,F)] is V15() set
{(A,B,A,B),(A,B,A,F)} is set
{(A,B,A,B)} is set
{{(A,B,A,B),(A,B,A,F)},{(A,B,A,B)}} is set
the Arrows of B . [(A,B,A,B),(A,B,A,F)] is set
A is non empty AltGraph
B is non empty AltGraph
the carrier of A 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
A is (A,B) (A,B)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
B is Element of the carrier of A
F is Element of the carrier of A
the of A . (B,F) is Element of [: the carrier of B, the carrier of B:]
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
the of A . [B,F] is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
[(A,B,A,F),(A,B,A,B)] is V15() set
{(A,B,A,F),(A,B,A,B)} is set
{(A,B,A,F)} is set
{{(A,B,A,F),(A,B,A,B)},{(A,B,A,F)}} is 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
G is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:G,G:]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
dom [:G,G:] 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
[:G,G:] . (B,B) is Element of [: the carrier of B, the carrier of B:]
[:G,G:] . [B,B] is set
([:G,G:] . (B,B)) `1 is set
G . B is Element of the carrier of B
[(G . B),(G . B)] is V15() set
{(G . B),(G . B)} is set
{(G . B)} is set
{{(G . B),(G . B)},{(G . B)}} is set
[(G . B),(G . B)] `1 is set
[:G,G:] . (F,F) is Element of [: the carrier of B, the carrier of B:]
[:G,G:] . [F,F] is set
([:G,G:] . (F,F)) `1 is set
G . F is Element of the carrier of B
[(G . F),(G . F)] is V15() set
{(G . F),(G . F)} is set
{(G . F)} is set
{{(G . F),(G . F)},{(G . F)}} is set
[(G . F),(G . F)] `1 is set
[F,B] is V15() set
{F,B} is set
{{F,B},{F}} is set
[:G,G:] . (F,B) is Element of [: the carrier of B, the carrier of B:]
[:G,G:] . [F,B] is set
A is non empty AltGraph
B is non empty AltGraph
A is (A,B) (A,B)
the carrier of A is non empty set
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
(A,B,A,F) is Element of the carrier of B
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
<^(A,B,A,F),(A,B,A,B)^> is set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the Arrows of B . ((A,B,A,F),(A,B,A,B)) is set
[(A,B,A,F),(A,B,A,B)] is V15() set
{(A,B,A,F),(A,B,A,B)} is set
{(A,B,A,F)} is set
{{(A,B,A,F),(A,B,A,B)},{(A,B,A,F)}} is set
the Arrows of B . [(A,B,A,F),(A,B,A,B)] is set
the of A . (B,F) is Element of [: the carrier of B, the carrier of B:]
[B,F] is V15() set
{B,F} is set
{{B,F},{B}} is set
the of A . [B,F] is set
the Arrows of B . ( the of A . (B,F)) is set
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
the of A . (B,F) is Element of [: the carrier of B, the carrier of B:]
[B,F] is V15() set
{B,F} is set
{B} is set
{{B,F},{B}} is set
the of A . [B,F] is set
the Arrows of B . ( the of A . (B,F)) is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
<^(A,B,A,F),(A,B,A,B)^> is set
the Arrows of B . ((A,B,A,F),(A,B,A,B)) is set
[(A,B,A,F),(A,B,A,B)] is V15() set
{(A,B,A,F),(A,B,A,B)} is set
{(A,B,A,F)} is set
{{(A,B,A,F),(A,B,A,B)},{(A,B,A,F)}} is set
the Arrows of B . [(A,B,A,F),(A,B,A,B)] is set
A is AltGraph
B is AltGraph
A is (A,B)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the carrier of A is set
[: the carrier of A, the carrier of A:] is Relation-like set
the carrier of B is set
[: the carrier of B, the carrier of B:] is Relation-like set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) set
the non empty transitive V129() with_units reflexive AltCatStr is non empty transitive V129() with_units reflexive AltCatStr
A is non empty with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
B is non empty AltGraph
the carrier of B is non empty set
A is non empty AltGraph
the carrier of A is non empty set
A is Element of the carrier of B
<^A,A^> is set
B is Element of <^A,A^>
(A,B,A,B) is (A,B) (A,B)
F is Element of the carrier of A
G is Element of the carrier of A
<^F,G^> is set
(A,B,(A,B,A,B),F,G) is Relation-like Function-like set
the of (A,B,A,B) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of (A,B,A,B), the Arrows of A, the Arrows of B)
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of (A,B,A,B) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of (A,B,A,B) . (F,G) is set
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
the of (A,B,A,B) . [F,G] is Relation-like Function-like set
c<sub>7</sub> is Element of <^F,G^>
(A,B,(A,B,A,B),F,G) . c<sub>7</sub> is set
{ [[b<sub>1</sub>,b<sub>2</sub>],(<^b<sub>1</sub>,b<sub>2</sub>^> --> B)] where b<sub>1</sub>, b<sub>2</sub> is Element of the carrier of A : verum } is set
{ [[b<sub>1</sub>,b<sub>2</sub>],(( the Arrows of A . (b<sub>1</sub>,b<sub>2</sub>)) --> B)] where b<sub>1</sub>, b<sub>2</sub> is Element of the carrier of A : verum } is set
f is set
g is Element of the carrier of A
K is Element of the carrier of A
[g,K] is V15() set
{g,K} is set
{g} is set
{{g,K},{g}} is set
<^g,K^> is set
<^g,K^> --> B is Relation-like <^g,K^> -defined {B} -valued Function-like constant V14(<^g,K^>) quasi_total Element of bool [:<^g,K^>,{B}:]
{B} is set
[:<^g,K^>,{B}:] is Relation-like set
bool [:<^g,K^>,{B}:] is non empty set
[[g,K],(<^g,K^> --> B)] is V15() set
{[g,K],(<^g,K^> --> B)} is set
{[g,K]} is Relation-like Function-like set
{{[g,K],(<^g,K^> --> B)},{[g,K]}} is set
the Arrows of A . (g,K) is set
the Arrows of A . [g,K] is set
( the Arrows of A . (g,K)) --> B is Relation-like the Arrows of A . (g,K) -defined {B} -valued Function-like constant V14( the Arrows of A . (g,K)) quasi_total Element of bool [:( the Arrows of A . (g,K)),{B}:]
[:( the Arrows of A . (g,K)),{B}:] is Relation-like set
bool [:( the Arrows of A . (g,K)),{B}:] is non empty set
[[g,K],(( the Arrows of A . (g,K)) --> B)] is V15() set
{[g,K],(( the Arrows of A . (g,K)) --> B)} is set
{{[g,K],(( the Arrows of A . (g,K)) --> B)},{[g,K]}} is set
f is set
g is Element of the carrier of A
K is Element of the carrier of A
[g,K] is V15() set
{g,K} is set
{g} is set
{{g,K},{g}} is set
the Arrows of A . (g,K) is set
the Arrows of A . [g,K] is set
( the Arrows of A . (g,K)) --> B is Relation-like the Arrows of A . (g,K) -defined {B} -valued Function-like constant V14( the Arrows of A . (g,K)) quasi_total Element of bool [:( the Arrows of A . (g,K)),{B}:]
{B} is set
[:( the Arrows of A . (g,K)),{B}:] is Relation-like set
bool [:( the Arrows of A . (g,K)),{B}:] is non empty set
[[g,K],(( the Arrows of A . (g,K)) --> B)] is V15() set
{[g,K],(( the Arrows of A . (g,K)) --> B)} is set
{[g,K]} is Relation-like Function-like set
{{[g,K],(( the Arrows of A . (g,K)) --> B)},{[g,K]}} is set
f9 is Element of the carrier of A
g9 is Element of the carrier of A
[f9,g9] is V15() set
{f9,g9} is set
{f9} is set
{{f9,g9},{f9}} is set
<^f9,g9^> is set
<^f9,g9^> --> B is Relation-like <^f9,g9^> -defined {B} -valued Function-like constant V14(<^f9,g9^>) quasi_total Element of bool [:<^f9,g9^>,{B}:]
[:<^f9,g9^>,{B}:] is Relation-like set
bool [:<^f9,g9^>,{B}:] is non empty set
[[f9,g9],(<^f9,g9^> --> B)] is V15() set
{[f9,g9],(<^f9,g9^> --> B)} is set
{[f9,g9]} is Relation-like Function-like set
{{[f9,g9],(<^f9,g9^> --> B)},{[f9,g9]}} is set
{B} is set
{ [[b<sub>1</sub>,b<sub>2</sub>],H<sub>1</sub>(b<sub>1</sub>,b<sub>2</sub>)] where b<sub>1</sub>, b<sub>2</sub> is Element of the carrier of A : S<sub>1</sub>[b<sub>1</sub>,b<sub>2</sub>] } is set
the Arrows of A . (F,G) is set
the Arrows of A . [F,G] is set
( the Arrows of A . (F,G)) --> B is Relation-like the Arrows of A . (F,G) -defined {B} -valued Function-like constant V14( the Arrows of A . (F,G)) quasi_total Element of bool [:( the Arrows of A . (F,G)),{B}:]
[:( the Arrows of A . (F,G)),{B}:] is Relation-like set
bool [:( the Arrows of A . (F,G)),{B}:] is non empty set
<^F,G^> --> B is Relation-like <^F,G^> -defined {B} -valued Function-like constant V14(<^F,G^>) quasi_total Element of bool [:<^F,G^>,{B}:]
[:<^F,G^>,{B}:] is Relation-like set
bool [:<^F,G^>,{B}:] is non empty set
(<^F,G^> --> B) . c<sub>7</sub> is set
A is non empty AltCatStr
B is non empty with_units reflexive AltCatStr
the carrier of B is non empty set
A is non empty with_units reflexive AltCatStr
A is Element of the carrier of B
idm A is Element of <^A,A^>
<^A,A^> is set
(A,B,A,(idm A)) is (A,B) (A,B) (A,B) (A,B) (A,B)
the carrier of A is non empty set
B is Element of the carrier of A
(A,B,(A,B,A,(idm A)),B,B) is Relation-like Function-like set
the of (A,B,A,(idm A)) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of (A,B,A,(idm A)), the Arrows of A, the Arrows of B)
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of (A,B,A,(idm A)) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of (A,B,A,(idm A)) . (B,B) is set
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of (A,B,A,(idm A)) . [B,B] is Relation-like Function-like set
idm B is Element of <^B,B^>
<^B,B^> is set
(A,B,(A,B,A,(idm A)),B,B) . (idm B) is set
(A,B,(A,B,A,(idm A)),B) is Element of the carrier of B
the of (A,B,A,(idm A)) . (B,B) is Element of [: the carrier of B, the carrier of B:]
the of (A,B,A,(idm A)) . [B,B] is set
( the of (A,B,A,(idm A)) . (B,B)) `1 is set
idm (A,B,(A,B,A,(idm A)),B) is Element of <^(A,B,(A,B,A,(idm A)),B),(A,B,(A,B,A,(idm A)),B)^>
<^(A,B,(A,B,A,(idm A)),B),(A,B,(A,B,A,(idm A)),B)^> is set
(A,B,(A,B,A,(idm A)),B,B) is Relation-like <^B,B^> -defined <^(A,B,(A,B,A,(idm A)),B),(A,B,(A,B,A,(idm A)),B)^> -valued Function-like quasi_total Element of bool [:<^B,B^>,<^(A,B,(A,B,A,(idm A)),B),(A,B,(A,B,A,(idm A)),B)^>:]
[:<^B,B^>,<^(A,B,(A,B,A,(idm A)),B),(A,B,(A,B,A,(idm A)),B)^>:] is Relation-like set
bool [:<^B,B^>,<^(A,B,(A,B,A,(idm A)),B),(A,B,(A,B,A,(idm A)),B)^>:] is non empty set
(A,B,(A,B,A,(idm A)),B,B) . (idm B) is set
B is non empty reflexive AltGraph
the carrier of B is non empty set
A is Element of the carrier of B
<^A,A^> is set
A is non empty AltGraph
B is Element of <^A,A^>
(A,B,A,B) is (A,B) (A,B) (A,B) (A,B) (A,B)
the carrier of A is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of (A,B,A,B) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
F is Element of the carrier of A
the of (A,B,A,B) . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of (A,B,A,B) . [F,F] is set
(A,B,(A,B,A,B),F) is Element of the carrier of B
( the of (A,B,A,B) . (F,F)) `1 is set
[(A,B,(A,B,A,B),F),(A,B,(A,B,A,B),F)] is V15() set
{(A,B,(A,B,A,B),F),(A,B,(A,B,A,B),F)} is set
{(A,B,(A,B,A,B),F)} is set
{{(A,B,(A,B,A,B),F),(A,B,(A,B,A,B),F)},{(A,B,(A,B,A,B),F)}} is set
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
[: the carrier of A, the carrier of A:] --> [A,A] is Relation-like [: the carrier of A, the carrier of A:] -defined {[A,A]} -valued Function-like constant non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],{[A,A]}:]
{[A,A]} is Relation-like Function-like set
[:[: the carrier of A, the carrier of A:],{[A,A]}:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],{[A,A]}:] is non empty set
([: the carrier of A, the carrier of A:] --> [A,A]) . [F,F] is set
A is non empty AltGraph
B is non empty reflexive AltGraph
the carrier of B is non empty set
the Element of the carrier of B is Element of the carrier of B
<^ the Element of the carrier of B, the Element of the carrier of B^> is set
the Element of <^ the Element of the carrier of B, the Element of the carrier of B^> is Element of <^ the Element of the carrier of B, the Element of the carrier of B^>
(A,B, the Element of the carrier of B, the Element of <^ the Element of the carrier of B, the Element of the carrier of B^>) is (A,B) (A,B) (A,B) (A,B) (A,B) (A,B)
A is non empty with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
the carrier of B is non empty set
the Element of the carrier of B is Element of the carrier of B
idm the Element of the carrier of B is Element of <^ the Element of the carrier of B, the Element of the carrier of B^>
<^ the Element of the carrier of B, the Element of the carrier of B^> is set
(A,B, the Element of the carrier of B,(idm the Element of the carrier of B)) is (A,B) (A,B) (A,B) (A,B) (A,B) (A,B) (A,B)
A is non empty AltCatStr
B is non empty AltCatStr
A is non empty AltCatStr
B is non empty AltCatStr
A is non empty transitive AltCatStr
B is non empty reflexive AltCatStr
A is (A,B) (A,B) (A,B)
the carrier of A is non empty set
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
G is Element of the carrier of A
<^F,G^> is set
(A,B,A,B) is Element of the carrier of B
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
<^(A,B,A,B),(A,B,A,F)^> is set
(A,B,A,G) is Element of the carrier of B
the of A . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of A . [G,G] is set
( the of A . (G,G)) `1 is set
<^(A,B,A,F),(A,B,A,G)^> is set
(A,B,A,B,F) is Relation-like <^B,F^> -defined <^(A,B,A,B),(A,B,A,F)^> -valued Function-like quasi_total Element of bool [:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:]
[:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:] is Relation-like set
bool [:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
c₇ is Element of <^B,F^>
(A,B,A,B,F) . c₇ is set
(A,B,A,F,G) is Relation-like <^F,G^> -defined <^(A,B,A,F),(A,B,A,G)^> -valued Function-like quasi_total Element of bool [:<^F,G^>,<^(A,B,A,F),(A,B,A,G)^>:]
[:<^F,G^>,<^(A,B,A,F),(A,B,A,G)^>:] is Relation-like set
bool [:<^F,G^>,<^(A,B,A,F),(A,B,A,G)^>:] is non empty set
the of A . (F,G) is set
[F,G] is V15() set
{F,G} is set
{{F,G},{F}} is set
the of A . [F,G] is Relation-like Function-like set
o2 is Element of <^F,G^>
(A,B,A,F,G) . o2 is set
(A,B,A,B,G) is Relation-like <^B,G^> -defined <^(A,B,A,B),(A,B,A,G)^> -valued Function-like quasi_total Element of bool [:<^B,G^>,<^(A,B,A,B),(A,B,A,G)^>:]
<^B,G^> is set
<^(A,B,A,B),(A,B,A,G)^> is set
[:<^B,G^>,<^(A,B,A,B),(A,B,A,G)^>:] is Relation-like set
bool [:<^B,G^>,<^(A,B,A,B),(A,B,A,G)^>:] is non empty set
the of A . (B,G) is set
[B,G] is V15() set
{B,G} is set
{{B,G},{B}} is set
the of A . [B,G] is Relation-like Function-like set
o2 * c₇ is Element of <^B,G^>
(A,B,A,B,G) . (o2 * c₇) is set
o3 is Element of <^(A,B,A,B),(A,B,A,F)^>
f is Element of <^(A,B,A,F),(A,B,A,G)^>
f * o3 is Element of <^(A,B,A,B),(A,B,A,G)^>
(A,B,A,B,F,c₇) is Element of <^(A,B,A,B),(A,B,A,F)^>
(A,B,A,F,G,o2) is Element of <^(A,B,A,F),(A,B,A,G)^>
(A,B,A,B,G,(o2 * c₇)) is Element of <^(A,B,A,B),(A,B,A,G)^>
(A,B,A,F,G,o2) * (A,B,A,B,F,c₇) is Element of <^(A,B,A,B),(A,B,A,G)^>
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
G is Element of the carrier of A
<^F,G^> is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
<^(A,B,A,B),(A,B,A,F)^> is set
(A,B,A,G) is Element of the carrier of B
the of A . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of A . [G,G] is set
( the of A . (G,G)) `1 is set
<^(A,B,A,F),(A,B,A,G)^> is set
(A,B,A,B,F) is Relation-like Function-like set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
(A,B,A,F,G) is Relation-like Function-like set
the of A . (F,G) is set
[F,G] is V15() set
{F,G} is set
{{F,G},{F}} is set
the of A . [F,G] is Relation-like Function-like set
(A,B,A,B,G) is Relation-like Function-like set
the of A . (B,G) is set
[B,G] is V15() set
{B,G} is set
{{B,G},{B}} is set
the of A . [B,G] is Relation-like Function-like set
c<sub>7</sub> is Element of <^B,F^>
(A,B,A,B,F) . c<sub>7</sub> is set
o2 is Element of <^F,G^>
(A,B,A,F,G) . o2 is set
o2 * c<sub>7</sub> is Element of <^B,G^>
<^B,G^> is set
(A,B,A,B,G) . (o2 * c<sub>7</sub>) is set
(A,B,A,B,F) is Relation-like <^B,F^> -defined <^(A,B,A,B),(A,B,A,F)^> -valued Function-like quasi_total Element of bool [:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:]
[:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:] is Relation-like set
bool [:<^B,F^>,<^(A,B,A,B),(A,B,A,F)^>:] is non empty set
(A,B,A,B,F) . c<sub>7</sub> is set
(A,B,A,F,G) is Relation-like <^F,G^> -defined <^(A,B,A,F),(A,B,A,G)^> -valued Function-like quasi_total Element of bool [:<^F,G^>,<^(A,B,A,F),(A,B,A,G)^>:]
[:<^F,G^>,<^(A,B,A,F),(A,B,A,G)^>:] is Relation-like set
bool [:<^F,G^>,<^(A,B,A,F),(A,B,A,G)^>:] is non empty set
(A,B,A,F,G) . o2 is set
o3 is Element of <^(A,B,A,B),(A,B,A,F)^>
f is Element of <^(A,B,A,F),(A,B,A,G)^>
f * o3 is Element of <^(A,B,A,B),(A,B,A,G)^>
<^(A,B,A,B),(A,B,A,G)^> is set
(A,B,A,B,F,c<sub>7</sub>) is Element of <^(A,B,A,B),(A,B,A,F)^>
(A,B,A,F,G,o2) is Element of <^(A,B,A,F),(A,B,A,G)^>
(A,B,A,B,G) is Relation-like <^B,G^> -defined <^(A,B,A,B),(A,B,A,G)^> -valued Function-like quasi_total Element of bool [:<^B,G^>,<^(A,B,A,B),(A,B,A,G)^>:]
[:<^B,G^>,<^(A,B,A,B),(A,B,A,G)^>:] is Relation-like set
bool [:<^B,G^>,<^(A,B,A,B),(A,B,A,G)^>:] is non empty set
(A,B,A,B,G) . (o2 * c<sub>7</sub>) is set
(A,B,A,B,G,(o2 * c<sub>7</sub>)) is Element of <^(A,B,A,B),(A,B,A,G)^>
A is non empty transitive AltCatStr
B is non empty reflexive AltCatStr
A is (A,B) (A,B) (A,B)
the carrier of A is non empty set
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
G is Element of the carrier of A
<^F,G^> is set
(A,B,A,F) is Element of the carrier of B
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
<^(A,B,A,F),(A,B,A,B)^> is set
(A,B,A,G) is Element of the carrier of B
the of A . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of A . [G,G] is set
( the of A . (G,G)) `1 is set
<^(A,B,A,G),(A,B,A,F)^> is set
(A,B,A,B,F) is Relation-like <^B,F^> -defined <^(A,B,A,F),(A,B,A,B)^> -valued Function-like quasi_total Element of bool [:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:]
[:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:] is Relation-like set
bool [:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
c₇ is Element of <^B,F^>
(A,B,A,B,F) . c₇ is set
(A,B,A,F,G) is Relation-like <^F,G^> -defined <^(A,B,A,G),(A,B,A,F)^> -valued Function-like quasi_total Element of bool [:<^F,G^>,<^(A,B,A,G),(A,B,A,F)^>:]
[:<^F,G^>,<^(A,B,A,G),(A,B,A,F)^>:] is Relation-like set
bool [:<^F,G^>,<^(A,B,A,G),(A,B,A,F)^>:] is non empty set
the of A . (F,G) is set
[F,G] is V15() set
{F,G} is set
{{F,G},{F}} is set
the of A . [F,G] is Relation-like Function-like set
o2 is Element of <^F,G^>
(A,B,A,F,G) . o2 is set
(A,B,A,B,G) is Relation-like <^B,G^> -defined <^(A,B,A,G),(A,B,A,B)^> -valued Function-like quasi_total Element of bool [:<^B,G^>,<^(A,B,A,G),(A,B,A,B)^>:]
<^B,G^> is set
<^(A,B,A,G),(A,B,A,B)^> is set
[:<^B,G^>,<^(A,B,A,G),(A,B,A,B)^>:] is Relation-like set
bool [:<^B,G^>,<^(A,B,A,G),(A,B,A,B)^>:] is non empty set
the of A . (B,G) is set
[B,G] is V15() set
{B,G} is set
{{B,G},{B}} is set
the of A . [B,G] is Relation-like Function-like set
o2 * c₇ is Element of <^B,G^>
(A,B,A,B,G) . (o2 * c₇) is set
o3 is Element of <^(A,B,A,F),(A,B,A,B)^>
f is Element of <^(A,B,A,G),(A,B,A,F)^>
o3 * f is Element of <^(A,B,A,G),(A,B,A,B)^>
(A,B,A,B,F,c₇) is Element of <^(A,B,A,F),(A,B,A,B)^>
(A,B,A,F,G,o2) is Element of <^(A,B,A,G),(A,B,A,F)^>
(A,B,A,B,G,(o2 * c₇)) is Element of <^(A,B,A,G),(A,B,A,B)^>
(A,B,A,B,F,c₇) * (A,B,A,F,G,o2) is Element of <^(A,B,A,G),(A,B,A,B)^>
B is Element of the carrier of A
F is Element of the carrier of A
<^B,F^> is set
G is Element of the carrier of A
<^F,G^> is set
(A,B,A,F) is Element of the carrier of B
the of A . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of A . [F,F] is set
( the of A . (F,F)) `1 is set
(A,B,A,B) is Element of the carrier of B
the of A . (B,B) is Element of [: the carrier of B, the carrier of B:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of A . [B,B] is set
( the of A . (B,B)) `1 is set
<^(A,B,A,F),(A,B,A,B)^> is set
(A,B,A,G) is Element of the carrier of B
the of A . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of A . [G,G] is set
( the of A . (G,G)) `1 is set
<^(A,B,A,G),(A,B,A,F)^> is set
(A,B,A,B,F) is Relation-like Function-like set
the of A . (B,F) is set
[B,F] is V15() set
{B,F} is set
{{B,F},{B}} is set
the of A . [B,F] is Relation-like Function-like set
(A,B,A,F,G) is Relation-like Function-like set
the of A . (F,G) is set
[F,G] is V15() set
{F,G} is set
{{F,G},{F}} is set
the of A . [F,G] is Relation-like Function-like set
(A,B,A,B,G) is Relation-like Function-like set
the of A . (B,G) is set
[B,G] is V15() set
{B,G} is set
{{B,G},{B}} is set
the of A . [B,G] is Relation-like Function-like set
c<sub>7</sub> is Element of <^B,F^>
(A,B,A,B,F) . c<sub>7</sub> is set
o2 is Element of <^F,G^>
(A,B,A,F,G) . o2 is set
o2 * c<sub>7</sub> is Element of <^B,G^>
<^B,G^> is set
(A,B,A,B,G) . (o2 * c<sub>7</sub>) is set
(A,B,A,B,F) is Relation-like <^B,F^> -defined <^(A,B,A,F),(A,B,A,B)^> -valued Function-like quasi_total Element of bool [:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:]
[:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:] is Relation-like set
bool [:<^B,F^>,<^(A,B,A,F),(A,B,A,B)^>:] is non empty set
(A,B,A,B,F) . c<sub>7</sub> is set
(A,B,A,F,G) is Relation-like <^F,G^> -defined <^(A,B,A,G),(A,B,A,F)^> -valued Function-like quasi_total Element of bool [:<^F,G^>,<^(A,B,A,G),(A,B,A,F)^>:]
[:<^F,G^>,<^(A,B,A,G),(A,B,A,F)^>:] is Relation-like set
bool [:<^F,G^>,<^(A,B,A,G),(A,B,A,F)^>:] is non empty set
(A,B,A,F,G) . o2 is set
o3 is Element of <^(A,B,A,F),(A,B,A,B)^>
f is Element of <^(A,B,A,G),(A,B,A,F)^>
o3 * f is Element of <^(A,B,A,G),(A,B,A,B)^>
<^(A,B,A,G),(A,B,A,B)^> is set
(A,B,A,B,F,c<sub>7</sub>) is Element of <^(A,B,A,F),(A,B,A,B)^>
(A,B,A,F,G,o2) is Element of <^(A,B,A,G),(A,B,A,F)^>
(A,B,A,B,G) is Relation-like <^B,G^> -defined <^(A,B,A,G),(A,B,A,B)^> -valued Function-like quasi_total Element of bool [:<^B,G^>,<^(A,B,A,G),(A,B,A,B)^>:]
[:<^B,G^>,<^(A,B,A,G),(A,B,A,B)^>:] is Relation-like set
bool [:<^B,G^>,<^(A,B,A,G),(A,B,A,B)^>:] is non empty set
(A,B,A,B,G) . (o2 * c<sub>7</sub>) is set
(A,B,A,B,G,(o2 * c<sub>7</sub>)) is Element of <^(A,B,A,G),(A,B,A,B)^>
A is non empty AltGraph
the carrier of A is non empty set
B is non empty reflexive AltGraph
the carrier of B is non empty set
A is Element of the carrier of B
<^A,A^> is set
B is Element of <^A,A^>
(A,B,A,B) is (A,B) (A,B) (A,B) (A,B) (A,B) (A,B)
F is (A,B) (A,B) (A,B)
G is Element of the carrier of A
c<sub>7</sub> is Element of the carrier of A
<^G,c<sub>7</sub>^> is set
o2 is Element of <^G,c<sub>7</sub>^>
(A,B,F,G,c<sub>7</sub>,o2) is Element of <^(A,B,F,G),(A,B,F,c<sub>7</sub>)^>
(A,B,F,G) is Element of the carrier of B
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of F . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of F . [G,G] is set
( the of F . (G,G)) `1 is set
(A,B,F,c₇) is Element of the carrier of B
the of F . (c₇,c₇) is Element of [: the carrier of B, the carrier of B:]
[c₇,c₇] is V15() set
{c₇,c₇} is set
{c₇} is set
{{c₇,c₇},{c₇}} is set
the of F . [c₇,c₇] is set
( the of F . (c₇,c₇)) `1 is set
<^(A,B,F,G),(A,B,F,c<sub>7</sub>)^> is set
(A,B,F,G,c<sub>7</sub>) is Relation-like <^G,c<sub>7</sub>^> -defined <^(A,B,F,G),(A,B,F,c<sub>7</sub>)^> -valued Function-like quasi_total Element of bool [:<^G,c<sub>7</sub>^>,<^(A,B,F,G),(A,B,F,c<sub>7</sub>)^>:]
[:<^G,c<sub>7</sub>^>,<^(A,B,F,G),(A,B,F,c<sub>7</sub>)^>:] is Relation-like set
bool [:<^G,c<sub>7</sub>^>,<^(A,B,F,G),(A,B,F,c<sub>7</sub>)^>:] is non empty set
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of F, the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of F . (G,c<sub>7</sub>) is set
[G,c<sub>7</sub>] is V15() set
{G,c<sub>7</sub>} is set
{{G,c<sub>7</sub>},{G}} is set
the of F . [G,c<sub>7</sub>] is Relation-like Function-like set
(A,B,F,G,c<sub>7</sub>) . o2 is set
A is non empty AltGraph
the carrier of A is non empty set
B is non empty reflexive AltGraph
the carrier of B is non empty set
A is Element of the carrier of B
<^A,A^> is set
B is Element of <^A,A^>
(A,B,A,B) is (A,B) (A,B) (A,B) (A,B) (A,B) (A,B)
G is Element of the carrier of A
c<sub>7</sub> is Element of the carrier of A
<^G,c<sub>7</sub>^> is set
o2 is Element of <^G,c<sub>7</sub>^>
(A,B,(A,B,A,B),G,c<sub>7</sub>,o2) is Element of <^(A,B,(A,B,A,B),c<sub>7</sub>),(A,B,(A,B,A,B),G)^>
(A,B,(A,B,A,B),c<sub>7</sub>) is Element of the carrier of B
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of (A,B,A,B) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of (A,B,A,B) . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of B, the carrier of B:]
[c<sub>7</sub>,c<sub>7</sub>] is V15() set
{c<sub>7</sub>,c<sub>7</sub>} is set
{c<sub>7</sub>} is set
{{c<sub>7</sub>,c<sub>7</sub>},{c<sub>7</sub>}} is set
the of (A,B,A,B) . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of (A,B,A,B) . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
(A,B,(A,B,A,B),G) is Element of the carrier of B
the of (A,B,A,B) . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of (A,B,A,B) . [G,G] is set
( the of (A,B,A,B) . (G,G)) `1 is set
<^(A,B,(A,B,A,B),c<sub>7</sub>),(A,B,(A,B,A,B),G)^> is set
(A,B,(A,B,A,B),G,c<sub>7</sub>) is Relation-like <^G,c<sub>7</sub>^> -defined <^(A,B,(A,B,A,B),c<sub>7</sub>),(A,B,(A,B,A,B),G)^> -valued Function-like quasi_total Element of bool [:<^G,c<sub>7</sub>^>,<^(A,B,(A,B,A,B),c<sub>7</sub>),(A,B,(A,B,A,B),G)^>:]
[:<^G,c<sub>7</sub>^>,<^(A,B,(A,B,A,B),c<sub>7</sub>),(A,B,(A,B,A,B),G)^>:] is Relation-like set
bool [:<^G,c<sub>7</sub>^>,<^(A,B,(A,B,A,B),c<sub>7</sub>),(A,B,(A,B,A,B),G)^>:] is non empty set
the of (A,B,A,B) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of (A,B,A,B), the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of (A,B,A,B) . (G,c<sub>7</sub>) is set
[G,c<sub>7</sub>] is V15() set
{G,c<sub>7</sub>} is set
{{G,c<sub>7</sub>},{G}} is set
the of (A,B,A,B) . [G,c<sub>7</sub>] is Relation-like Function-like set
(A,B,(A,B,A,B),G,c<sub>7</sub>) . o2 is set
B is non empty with_units reflexive AltCatStr
the carrier of B is non empty set
A is non empty transitive AltCatStr
A is Element of the carrier of B
idm A is Element of <^A,A^>
<^A,A^> is set
(A,B,A,(idm A)) is (A,B) (A,B) (A,B) (A,B) (A,B) (A,B)
F is (A,B) (A,B) (A,B)
the carrier of A is non empty set
G is Element of the carrier of A
c<sub>7</sub> is Element of the carrier of A
<^G,c<sub>7</sub>^> is set
o2 is Element of the carrier of A
<^c<sub>7</sub>,o2^> is set
(A,B,F,G) is Element of the carrier of B
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of F . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of F . [G,G] is set
( the of F . (G,G)) `1 is set
(A,B,F,c₇) is Element of the carrier of B
the of F . (c₇,c₇) is Element of [: the carrier of B, the carrier of B:]
[c₇,c₇] is V15() set
{c₇,c₇} is set
{c₇} is set
{{c₇,c₇},{c₇}} is set
the of F . [c₇,c₇] is set
( the of F . (c₇,c₇)) `1 is set
(A,B,F,o2) is Element of the carrier of B
the of F . (o2,o2) is Element of [: the carrier of B, the carrier of B:]
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the of F . [o2,o2] is set
( the of F . (o2,o2)) `1 is set
<^G,o2^> is set
o3 is Element of <^G,c₇^>
(A,B,F,G,c₇,o3) is Element of <^(A,B,F,G),(A,B,F,c₇)^>
<^(A,B,F,G),(A,B,F,c₇)^> is set
f is Element of <^c₇,o2^>
f * o3 is Element of <^G,o2^>
(A,B,F,G,o2,(f * o3)) is Element of <^(A,B,F,G),(A,B,F,o2)^>
<^(A,B,F,G),(A,B,F,o2)^> is set
(A,B,F,c₇,o2,f) is Element of <^(A,B,F,c₇),(A,B,F,o2)^>
<^(A,B,F,c₇),(A,B,F,o2)^> is set
(A,B,F,c₇,o2,f) * (A,B,F,G,c₇,o3) is Element of <^(A,B,F,G),(A,B,F,o2)^>
the carrier of A is non empty set
G is Element of the carrier of A
c₇ is Element of the carrier of A
<^G,c₇^> is set
o2 is Element of the carrier of A
<^c₇,o2^> is set
(A,B,(A,B,A,(idm A)),o2) is Element of the carrier of B
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of (A,B,A,(idm A)) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: 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 B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of (A,B,A,(idm A)) . (o2,o2) is Element of [: the carrier of B, the carrier of B:]
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the of (A,B,A,(idm A)) . [o2,o2] is set
( the of (A,B,A,(idm A)) . (o2,o2)) `1 is set
(A,B,(A,B,A,(idm A)),c<sub>7</sub>) is Element of the carrier of B
the of (A,B,A,(idm A)) . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of B, the carrier of B:]
[c<sub>7</sub>,c<sub>7</sub>] is V15() set
{c<sub>7</sub>,c<sub>7</sub>} is set
{c<sub>7</sub>} is set
{{c<sub>7</sub>,c<sub>7</sub>},{c<sub>7</sub>}} is set
the of (A,B,A,(idm A)) . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of (A,B,A,(idm A)) . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
(A,B,(A,B,A,(idm A)),G) is Element of the carrier of B
the of (A,B,A,(idm A)) . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of (A,B,A,(idm A)) . [G,G] is set
( the of (A,B,A,(idm A)) . (G,G)) `1 is set
<^G,o2^> is set
o3 is Element of <^G,c<sub>7</sub>^>
(A,B,(A,B,A,(idm A)),G,c<sub>7</sub>,o3) is Element of <^(A,B,(A,B,A,(idm A)),c<sub>7</sub>),(A,B,(A,B,A,(idm A)),G)^>
<^(A,B,(A,B,A,(idm A)),c<sub>7</sub>),(A,B,(A,B,A,(idm A)),G)^> is set
f is Element of <^c<sub>7</sub>,o2^>
f * o3 is Element of <^G,o2^>
(A,B,(A,B,A,(idm A)),G,o2,(f * o3)) is Element of <^(A,B,(A,B,A,(idm A)),o2),(A,B,(A,B,A,(idm A)),G)^>
<^(A,B,(A,B,A,(idm A)),o2),(A,B,(A,B,A,(idm A)),G)^> is set
(A,B,(A,B,A,(idm A)),c<sub>7</sub>,o2,f) is Element of <^(A,B,(A,B,A,(idm A)),o2),(A,B,(A,B,A,(idm A)),c<sub>7</sub>)^>
<^(A,B,(A,B,A,(idm A)),o2),(A,B,(A,B,A,(idm A)),c<sub>7</sub>)^> is set
(A,B,(A,B,A,(idm A)),G,c<sub>7</sub>,o3) * (A,B,(A,B,A,(idm A)),c<sub>7</sub>,o2,f) is Element of <^(A,B,(A,B,A,(idm A)),o2),(A,B,(A,B,A,(idm A)),G)^>
A is non empty transitive with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
the carrier of B is non empty set
the Element of the carrier of B is Element of the carrier of B
idm the Element of the carrier of B is Element of <^ the Element of the carrier of B, the Element of the carrier of B^>
<^ the Element of the carrier of B, the Element of the carrier of B^> is set
(A,B, the Element of the carrier of B,(idm the Element of the carrier of B)) is (A,B) (A,B) (A,B) (A,B) (A,B) (A,B) (A,B) (A,B) (A,B)
A is non empty transitive with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
A is AltCatStr
B is SubCatStr of A
the carrier of B is set
[: the carrier of B, the carrier of B:] is Relation-like set
id [: the carrier of B, the carrier 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 one-to-one V14([: the carrier of B, the carrier of B:]) 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 set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) set
id the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ManySortedFunction of the Arrows of B, the Arrows of B
the carrier of A is set
[: the carrier of A, the carrier of A:] is Relation-like set
bool [: the carrier of A, the carrier of A:] is non empty set
A is Relation-like the carrier of A -defined the carrier of A -valued Element of bool [: the carrier of A, the carrier of A:]
incl A is Relation-like A -defined [: the carrier of A, the carrier of A:] -valued A -valued Function-like one-to-one V14(A) quasi_total Element of bool [:A,[: the carrier of A, the carrier of A:]:]
[:A,[: the carrier of A, the carrier of A:]:] is Relation-like set
bool [:A,[: the carrier of A, the carrier of A:]:] is non empty set
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
c<sub>7</sub> is non empty set
[:[: the carrier of B, the carrier of B:],c<sub>7</sub>:] is Relation-like set
bool [:[: the carrier of B, the carrier of B:],c<sub>7</sub>:] is non empty set
o2 is Relation-like c<sub>7</sub> -defined Function-like non empty V14(c<sub>7</sub>) set
o3 is Relation-like [: the carrier of B, the carrier of B:] -defined c<sub>7</sub> -valued Function-like V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],c<sub>7</sub>:]
o3 * o2 is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) set
f is set
(id the Arrows of B) . f is Relation-like Function-like set
the Arrows of B . f is set
(o3 * o2) . f is set
[:( the Arrows of B . f),((o3 * o2) . f):] is Relation-like set
bool [:( the Arrows of B . f),((o3 * o2) . f):] is non empty set
[:( the Arrows of B . f),( the Arrows of B . f):] is Relation-like set
bool [:( the Arrows of B . f),( the Arrows of B . f):] is non empty set
o3 . f is set
o2 . (o3 . f) is set
the Arrows of A . f is set
[[0]] [: the carrier of B, the carrier of B:] is Relation-like empty-yielding [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) Function-yielding V37() set
[: the carrier of B, the carrier of B:] --> {} is Relation-like [: the carrier of B, the carrier of B:] -defined {{}} -valued Function-like constant V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],{{}}:]
[:[: the carrier of B, the carrier of B:],{{}}:] is Relation-like set
bool [:[: the carrier of B, the carrier of B:],{{}}:] is non empty set
c<sub>7</sub> is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:],F, the Arrows of B, the Arrows of A)
(B,A,F,c<sub>7</sub>) is (B,A) (B,A)
the of (B,A,F,c<sub>7</sub>) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of (B,A,F,c<sub>7</sub>) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of (B,A,F,c<sub>7</sub>), the Arrows of B, the Arrows of A)
A is (B,A) (B,A)
the of A is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the carrier of A is set
[: the carrier of A, the carrier of A:] is Relation-like set
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of A, the Arrows of B, the Arrows of A)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
B is (B,A) (B,A)
the of B is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of B, the Arrows of B, the Arrows of A)
A is AltGraph
the carrier of A is set
[: the carrier of A, the carrier of A:] is Relation-like set
id [: the carrier of A, the carrier 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 one-to-one V14([: the carrier of A, the carrier of A:]) 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 set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
id the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the Arrows of A
B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
B is non empty set
[:[: the carrier of A, the carrier of A:],B:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],B:] is non empty set
F is Relation-like B -defined Function-like non empty V14(B) set
G is Relation-like [: the carrier of A, the carrier of A:] -defined B -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],B:]
G * F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
c<sub>7</sub> is set
(id the Arrows of A) . c<sub>7</sub> is Relation-like Function-like set
the Arrows of A . c<sub>7</sub> is set
(G * F) . c<sub>7</sub> is set
[:( the Arrows of A . c<sub>7</sub>),((G * F) . c<sub>7</sub>):] is Relation-like set
bool [:( the Arrows of A . c<sub>7</sub>),((G * F) . c<sub>7</sub>):] is non empty set
G . c<sub>7</sub> is set
F . (G . c<sub>7</sub>) is set
[[0]] [: the carrier of A, the carrier of A:] is Relation-like empty-yielding [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
[: the carrier of A, the carrier of A:] --> {} is Relation-like [: the carrier of A, the carrier of A:] -defined {{}} -valued Function-like constant V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],{{}}:]
[:[: the carrier of A, the carrier of A:],{{}}:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],{{}}:] is non empty set
B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:],B, the Arrows of A, the Arrows of A)
(A,A,B,B) is (A,A) (A,A)
the of (A,A,B,B) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of (A,A,B,B) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A,A,B,B), the Arrows of A, the Arrows of A)
B is (A,A) (A,A)
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of B, the Arrows of A, the Arrows of A)
A is (A,A) (A,A)
the 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 V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of A, the Arrows of A, the Arrows of A)
A is AltCatStr
B is SubCatStr of A
(A,B) is (B,A) (B,A)
the carrier of A is set
bool the carrier of A is non empty set
the carrier of B is set
A is Element of bool the carrier of A
incl A is Relation-like A -defined the carrier of A -valued A -valued Function-like one-to-one V14(A) quasi_total Element of bool [:A, the carrier of A:]
[:A, the carrier of A:] is Relation-like set
bool [:A, the carrier of A:] is non empty set
id A is Relation-like A -defined A -valued Function-like one-to-one V14(A) quasi_total Element of bool [:A,A:]
[:A,A:] is Relation-like set
bool [:A,A:] is non empty set
[: the carrier of B, the carrier of A:] is Relation-like set
bool [: the carrier of B, the carrier of A:] is non empty set
id the carrier of B is Relation-like the carrier of B -defined the carrier of B -valued Function-like one-to-one V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of B:]
[: the carrier of B, the carrier of B:] is Relation-like set
bool [: the carrier of B, the carrier of B:] is non empty set
B 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 A, the carrier of A:] is Relation-like set
the of (A,B) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[:B,B:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
id [: the carrier of B, the carrier 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 one-to-one V14([: the carrier of B, the carrier of B:]) 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 set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:] is non empty set
A is non empty AltCatStr
B is non empty SubCatStr of A
the carrier of B is non empty set
(A,B) is (B,A) (B,A) (B,A)
A is Element of the carrier of B
(B,A,(A,B),A) is Element of 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 of (A,B) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[: 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 A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of (A,B) . (A,A) is Element of [: the carrier of A, the carrier of A:]
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
the of (A,B) . [A,A] is set
( the of (A,B) . (A,A)) `1 is set
id [: the carrier of B, the carrier 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 one-to-one non empty V14([: the carrier of B, the carrier of B:]) 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
(id [: the carrier of B, the carrier of B:]) . [A,A] is set
((id [: the carrier of B, the carrier of B:]) . [A,A]) `1 is set
[A,A] `1 is set
A is non empty AltCatStr
B is non empty SubCatStr of A
the carrier of B is non empty set
(A,B) is (B,A) (B,A) (B,A)
A is Element of the carrier of B
B is Element of the carrier of B
<^A,B^> is set
(B,A,(A,B),A) is Element of 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 of (A,B) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[: 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 A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of (A,B) . (A,A) is Element of [: the carrier of A, the carrier of A:]
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
the of (A,B) . [A,A] is set
( the of (A,B) . (A,A)) `1 is set
(B,A,(A,B),B) is Element of the carrier of A
the of (A,B) . (B,B) is Element of [: the carrier of A, the carrier of A:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of (A,B) . [B,B] is set
( the of (A,B) . (B,B)) `1 is set
<^(B,A,(A,B),A),(B,A,(A,B),B)^> is set
[A,B] is V15() set
{A,B} is set
{{A,B},{A}} is set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the Arrows of B . (A,B) is set
the Arrows of B . [A,B] is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A . (A,B) is set
the Arrows of A . [A,B] is set
A is non empty AltCatStr
B is non empty SubCatStr of A
(A,B) is (B,A) (B,A) (B,A)
the carrier of B is non empty set
A is Element of the carrier of B
B is Element of the carrier of B
<^A,B^> is set
(B,A,(A,B),A) is Element of 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 of (A,B) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[: 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 A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of (A,B) . (A,A) is Element of [: the carrier of A, the carrier of A:]
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
the of (A,B) . [A,A] is set
( the of (A,B) . (A,A)) `1 is set
(B,A,(A,B),B) is Element of the carrier of A
the of (A,B) . (B,B) is Element of [: the carrier of A, the carrier of A:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of (A,B) . [B,B] is set
( the of (A,B) . (B,B)) `1 is set
<^(B,A,(A,B),A),(B,A,(A,B),B)^> is set
A is AltGraph
B is AltGraph
A is AltGraph
B is AltGraph
A is AltGraph
B is non empty AltGraph
A is (A,B)
the carrier of A is set
[: the carrier of A, the carrier of A:] is Relation-like set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A,B
G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
c₇ is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
A is AltGraph
B is AltGraph
A is AltGraph
B is AltGraph
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
the carrier of B is non empty set
the Element of the carrier of B is Element of the carrier of B
idm the Element of the carrier of B is Element of <^ the Element of the carrier of B, the Element of the carrier of B^>
<^ the Element of the carrier of B, the Element of the carrier of B^> is set
(A,B, the Element of the carrier of B,(idm the Element of the carrier of B)) is (A,B) (A,B) (A,B) (A,B) (A,B) (A,B) (A,B) (A,B) (A,B)
B is (A,B)
A is non empty AltGraph
the carrier of A is non empty set
(A) is (A,A) (A,A)
B is Element of the carrier of A
(A,A,(A),B) is Element of the carrier of A
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the 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 non empty V14([: the carrier of A, the carrier of A:]) 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 of (A) . (B,B) is Element of [: the carrier of A, the carrier of A:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of (A) . [B,B] is set
( the of (A) . (B,B)) `1 is set
id [: the carrier of A, the carrier 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 one-to-one non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
(id [: the carrier of A, the carrier of A:]) . [B,B] is set
((id [: the carrier of A, the carrier of A:]) . [B,B]) `1 is set
[B,B] `1 is set
A is non empty AltGraph
the carrier of A is non empty set
(A) is (A,A) (A,A)
B is Element of the carrier of A
A is Element of the carrier of A
<^B,A^> is set
(A,A,(A),B,A) is Relation-like Function-like set
the of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A), the Arrows of A, the Arrows of A)
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the 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 non empty V14([: the carrier of A, the carrier of A:]) 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 Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of (A) . (B,A) is set
[B,A] is V15() set
{B,A} is set
{B} is set
{{B,A},{B}} is set
the of (A) . [B,A] is Relation-like Function-like set
B is Element of <^B,A^>
(A,A,(A),B,A) . B is set
id the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the Arrows of A
(id the Arrows of A) . [B,A] is Relation-like Function-like set
the Arrows of A . (B,A) is set
the Arrows of A . [B,A] is set
id ( the Arrows of A . (B,A)) is Relation-like the Arrows of A . (B,A) -defined the Arrows of A . (B,A) -valued Function-like one-to-one V14( the Arrows of A . (B,A)) quasi_total Element of bool [:( the Arrows of A . (B,A)),( the Arrows of A . (B,A)):]
[:( the Arrows of A . (B,A)),( the Arrows of A . (B,A)):] is Relation-like set
bool [:( the Arrows of A . (B,A)),( the Arrows of A . (B,A)):] is non empty set
(id ( the Arrows of A . (B,A))) . B is set
id <^B,A^> is Relation-like <^B,A^> -defined <^B,A^> -valued Function-like one-to-one V14(<^B,A^>) quasi_total Element of bool [:<^B,A^>,<^B,A^>:]
[:<^B,A^>,<^B,A^>:] is Relation-like set
bool [:<^B,A^>,<^B,A^>:] is non empty set
(id <^B,A^>) . B is set
A is non empty AltGraph
(A) is (A,A) (A,A)
the carrier of A is non empty set
B is Element of the carrier of A
A is Element of the carrier of A
<^B,A^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the 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 non empty V14([: the carrier of A, the carrier of A:]) 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 of (A) . (B,A) is Element of [: the carrier of A, the carrier of A:]
[B,A] is V15() set
{B,A} is set
{B} is set
{{B,A},{B}} is set
the of (A) . [B,A] is set
the Arrows of A . ( the of (A) . (B,A)) is set
id [: the carrier of A, the carrier 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 one-to-one non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
(id [: the carrier of A, the carrier of A:]) . [B,A] is set
the Arrows of A . (B,A) is set
the Arrows of A . [B,A] is 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
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
the 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 non empty V14([: the carrier of A, the carrier of A:]) 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
B is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like one-to-one non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
id [: the carrier of A, the carrier 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 one-to-one non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
A is non empty AltGraph
(A) is (A,A) (A,A) (A,A) (A,A)
A is non empty AltGraph
the carrier of A is non empty set
(A) is (A,A) (A,A) (A,A) (A,A)
B is Element of the carrier of A
A is Element of the carrier of A
<^B,A^> is set
B is (A,A) (A,A) (A,A)
F is Element of <^B,A^>
(A,A,B,B,A,F) is Element of <^(A,A,B,B),(A,A,B,A)^>
(A,A,B,B) is Element of the carrier of A
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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 of B . (B,B) is Element of [: the carrier of A, the carrier of A:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of B . [B,B] is set
( the of B . (B,B)) `1 is set
(A,A,B,A) is Element of the carrier of A
the of B . (A,A) is Element of [: the carrier of A, the carrier of A:]
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
the of B . [A,A] is set
( the of B . (A,A)) `1 is set
<^(A,A,B,B),(A,A,B,A)^> is set
(A,A,B,B,A) is Relation-like <^B,A^> -defined <^(A,A,B,B),(A,A,B,A)^> -valued Function-like quasi_total Element of bool [:<^B,A^>,<^(A,A,B,B),(A,A,B,A)^>:]
[:<^B,A^>,<^(A,A,B,B),(A,A,B,A)^>:] is Relation-like set
bool [:<^B,A^>,<^(A,A,B,B),(A,A,B,A)^>:] is non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of B, the Arrows of A, the Arrows of A)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of B . (B,A) is set
[B,A] is V15() set
{B,A} is set
{{B,A},{B}} is set
the of B . [B,A] is Relation-like Function-like set
(A,A,B,B,A) . F is set
A is non empty transitive with_units reflexive AltCatStr
(A) is (A,A) (A,A) (A,A) (A,A)
the carrier of A is non empty set
B is Element of the carrier of A
(A,A,(A),B,B) is Relation-like Function-like set
the of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A), the Arrows of A, the Arrows of A)
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the 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 non empty V14([: the carrier of A, the carrier of A:]) 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 Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of (A) . (B,B) is set
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of (A) . [B,B] is Relation-like Function-like set
idm B is Element of <^B,B^>
<^B,B^> is set
(A,A,(A),B,B) . (idm B) is set
(A,A,(A),B) is Element of the carrier of A
the of (A) . (B,B) is Element of [: the carrier of A, the carrier of A:]
the of (A) . [B,B] is set
( the of (A) . (B,B)) `1 is set
idm (A,A,(A),B) is Element of <^(A,A,(A),B),(A,A,(A),B)^>
<^(A,A,(A),B),(A,A,(A),B)^> is set
(A,A,(A),B,B) is Relation-like <^B,B^> -defined <^(A,A,(A),B),(A,A,(A),B)^> -valued Function-like quasi_total Element of bool [:<^B,B^>,<^(A,A,(A),B),(A,A,(A),B)^>:]
[:<^B,B^>,<^(A,A,(A),B),(A,A,(A),B)^>:] is Relation-like set
bool [:<^B,B^>,<^(A,A,(A),B),(A,A,(A),B)^>:] is non empty set
(A,A,(A),B,B) . (idm B) is set
the carrier of A is non empty set
A is Element of the carrier of A
B is Element of the carrier of A
<^A,B^> is set
F is Element of the carrier of A
<^B,F^> is set
(A,A,(A),A) is Element of the carrier of A
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the 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 non empty V14([: the carrier of A, the carrier of A:]) 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 of (A) . (A,A) is Element of [: the carrier of A, the carrier of A:]
[A,A] is V15() set
{A,A} is set
{A} is set
{{A,A},{A}} is set
the of (A) . [A,A] is set
( the of (A) . (A,A)) `1 is set
(A,A,(A),B) is Element of the carrier of A
the of (A) . (B,B) is Element of [: the carrier of A, the carrier of A:]
[B,B] is V15() set
{B,B} is set
{B} is set
{{B,B},{B}} is set
the of (A) . [B,B] is set
( the of (A) . (B,B)) `1 is set
(A,A,(A),F) is Element of the carrier of A
the of (A) . (F,F) is Element of [: the carrier of A, the carrier of A:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of (A) . [F,F] is set
( the of (A) . (F,F)) `1 is set
G is Element of <^A,B^>
(A,A,(A),A,B,G) is Element of <^(A,A,(A),A),(A,A,(A),B)^>
<^(A,A,(A),A),(A,A,(A),B)^> is set
c<sub>7</sub> is Element of <^B,F^>
c<sub>7</sub> * G is Element of <^A,F^>
<^A,F^> is set
(A,A,(A),A,F,(c<sub>7</sub> * G)) is Element of <^(A,A,(A),A),(A,A,(A),F)^>
<^(A,A,(A),A),(A,A,(A),F)^> is set
(A,A,(A),B,F,c<sub>7</sub>) is Element of <^(A,A,(A),B),(A,A,(A),F)^>
<^(A,A,(A),B),(A,A,(A),F)^> is set
(A,A,(A),B,F,c<sub>7</sub>) * (A,A,(A),A,B,G) is Element of <^(A,A,(A),A),(A,A,(A),F)^>
A is non empty transitive with_units reflexive AltCatStr
(A) is (A,A) (A,A) (A,A) (A,A) (A,A) (A,A)
A is AltGraph
(A) is (A,A) (A,A)
the carrier of A is set
[: the carrier of A, the carrier of A:] is Relation-like set
the 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 V14([: the carrier of A, the carrier of A:]) 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 set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:] is non empty set
id [: the carrier of A, the carrier 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 one-to-one V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
A is set
the of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A), the Arrows of A, the Arrows of A)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
proj1 the of (A) is set
the of (A) . A is Relation-like Function-like set
B is Relation-like Function-like set
dom the of (A) is Relation-like the carrier of A -defined the carrier of A -valued Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
F is Element of the carrier of A
G is Element of the carrier of A
[F,G] is V15() set
{F,G} is set
{F} is set
{{F,G},{F}} is set
c<sub>7</sub> is Element of the carrier of A
o2 is Element of the carrier of A
[c<sub>7</sub>,o2] is V15() set
{c<sub>7</sub>,o2} is set
{c<sub>7</sub>} is set
{{c<sub>7</sub>,o2},{c<sub>7</sub>}} is set
id the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the Arrows of A
(id the Arrows of A) . (c<sub>7</sub>,o2) is set
(id the Arrows of A) . [c<sub>7</sub>,o2] is Relation-like Function-like set
the Arrows of A . [c<sub>7</sub>,o2] is set
id ( the Arrows of A . [c<sub>7</sub>,o2]) is Relation-like the Arrows of A . [c<sub>7</sub>,o2] -defined the Arrows of A . [c<sub>7</sub>,o2] -valued Function-like one-to-one V14( the Arrows of A . [c<sub>7</sub>,o2]) quasi_total Element of bool [:( the Arrows of A . [c<sub>7</sub>,o2]),( the Arrows of A . [c<sub>7</sub>,o2]):]
[:( the Arrows of A . [c<sub>7</sub>,o2]),( the Arrows of A . [c<sub>7</sub>,o2]):] is Relation-like set
bool [:( the Arrows of A . [c<sub>7</sub>,o2]),( the Arrows of A . [c<sub>7</sub>,o2]):] is non empty set
A is set
the of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A), the Arrows of A, the Arrows of A)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
proj1 the of (A) is set
the of (A) . A is Relation-like Function-like set
B is Relation-like Function-like set
dom the of (A) is Relation-like the carrier of A -defined the carrier of A -valued Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
A is non empty AltGraph
(A) is (A,A) (A,A) (A,A) (A,A)
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the 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 non empty V14([: the carrier of A, the carrier of A:]) 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 of (A) * the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A), the Arrows of A, the Arrows of A)
B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of (A) * the Arrows of A
F is set
B . F is Relation-like Function-like set
proj2 (B . F) is set
( the of (A) * the Arrows of A) . F is set
G is Element of the carrier of A
c<sub>7</sub> is Element of the carrier of A
[G,c<sub>7</sub>] is V15() set
{G,c<sub>7</sub>} is set
{G} is set
{{G,c<sub>7</sub>},{G}} is set
o2 is Element of the carrier of A
o3 is Element of the carrier of A
[o2,o3] is V15() set
{o2,o3} is set
{o2} is set
{{o2,o3},{o2}} is set
dom the of (A) 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
id the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the Arrows of A
(id the Arrows of A) . (o2,o3) is set
(id the Arrows of A) . [o2,o3] is Relation-like Function-like set
the Arrows of A . [o2,o3] is set
id ( the Arrows of A . [o2,o3]) is Relation-like the Arrows of A . [o2,o3] -defined the Arrows of A . [o2,o3] -valued Function-like one-to-one V14( the Arrows of A . [o2,o3]) quasi_total Element of bool [:( the Arrows of A . [o2,o3]),( the Arrows of A . [o2,o3]):]
[:( the Arrows of A . [o2,o3]),( the Arrows of A . [o2,o3]):] is Relation-like set
bool [:( the Arrows of A . [o2,o3]),( the Arrows of A . [o2,o3]):] is non empty set
the of (A) . F is set
the Arrows of A . ( the of (A) . F) is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
the of (A) * the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like set
the of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A), the Arrows of A, the Arrows of A)
B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) set
F is set
B . F is set
the Arrows of A . F is set
A . F is set
[:( the Arrows of A . F),(A . F):] is Relation-like set
bool [:( the Arrows of A . F),(A . F):] is non empty set
F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A,A
G is set
F . G is Relation-like Function-like set
proj2 (F . G) is set
A . G is set
rng (id [: the carrier of A, the carrier of A:]) is Relation-like the carrier of A -defined the carrier of A -valued Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
A is non empty AltGraph
B is non empty reflexive AltGraph
A is non empty reflexive AltGraph
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
[: the carrier of A, the carrier of A:] is Relation-like 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
B is (A,B) (A,B)
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
F is (B,A)
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of F * the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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 of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of B, the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of F, the Arrows of B, the Arrows of A)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of B * the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
( the of B * the of F) ** the of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
G is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of B * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
G * the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
o3 is set
( the of B * the Arrows of B) . o3 is set
the Arrows of A . o3 is set
(G * the Arrows of A) . o3 is set
dom the of B 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
o3 `1 is set
o3 `2 is set
f is Element of the carrier of A
g is Element of the carrier of A
[f,g] is V15() set
{f,g} is set
{f} is set
{{f,g},{f}} is set
the of B . (f,g) is Element of [: the carrier of B, the carrier of B:]
the of B . [f,g] is set
the Arrows of B . ( the of B . (f,g)) is set
the Arrows of A . (f,g) is set
the Arrows of A . [f,g] is set
<^f,g^> is set
o2 is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:],G, the of B * the Arrows of B, the Arrows of A)
o2 ** the of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
o3 is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:],G, the Arrows of A, the Arrows of A)
(A,A,G,o3) is (A,A) (A,A)
the of (A,A,G,o3) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of (A,A,G,o3) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A,A,G,o3), the Arrows of A, the Arrows of A)
G is (A,A) (A,A)
the of G is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of G, the Arrows of A, the Arrows of A)
c<sub>7</sub> is (A,A) (A,A)
the of c<sub>7</sub> is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of c<sub>7</sub> is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of c<sub>7</sub>, the Arrows of A, the Arrows of A)
A is non empty AltGraph
B is non empty reflexive AltGraph
A is non empty reflexive AltGraph
B is (A,B) (A,B) (A,B)
F is (B,A) (B,A)
(A,B,A,B,F) is (A,A) (A,A)
the carrier of A is non empty set
the carrier of B is non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] 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
G is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the carrier of A is non empty set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: 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 B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[: 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
c<sub>7</sub> is Relation-like the carrier of B -defined the carrier of A -valued Function-like non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of A:]
[:c<sub>7</sub>,c<sub>7</sub>:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
c<sub>7</sub> * G is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty V14( the carrier of A) 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 of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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
[:(c<sub>7</sub> * G),(c<sub>7</sub> * G):] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of F * the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
A is non empty AltGraph
B is non empty reflexive AltGraph
A is non empty reflexive AltGraph
B is (A,B) (A,B) (A,B)
F is (B,A) (B,A)
(A,B,A,B,F) is (A,A) (A,A)
the carrier of A is non empty set
the carrier of B is non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] 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
G is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:G,G:]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the carrier of A is non empty set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: 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 B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[: 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
c<sub>7</sub> is Relation-like the carrier of B -defined the carrier of A -valued Function-like non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of A:]
[:c<sub>7</sub>,c<sub>7</sub>:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
c<sub>7</sub> * G is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty V14( the carrier of A) 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 of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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
[:(c<sub>7</sub> * G),(c<sub>7</sub> * G):] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:],[:(c<sub>7</sub> * G),(c<sub>7</sub> * G):]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of F * the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
[:c<sub>7</sub>,c<sub>7</sub>:] * [:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:],([:c<sub>7</sub>,c<sub>7</sub>:] * [:G,G:])) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
A is non empty AltGraph
B is non empty reflexive AltGraph
A is non empty reflexive AltGraph
B is (A,B) (A,B) (A,B)
F is (B,A) (B,A)
(A,B,A,B,F) is (A,A) (A,A)
the carrier of A is non empty set
the carrier of B is non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] 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
G is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the carrier of A is non empty set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: 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 B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[: 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
c<sub>7</sub> is Relation-like the carrier of B -defined the carrier of A -valued Function-like non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of A:]
[:c<sub>7</sub>,c<sub>7</sub>:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
( the carrier of B, the carrier of B,[: the carrier of A, the carrier of A:],[:c<sub>7</sub>,c<sub>7</sub>:]) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
c<sub>7</sub> * G is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty V14( the carrier of A) 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 of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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
[:(c<sub>7</sub> * G),(c<sub>7</sub> * G):] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:],[:(c<sub>7</sub> * G),(c<sub>7</sub> * G):]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of F * the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
[:c<sub>7</sub>,c<sub>7</sub>:] * [:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:],([:c<sub>7</sub>,c<sub>7</sub>:] * [:G,G:])) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
A is non empty AltGraph
B is non empty reflexive AltGraph
A is non empty reflexive AltGraph
B is (A,B) (A,B) (A,B)
F is (B,A) (B,A)
(A,B,A,B,F) is (A,A) (A,A)
the carrier of A is non empty set
the carrier of B is non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] 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
G is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:G,G:]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the carrier of A is non empty set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: 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 B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[: 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
c<sub>7</sub> is Relation-like the carrier of B -defined the carrier of A -valued Function-like non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of A:]
[:c<sub>7</sub>,c<sub>7</sub>:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
( the carrier of B, the carrier of B,[: the carrier of A, the carrier of A:],[:c<sub>7</sub>,c<sub>7</sub>:]) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
c<sub>7</sub> * G is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty V14( the carrier of A) 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 of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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
[:(c<sub>7</sub> * G),(c<sub>7</sub> * G):] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of F * the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
( the carrier of B, the carrier of B,[: the carrier of A, the carrier of A:],[:c<sub>7</sub>,c<sub>7</sub>:]) * [:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:],(( the carrier of B, the carrier of B,[: the carrier of A, the carrier of A:],[:c<sub>7</sub>,c<sub>7</sub>:]) * [:G,G:])) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
[:c<sub>7</sub>,c<sub>7</sub>:] * [:G,G:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:],([:c<sub>7</sub>,c<sub>7</sub>:] * [:G,G:])) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:],( the carrier of A, the carrier of A,[: the carrier of A, the carrier of A:],([:c<sub>7</sub>,c<sub>7</sub>:] * [:G,G:]))) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
A is non empty AltGraph
B is non empty reflexive AltGraph
A is non empty reflexive AltGraph
B is (A,B) (A,B)
F is (B,A) (B,A)
(A,B,A,B,F) is (A,A) (A,A)
the carrier of A is non empty set
G is Element of the carrier of A
c<sub>7</sub> is Element of the carrier of A
<^G,c<sub>7</sub>^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:] is Relation-like non empty set
[:[: 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 of (A,B,A,B,F) . (G,c<sub>7</sub>) is Element of [: the carrier of A, the carrier of A:]
[G,c<sub>7</sub>] is V15() set
{G,c<sub>7</sub>} is set
{G} is set
{{G,c<sub>7</sub>},{G}} is set
the of (A,B,A,B,F) . [G,c<sub>7</sub>] is set
the Arrows of A . ( the of (A,B,A,B,F) . (G,c<sub>7</sub>)) is set
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of B . (G,c<sub>7</sub>) is Element of [: the carrier of B, the carrier of B:]
the of B . [G,c<sub>7</sub>] is set
( the of B . (G,c<sub>7</sub>)) `1 is set
( the of B . (G,c₇)) `2 is set
o2 is Element of the carrier of B
o3 is Element of the carrier of B
dom the of B 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
f is Element of the carrier of B
g is Element of the carrier of B
[f,g] is V15() set
{f,g} is set
{f} is set
{{f,g},{f}} is set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of F * the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
( the of F * the of B) . [G,c<sub>7</sub>] is set
the of F . (f,g) is Element of [: the carrier of A, the carrier of A:]
the of F . [f,g] is set
<^f,g^> is set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the Arrows of B . (f,g) is set
the Arrows of B . [f,g] is set
the Arrows of B . ( the of B . (G,c<sub>7</sub>)) is set
A is non empty AltGraph
B is non empty reflexive AltGraph
A is non empty reflexive AltGraph
B is non empty reflexive AltGraph
F is (A,B) (A,B)
G is (B,A) (B,A)
(A,B,A,F,G) is (A,A) (A,A) (A,A)
c<sub>7</sub> is (A,B)
(B,A,B,G,c<sub>7</sub>) is (B,B) (B,B)
(A,B,B,F,(B,A,B,G,c<sub>7</sub>)) is (A,B) (A,B)
(A,A,B,(A,B,A,F,G),c<sub>7</sub>) is (A,B) (A,B)
the of (A,B,B,F,(B,A,B,G,c<sub>7</sub>)) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
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 B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: 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
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of (B,A,B,G,c<sub>7</sub>) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) 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 of (B,A,B,G,c<sub>7</sub>) * the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the of G is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of c<sub>7</sub> is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of c<sub>7</sub> * the of G is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
( the of c<sub>7</sub> * the of G) * the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the of G * the of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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 of c<sub>7</sub> * ( the of G * the of F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the of (A,B,A,F,G) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
the of c<sub>7</sub> * the of (A,B,A,F,G) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the of (A,A,B,(A,B,A,F,G),c<sub>7</sub>) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the of (A,B,B,F,(B,A,B,G,c<sub>7</sub>)) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of (A,B,B,F,(B,A,B,G,c<sub>7</sub>)), the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of F, the Arrows of A, the Arrows of B)
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of (B,A,B,G,c<sub>7</sub>) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:], the of (B,A,B,G,c<sub>7</sub>), the Arrows of B, the Arrows of B)
the of F * the of (B,A,B,G,c<sub>7</sub>) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
( the of F * the of (B,A,B,G,c<sub>7</sub>)) ** the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
the of G is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of G, the Arrows of B, the Arrows of A)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of c<sub>7</sub> is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of c<sub>7</sub>, the Arrows of A, the Arrows of B)
the of G * the of c<sub>7</sub> is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() set
( the of G * the of c<sub>7</sub>) ** the of G is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() set
the of F * (( the of G * the of c<sub>7</sub>) ** the of G) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
( the of F * (( the of G * the of c<sub>7</sub>) ** the of G)) ** the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
the of F * the of G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
the of F * ( the of G * the of c<sub>7</sub>) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
( the of F * ( the of G * the of c<sub>7</sub>)) ** ( the of F * the of G) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
(( the of F * ( the of G * the of c<sub>7</sub>)) ** ( the of F * the of G)) ** the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
( the of G * the of F) * the of c<sub>7</sub> is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
(( the of G * the of F) * the of c<sub>7</sub>) ** ( the of F * the of G) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
((( the of G * the of F) * the of c<sub>7</sub>) ** ( the of F * the of G)) ** the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
the of (A,B,A,F,G) * the of c<sub>7</sub> is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
( the of (A,B,A,F,G) * the of c<sub>7</sub>) ** ( the of F * the of G) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
(( the of (A,B,A,F,G) * the of c<sub>7</sub>) ** ( the of F * the of G)) ** the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
( the of F * the of G) ** the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
( the of (A,B,A,F,G) * the of c<sub>7</sub>) ** (( the of F * the of G) ** the of F) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
the of (A,B,A,F,G) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A,B,A,F,G), the Arrows of A, the Arrows of A)
( the of (A,B,A,F,G) * the of c<sub>7</sub>) ** the of (A,B,A,F,G) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
the of (A,A,B,(A,B,A,F,G),c<sub>7</sub>) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of (A,A,B,(A,B,A,F,G),c<sub>7</sub>), the Arrows of A, the Arrows of B)
A is non empty AltCatStr
the carrier of A is non empty set
B is non empty reflexive AltCatStr
A is non empty reflexive AltCatStr
B is (A,B) (A,B) (A,B)
F is (B,A)
(A,B,A,B,F) is (A,A) (A,A)
G is Element of the carrier of A
(A,A,(A,B,A,B,F),G) is Element of 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 of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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:] is Relation-like non empty set
[:[: 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 of (A,B,A,B,F) . (G,G) is Element of [: the carrier of A, the carrier of A:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of (A,B,A,B,F) . [G,G] is set
( the of (A,B,A,B,F) . (G,G)) `1 is set
(A,B,B,G) is Element of the carrier of B
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of B . (G,G) is Element of [: the carrier of B, the carrier of B:]
the of B . [G,G] is set
( the of B . (G,G)) `1 is set
(B,A,F,(A,B,B,G)) is Element of the carrier of A
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of F . ((A,B,B,G),(A,B,B,G)) is Element of [: the carrier of A, the carrier of A:]
[(A,B,B,G),(A,B,B,G)] is V15() set
{(A,B,B,G),(A,B,B,G)} is set
{(A,B,B,G)} is set
{{(A,B,B,G),(A,B,B,G)},{(A,B,B,G)}} is set
the of F . [(A,B,B,G),(A,B,B,G)] is set
( the of F . ((A,B,B,G),(A,B,B,G))) `1 is set
dom the of B 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
the of F * the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
( the of F * the of B) . (G,G) is Element of [: the carrier of A, the carrier of A:]
( the of F * the of B) . [G,G] is set
(( the of F * the of B) . (G,G)) `1 is set
the of F . ( the of B . [G,G]) is set
( the of F . ( the of B . [G,G])) `1 is set
A is non empty AltGraph
the carrier of A is non empty set
B is non empty reflexive AltGraph
A is non empty reflexive AltGraph
B is (A,B) (A,B) (A,B)
F is (B,A)
(A,B,A,B,F) is (A,A) (A,A)
G is Element of the carrier of A
(A,A,(A,B,A,B,F),G,G) is Relation-like Function-like set
the of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A,B,A,B,F), the Arrows of A, the Arrows of A)
[: 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 of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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 Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of (A,B,A,B,F) . (G,G) is set
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of (A,B,A,B,F) . [G,G] is Relation-like Function-like set
(A,B,B,G,G) is Relation-like Function-like set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of B, the Arrows of A, the Arrows of B)
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of B . (G,G) is set
the of B . [G,G] is Relation-like Function-like set
(A,B,B,G) is Element of the carrier of B
the of B . (G,G) is Element of [: the carrier of B, the carrier of B:]
the of B . [G,G] is set
( the of B . (G,G)) `1 is set
(B,A,F,(A,B,B,G),(A,B,B,G)) is Relation-like Function-like set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of F, the Arrows of B, the Arrows of A)
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of F . ((A,B,B,G),(A,B,B,G)) is set
[(A,B,B,G),(A,B,B,G)] is V15() set
{(A,B,B,G),(A,B,B,G)} is set
{(A,B,B,G)} is set
{{(A,B,B,G),(A,B,B,G)},{(A,B,B,G)}} is set
the of F . [(A,B,B,G),(A,B,B,G)] is Relation-like Function-like set
(A,B,B,G,G) * (B,A,F,(A,B,B,G),(A,B,B,G)) is Relation-like Function-like set
dom the of F is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
rng the of B is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
the of B * the of F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
dom ( the of B * the of F) 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
dom the of B 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:]
dom the of B 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:]
(dom ( the of B * the of F)) /\ (dom the of B) is Relation-like the carrier of A -defined the carrier of A -valued Element of bool [: the carrier of A, the carrier of A:]
( the of B * the of F) ** the of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() set
dom (( the of B * the of F) ** the of B) 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:]
( the of B * the of F) . [G,G] is Relation-like Function-like set
the of F . ( the of B . (G,G)) is Relation-like Function-like set
(( the of B * the of F) ** the of B) . (G,G) is set
(( the of B * the of F) ** the of B) . [G,G] is Relation-like Function-like set
A is non empty with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
A is non empty with_units reflexive AltCatStr
B is (A,B) (A,B) (A,B) (A,B)
F is (B,A) (B,A)
(A,B,A,B,F) is (A,A) (A,A)
the carrier of A is non empty set
G is Element of the carrier of A
(A,A,(A,B,A,B,F),G,G) is Relation-like Function-like set
the of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:], the of (A,B,A,B,F), the Arrows of A, the Arrows of A)
[: 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 of (A,B,A,B,F) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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 Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of (A,B,A,B,F) . (G,G) is set
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of (A,B,A,B,F) . [G,G] is Relation-like Function-like set
idm G is Element of <^G,G^>
<^G,G^> is set
(A,A,(A,B,A,B,F),G,G) . (idm G) is set
(A,A,(A,B,A,B,F),G) is Element of the carrier of A
the of (A,B,A,B,F) . (G,G) is Element of [: the carrier of A, the carrier of A:]
the of (A,B,A,B,F) . [G,G] is set
( the of (A,B,A,B,F) . (G,G)) `1 is set
idm (A,A,(A,B,A,B,F),G) is Element of <^(A,A,(A,B,A,B,F),G),(A,A,(A,B,A,B,F),G)^>
<^(A,A,(A,B,A,B,F),G),(A,A,(A,B,A,B,F),G)^> is set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
dom the of B 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
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of B * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
( the of B * the Arrows of B) . [G,G] is set
the of B . (G,G) is Element of [: the carrier of B, the carrier of B:]
the of B . [G,G] is set
the Arrows of B . ( the of B . (G,G)) is set
(A,B,B,G) is Element of the carrier of B
( the of B . (G,G)) `1 is set
the Arrows of B . ((A,B,B,G),(A,B,B,G)) is set
[(A,B,B,G),(A,B,B,G)] is V15() set
{(A,B,B,G),(A,B,B,G)} is set
{(A,B,B,G)} is set
{{(A,B,B,G),(A,B,B,G)},{(A,B,B,G)}} is set
the Arrows of B . [(A,B,B,G),(A,B,B,G)] is set
<^(A,B,B,G),(A,B,B,G)^> is set
the of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of B, the Arrows of A, the Arrows of B)
(A,B,B,G,G) is Relation-like Function-like set
the of B . (G,G) is set
the of B . [G,G] is Relation-like Function-like set
the Arrows of A . [G,G] is set
[:( the Arrows of A . [G,G]),(( the of B * the Arrows of B) . [G,G]):] is Relation-like set
bool [:( the Arrows of A . [G,G]),(( the of B * the Arrows of B) . [G,G]):] is non empty set
proj1 (A,B,B,G,G) is set
the Arrows of A . (G,G) is set
(B,A,F,(A,B,B,G),(A,B,B,G)) is Relation-like Function-like set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of F, the Arrows of B, the Arrows of A)
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of F . ((A,B,B,G),(A,B,B,G)) is set
the of F . [(A,B,B,G),(A,B,B,G)] is Relation-like Function-like set
(A,B,B,G,G) * (B,A,F,(A,B,B,G),(A,B,B,G)) is Relation-like Function-like set
((A,B,B,G,G) * (B,A,F,(A,B,B,G),(A,B,B,G))) . (idm G) is set
(A,B,B,G,G) . (idm G) is set
(B,A,F,(A,B,B,G),(A,B,B,G)) . ((A,B,B,G,G) . (idm G)) is set
idm (A,B,B,G) is Element of <^(A,B,B,G),(A,B,B,G)^>
(B,A,F,(A,B,B,G),(A,B,B,G)) . (idm (A,B,B,G)) is set
(B,A,F,(A,B,B,G)) is Element of the carrier of A
the of F . ((A,B,B,G),(A,B,B,G)) is Element of [: the carrier of A, the carrier of A:]
the of F . [(A,B,B,G),(A,B,B,G)] is set
( the of F . ((A,B,B,G),(A,B,B,G))) `1 is set
idm (B,A,F,(A,B,B,G)) is Element of <^(B,A,F,(A,B,B,G)),(B,A,F,(A,B,B,G))^>
<^(B,A,F,(A,B,B,G)),(B,A,F,(A,B,B,G))^> is set
A is non empty reflexive AltCatStr
B is non empty reflexive AltCatStr
A is non empty SubCatStr of A
(A,A) is (A,A) (A,A) (A,A) (A,A)
B is (A,B)
(A,A,B,(A,A),B) is (A,B) (A,B)
A is non empty AltGraph
B is non empty AltGraph
A is (A,B)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
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 B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A " is Relation-like Function-like set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
rng the of A is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
F * ( the of A * the Arrows of B) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) 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 of A * F) * the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
id [: the carrier of B, the carrier 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 one-to-one non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
(id [: the carrier of B, the carrier of B:]) * the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
G "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
F * (G "") is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() set
F * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
c₇ is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:],F, the Arrows of B, the Arrows of A)
(B,A,F,c₇) is (B,A) (B,A)
o2 is (B,A) (B,A)
the of o2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of o2 is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of o2, the Arrows of B, the Arrows of A)
( the of A ") * (G "") is Relation-like Function-like Function-yielding V37() set
B is (B,A) (B,A)
the of B is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
the of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of B, the Arrows of B, the Arrows of A)
G "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
( the of A ") * (G "") is Relation-like Function-like Function-yielding V37() set
F is (B,A) (B,A)
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
c₇ is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of F, the Arrows of B, the Arrows of A)
c₇ "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
( the of A ") * (c₇ "") is Relation-like Function-like Function-yielding V37() set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] 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 carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A " is Relation-like Function-like set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of (A,B,A), the Arrows of B, the Arrows of A)
F is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
F "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
( the of A ") * (F "") is Relation-like Function-like Function-yielding V37() set
rng the of A is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
the of (A,B,A) * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
o2 is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ManySortedFunction of the Arrows of B, the of (A,B,A) * the Arrows of A
o3 is set
proj1 o2 is non empty set
o2 . o3 is Relation-like Function-like set
f is Relation-like Function-like set
dom o2 is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
proj1 ( the of A ") is set
( the of A ") . o3 is set
proj2 ( the of A ") is set
dom the of A 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
dom F 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:]
F . (( the of A ") . o3) is Relation-like Function-like set
(F "") . (( the of A ") . o3) is Relation-like Function-like set
(F . (( the of A ") . o3)) " is Relation-like Function-like set
g is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
o3 is set
o2 . o3 is Relation-like Function-like set
proj2 (o2 . o3) is set
( the of (A,B,A) * the Arrows of A) . o3 is set
dom the of (A,B,A) is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
proj1 ( the of A ") is set
( the of A ") . o3 is set
proj2 ( the of A ") is set
dom the of A 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
the of (A,B,A) . o3 is set
dom F 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:]
F . ( the of (A,B,A) . o3) is Relation-like Function-like set
the Arrows of A . ( the of (A,B,A) . o3) is set
( the of A * the Arrows of B) . ( the of (A,B,A) . o3) is set
[:( the Arrows of A . ( the of (A,B,A) . o3)),(( the of A * the Arrows of B) . ( the of (A,B,A) . o3)):] is Relation-like set
bool [:( the Arrows of A . ( the of (A,B,A) . o3)),(( the of A * the Arrows of B) . ( the of (A,B,A) . o3)):] is non empty set
g is Element of the carrier of A
K is Element of the carrier of A
[g,K] is V15() set
{g,K} is set
{g} is set
{{g,K},{g}} is set
f9 is Element of the carrier of A
g9 is Element of the carrier of A
the Arrows of A . (f9,g9) is set
[f9,g9] is V15() set
{f9,g9} is set
{f9} is set
{{f9,g9},{f9}} is set
the Arrows of A . [f9,g9] is set
<^f9,g9^> is set
the of A . (f9,g9) is Element of [: the carrier of B, the carrier of B:]
the of A . [f9,g9] is set
the Arrows of B . ( the of A . (f9,g9)) is set
(F "") . (( the of A ") . o3) is Relation-like Function-like set
F . (( the of A ") . o3) is Relation-like Function-like set
(F . (( the of A ") . o3)) " is Relation-like Function-like set
g99 is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
proj1 (F . ( the of (A,B,A) . o3)) is set
rng the of (A,B,A) 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
dom the of A 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:]
o3 is Element of the carrier of B
f is Element of the carrier of B
<^o3,f^> is set
the of (A,B,A) . (o3,f) is Element of [: the carrier of A, the carrier of A:]
[o3,f] is V15() set
{o3,f} is set
{o3} is set
{{o3,f},{o3}} is set
the of (A,B,A) . [o3,f] is set
the Arrows of A . ( the of (A,B,A) . (o3,f)) is set
the Arrows of B . (o3,f) is set
the Arrows of B . [o3,f] is set
g is Element of the carrier of A
K is Element of the carrier of A
[g,K] is V15() set
{g,K} is set
{g} is set
{{g,K},{g}} is set
dom the of (A,B,A) is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
f9 is Element of the carrier of A
g9 is Element of the carrier of A
the of A . (f9,g9) is Element of [: the carrier of B, the carrier of B:]
[f9,g9] is V15() set
{f9,g9} is set
{f9} is set
{{f9,g9},{f9}} is set
the of A . [f9,g9] is set
the of A * the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) 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 of A * the of (A,B,A)) . [o3,f] is set
id [: the carrier of B, the carrier 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 one-to-one non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
(id [: the carrier of B, the carrier of B:]) . [o3,f] is set
F . [f9,g9] is Relation-like Function-like set
the Arrows of A . [f9,g9] is set
( the of A * the Arrows of B) . [f9,g9] is set
[:( the Arrows of A . [f9,g9]),(( the of A * the Arrows of B) . [f9,g9]):] is Relation-like set
bool [:( the Arrows of A . [f9,g9]),(( the of A * the Arrows of B) . [f9,g9]):] is non empty set
proj2 (F . [f9,g9]) is set
g99 is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] 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 carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A " is Relation-like Function-like set
F is Element of the carrier of B
the of (A,B,A) . (F,F) is Element of [: the carrier of A, the carrier of A:]
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the of (A,B,A) . [F,F] is set
(B,A,(A,B,A),F) is Element of the carrier of A
( the of (A,B,A) . (F,F)) `1 is set
[(B,A,(A,B,A),F),(B,A,(A,B,A),F)] is V15() set
{(B,A,(A,B,A),F),(B,A,(A,B,A),F)} is set
{(B,A,(A,B,A),F)} is set
{{(B,A,(A,B,A),F),(B,A,(A,B,A),F)},{(B,A,(A,B,A),F)}} is set
dom the of A 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
G is Element of the carrier of A
(A,B,A,G) is Element of the carrier of B
the of A . (G,G) is Element of [: the carrier of B, the carrier of B:]
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the of A . [G,G] is set
( the of A . (G,G)) `1 is set
(B,A,(A,B,A),(A,B,A,G)) is Element of the carrier of A
the of (A,B,A) . ((A,B,A,G),(A,B,A,G)) is Element of [: the carrier of A, the carrier of A:]
[(A,B,A,G),(A,B,A,G)] is V15() set
{(A,B,A,G),(A,B,A,G)} is set
{(A,B,A,G)} is set
{{(A,B,A,G),(A,B,A,G)},{(A,B,A,G)}} is set
the of (A,B,A) . [(A,B,A,G),(A,B,A,G)] is set
( the of (A,B,A) . ((A,B,A,G),(A,B,A,G))) `1 is set
(A,B,A,A,(A,B,A)) is (A,A) (A,A)
(A,A,(A,B,A,A,(A,B,A)),G) is Element of the carrier of A
the of (A,B,A,A,(A,B,A)) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) 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 of (A,B,A,A,(A,B,A)) . (G,G) is Element of [: the carrier of A, the carrier of A:]
the of (A,B,A,A,(A,B,A)) . [G,G] is set
( the of (A,B,A,A,(A,B,A)) . (G,G)) `1 is set
the of (A,B,A) * the 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 non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:]
( the of (A,B,A) * the of A) . (G,G) is Element of [: the carrier of A, the carrier of A:]
( the of (A,B,A) * the of A) . [G,G] is set
(( the of (A,B,A) * the of A) . (G,G)) `1 is set
id (dom the of A) is Relation-like dom the of A -defined dom the of A -valued Function-like one-to-one non empty V14( dom the of A) quasi_total Element of bool [:(dom the of A),(dom the of A):]
[:(dom the of A),(dom the of A):] is Relation-like non empty set
bool [:(dom the of A),(dom the of A):] is non empty set
(id (dom the of A)) . [G,G] is set
((id (dom the of A)) . [G,G]) `1 is set
[G,G] `1 is set
the of (A,B,A) . ( the of A . (G,G)) is Element of [: the carrier of A, the carrier of A:]
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B) (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] 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 carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A " is Relation-like Function-like set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of (A,B,A), the Arrows of B, the Arrows of A)
G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
G "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
( the of A ") * (G "") is Relation-like Function-like Function-yielding V37() set
c<sub>7</sub> is Element of the carrier of B
(B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>) is Relation-like Function-like set
the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>) is set
[c<sub>7</sub>,c<sub>7</sub>] is V15() set
{c<sub>7</sub>,c<sub>7</sub>} is set
{c<sub>7</sub>} is set
{{c<sub>7</sub>,c<sub>7</sub>},{c<sub>7</sub>}} is set
the of (A,B,A) . [c<sub>7</sub>,c<sub>7</sub>] is Relation-like Function-like set
idm c<sub>7</sub> is Element of <^c<sub>7</sub>,c<sub>7</sub>^>
<^c<sub>7</sub>,c<sub>7</sub>^> is set
(B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>) . (idm c<sub>7</sub>) is set
(B,A,(A,B,A),c<sub>7</sub>) is Element of the carrier of A
the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of A, the carrier of A:]
the of (A,B,A) . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
idm (B,A,(A,B,A),c₇) is Element of <^(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)^>
<^(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)^> is set
[(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)] is V15() set
{(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)} is set
{(B,A,(A,B,A),c₇)} is set
{{(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)},{(B,A,(A,B,A),c₇)}} is set
dom the of (A,B,A) is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
F is (B,A) (B,A) (B,A)
(B,A,B,F,A) is (B,B) (B,B) (B,B)
the of (B,A,B,F,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) 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 of (B,A,B,F,A) . (c₇,c₇) is Element of [: the carrier of B, the carrier of B:]
the of (B,A,B,F,A) . [c₇,c₇] is set
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of A * the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
( the of A * the of F) . [c₇,c₇] is set
( the of A ") * the of A is Relation-like [: the carrier of B, the carrier of B:] -valued Function-like set
(( the of A ") * the of A) . [c₇,c₇] is set
rng the of A is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
id (rng the of A) is Relation-like rng the of A -defined rng the of A -valued Function-like one-to-one non empty V14( rng the of A) quasi_total Element of bool [:(rng the of A),(rng the of A):]
[:(rng the of A),(rng the of A):] is Relation-like non empty set
bool [:(rng the of A),(rng the of A):] is non empty set
(id (rng the of A)) . [c₇,c₇] is set
id (dom the of (A,B,A)) is Relation-like dom the of (A,B,A) -defined dom the of (A,B,A) -valued Function-like one-to-one non empty V14( dom the of (A,B,A)) quasi_total Element of bool [:(dom the of (A,B,A)),(dom the of (A,B,A)):]
[:(dom the of (A,B,A)),(dom the of (A,B,A)):] is Relation-like non empty set
bool [:(dom the of (A,B,A)),(dom the of (A,B,A)):] is non empty set
(id (dom the of (A,B,A))) . [c₇,c₇] is set
id [: the carrier of B, the carrier 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 one-to-one non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
(id [: the carrier of B, the carrier of B:]) . [c₇,c₇] is set
(A,B,A,(B,A,(A,B,A),c₇)) is Element of the carrier of B
the of A . ((B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)) is Element of [: the carrier of B, the carrier of B:]
the of A . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)] is set
( the of A . ((B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇))) `1 is set
(B,B,(B,A,B,F,A),c<sub>7</sub>) is Element of the carrier of B
( the of (B,A,B,F,A) . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
dom the of A 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
(A,B,A,(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)) is set
the of A . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)] is Relation-like Function-like set
dom the of A 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:]
( the of A * the Arrows of B) . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)] is set
the Arrows of B . ( the of A . ((B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇))) is set
the Arrows of B . ((A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),c₇))) is set
[(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),c₇))] is V15() set
{(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),c₇))} is set
{(A,B,A,(B,A,(A,B,A),c₇))} is set
{{(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),c₇))},{(A,B,A,(B,A,(A,B,A),c₇))}} is set
the Arrows of B . [(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),c₇))] is set
the Arrows of A . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)] is set
[:( the Arrows of A . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)]),(( the of A * the Arrows of B) . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)]):] is Relation-like set
bool [:( the Arrows of A . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)]),(( the of A * the Arrows of B) . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)]):] is non empty set
proj1 (A,B,A,(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)) is set
the Arrows of A . ((B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)) is set
the of (A,B,A) * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
( the of (A,B,A) * the Arrows of A) . [c₇,c₇] is set
the of F . (c₇,c₇) is Element of [: the carrier of A, the carrier of A:]
the of F . [c₇,c₇] is set
the Arrows of A . ( the of F . (c₇,c₇)) is set
the Arrows of B . [c₇,c₇] is set
[:( the Arrows of B . [c₇,c₇]),(( the of (A,B,A) * the Arrows of A) . [c₇,c₇]):] is Relation-like set
bool [:( the Arrows of B . [c₇,c₇]),(( the of (A,B,A) * the Arrows of A) . [c₇,c₇]):] is non empty set
proj1 (B,A,(A,B,A),c₇,c₇) is set
the Arrows of B . (c₇,c₇) is set
(G "") . ( the of (A,B,A) . (c₇,c₇)) is Relation-like ( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,c₇)) -defined the Arrows of A . ( the of (A,B,A) . (c₇,c₇)) -valued Function-like quasi_total Element of bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,c₇))),( the Arrows of A . ( the of (A,B,A) . (c₇,c₇))):]
( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,c₇)) is set
the Arrows of A . ( the of (A,B,A) . (c₇,c₇)) is set
[:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,c₇))),( the Arrows of A . ( the of (A,B,A) . (c₇,c₇))):] is Relation-like set
bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,c₇))),( the Arrows of A . ( the of (A,B,A) . (c₇,c₇))):] is non empty set
(B,A,F,c₇) is Element of the carrier of A
( the of F . (c₇,c₇)) `1 is set
[(B,A,F,c<sub>7</sub>),(B,A,F,c<sub>7</sub>)] is V15() set
{(B,A,F,c<sub>7</sub>),(B,A,F,c<sub>7</sub>)} is set
{(B,A,F,c<sub>7</sub>)} is set
{{(B,A,F,c<sub>7</sub>),(B,A,F,c<sub>7</sub>)},{(B,A,F,c<sub>7</sub>)}} is set
(G "") . [(B,A,F,c<sub>7</sub>),(B,A,F,c<sub>7</sub>)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)) " is Relation-like Function-like set
o2 is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
proj2 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>) is set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)) . ((B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>) . (idm c<sub>7</sub>)) is set
(B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>) * (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)) is Relation-like Function-like set
((B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>) * (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))) . (idm c<sub>7</sub>) is set
proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)) is set
id (proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))) is Relation-like proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)) -defined proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)) -valued Function-like one-to-one V14( proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))) quasi_total Element of bool [:(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))),(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))):]
[:(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))),(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))):] is Relation-like set
bool [:(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))),(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))):] is non empty set
(id (proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)))) . (idm c<sub>7</sub>) is set
id (proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>)) is Relation-like proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>) -defined proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>) -valued Function-like one-to-one V14( proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>)) quasi_total Element of bool [:(proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>)):]
[:(proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>)):] is Relation-like set
bool [:(proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>)):] is non empty set
(id (proj1 (B,A,(A,B,A),c<sub>7</sub>,c<sub>7</sub>))) . (idm c<sub>7</sub>) is set
idm (A,B,A,(B,A,(A,B,A),c<sub>7</sub>)) is Element of <^(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),c<sub>7</sub>))^>
<^(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),c<sub>7</sub>))^> is set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)) . (idm (B,A,(A,B,A),c<sub>7</sub>)) is set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
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 B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] 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
B is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
B " is Relation-like Function-like set
proj1 (B ") is set
rng B is non empty Element of bool the carrier of B
bool the carrier of B is non empty set
proj2 (B ") is set
dom B is non empty Element of bool the carrier of A
bool the carrier of A is non empty set
rng [:B,B:] is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
[:(rng B),(rng B):] is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
[: 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
F is Relation-like the carrier of B -defined the carrier of A -valued Function-like non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of A:]
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[:F,F:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:B,B:] " is Relation-like Function-like set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
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 B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] 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
B is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:B,B:]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
B " is Relation-like Function-like set
proj1 (B ") is set
rng B is non empty Element of bool the carrier of B
bool the carrier of B is non empty set
proj2 (B ") is set
dom B is non empty Element of bool the carrier of A
bool the carrier of A is non empty set
rng [:B,B:] is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
[:(rng B),(rng B):] is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
[: 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
F is Relation-like the carrier of B -defined the carrier of A -valued Function-like non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of A:]
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[:F,F:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
( the carrier of B, the carrier of B,[: the carrier of A, the carrier of A:],[:F,F:]) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:B,B:] " is Relation-like Function-like set
the of A " is Relation-like Function-like set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
the carrier of B is non empty set
A is (A,B) (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[: the carrier of B, the carrier of B:] 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 carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A " is Relation-like Function-like set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of (A,B,A), the Arrows of B, the Arrows of A)
G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
G "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
( the of A ") * (G "") is Relation-like Function-like Function-yielding V37() set
c<sub>7</sub> is Element of the carrier of B
o2 is Element of the carrier of B
<^c<sub>7</sub>,o2^> is set
(B,A,(A,B,A),c<sub>7</sub>) is Element of the carrier of A
the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of A, the carrier of A:]
[c<sub>7</sub>,c<sub>7</sub>] is V15() set
{c<sub>7</sub>,c<sub>7</sub>} is set
{c<sub>7</sub>} is set
{{c<sub>7</sub>,c<sub>7</sub>},{c<sub>7</sub>}} is set
the of (A,B,A) . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
(B,A,(A,B,A),o2) is Element of the carrier of A
the of (A,B,A) . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the of (A,B,A) . [o2,o2] is set
( the of (A,B,A) . (o2,o2)) `1 is set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) is set
[(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)] is V15() set
{(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)} is set
{(B,A,(A,B,A),c<sub>7</sub>)} is set
{{(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)},{(B,A,(A,B,A),c<sub>7</sub>)}} is set
the of A . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)] is Relation-like Function-like set
(B,A,(A,B,A),c<sub>7</sub>,o2) is Relation-like Function-like set
the of (A,B,A) . (c<sub>7</sub>,o2) is set
[c<sub>7</sub>,o2] is V15() set
{c<sub>7</sub>,o2} is set
{{c<sub>7</sub>,o2},{c<sub>7</sub>}} is set
the of (A,B,A) . [c<sub>7</sub>,o2] is Relation-like Function-like set
o3 is Element of <^c<sub>7</sub>,o2^>
(B,A,(A,B,A),c<sub>7</sub>,o2) . o3 is set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) . ((B,A,(A,B,A),c<sub>7</sub>,o2) . o3) is set
dom the of (A,B,A) is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
dom the of A 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
the of (A,B,A) * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o2] is set
F is (B,A) (B,A) (B,A)
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of F . (c<sub>7</sub>,o2) is Element of [: the carrier of A, the carrier of A:]
the of F . [c<sub>7</sub>,o2] is set
the Arrows of A . ( the of F . (c<sub>7</sub>,o2)) is set
(B,A,F,c<sub>7</sub>) is Element of the carrier of A
the of F . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of A, the carrier of A:]
the of F . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of F . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
(B,A,F,o2) is Element of the carrier of A
the of F . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
the of F . [o2,o2] is set
( the of F . (o2,o2)) `1 is set
the Arrows of A . ((B,A,F,c<sub>7</sub>),(B,A,F,o2)) is set
[(B,A,F,c<sub>7</sub>),(B,A,F,o2)] is V15() set
{(B,A,F,c<sub>7</sub>),(B,A,F,o2)} is set
{(B,A,F,c<sub>7</sub>)} is set
{{(B,A,F,c<sub>7</sub>),(B,A,F,o2)},{(B,A,F,c<sub>7</sub>)}} is set
the Arrows of A . [(B,A,F,c<sub>7</sub>),(B,A,F,o2)] is set
<^(B,A,F,c<sub>7</sub>),(B,A,F,o2)^> is set
the Arrows of B . [c<sub>7</sub>,o2] is set
[:( the Arrows of B . [c<sub>7</sub>,o2]),(( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o2]):] is Relation-like set
bool [:( the Arrows of B . [c<sub>7</sub>,o2]),(( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o2]):] is non empty set
proj1 (B,A,(A,B,A),c<sub>7</sub>,o2) is set
the Arrows of B . (c<sub>7</sub>,o2) is set
the of (A,B,A) . (c<sub>7</sub>,o2) is Element of [: the carrier of A, the carrier of A:]
the of (A,B,A) . [c<sub>7</sub>,o2] is set
(G "") . ( the of (A,B,A) . (c<sub>7</sub>,o2)) is Relation-like ( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2)) -defined the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2)) -valued Function-like quasi_total Element of bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2))):]
( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2)) is set
the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2)) is set
[:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2))):] is Relation-like set
bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2))):] is non empty set
(G "") . [(B,A,F,c<sub>7</sub>),(B,A,F,o2)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) " is Relation-like Function-like set
f is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
(B,A,(A,B,A),c<sub>7</sub>,o2) * (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) is Relation-like Function-like set
((B,A,(A,B,A),c<sub>7</sub>,o2) * (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))) . o3 is set
proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) is set
id (proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))) is Relation-like proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) -defined proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) -valued Function-like one-to-one V14( proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))) quasi_total Element of bool [:(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))),(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))):]
[:(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))),(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))):] is Relation-like set
bool [:(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))),(proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2))):] is non empty set
(id (proj2 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)))) . o3 is set
id (proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)) is Relation-like proj1 (B,A,(A,B,A),c<sub>7</sub>,o2) -defined proj1 (B,A,(A,B,A),c<sub>7</sub>,o2) -valued Function-like one-to-one V14( proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)) quasi_total Element of bool [:(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)):]
[:(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)):] is Relation-like set
bool [:(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)):] is non empty set
(id (proj1 (B,A,(A,B,A),c<sub>7</sub>,o2))) . o3 is set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
the carrier of B is non empty set
A is (A,B) (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[: the carrier of B, the carrier of B:] 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 carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A " is Relation-like Function-like set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of (A,B,A), the Arrows of B, the Arrows of A)
G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
G "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
( the of A ") * (G "") is Relation-like Function-like Function-yielding V37() set
c<sub>7</sub> is Element of the carrier of B
o2 is Element of the carrier of B
<^c<sub>7</sub>,o2^> is set
(B,A,(A,B,A),o2) is Element of the carrier of A
the of (A,B,A) . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the of (A,B,A) . [o2,o2] is set
( the of (A,B,A) . (o2,o2)) `1 is set
(B,A,(A,B,A),c₇) is Element of the carrier of A
the of (A,B,A) . (c₇,c₇) is Element of [: the carrier of A, the carrier of A:]
[c₇,c₇] is V15() set
{c₇,c₇} is set
{c₇} is set
{{c₇,c₇},{c₇}} is set
the of (A,B,A) . [c₇,c₇] is set
( the of (A,B,A) . (c₇,c₇)) `1 is set
(A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)) is set
[(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)] is V15() set
{(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)} is set
{(B,A,(A,B,A),o2)} is set
{{(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)},{(B,A,(A,B,A),o2)}} is set
the of A . [(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)] is Relation-like Function-like set
(B,A,(A,B,A),c<sub>7</sub>,o2) is Relation-like Function-like set
the of (A,B,A) . (c<sub>7</sub>,o2) is set
[c<sub>7</sub>,o2] is V15() set
{c<sub>7</sub>,o2} is set
{{c<sub>7</sub>,o2},{c<sub>7</sub>}} is set
the of (A,B,A) . [c<sub>7</sub>,o2] is Relation-like Function-like set
o3 is Element of <^c<sub>7</sub>,o2^>
(B,A,(A,B,A),c<sub>7</sub>,o2) . o3 is set
(A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)) . ((B,A,(A,B,A),c<sub>7</sub>,o2) . o3) is set
dom the of (A,B,A) is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
dom the of A 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
the of (A,B,A) * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o2] is set
F is (B,A) (B,A) (B,A)
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of F . (c<sub>7</sub>,o2) is Element of [: the carrier of A, the carrier of A:]
the of F . [c<sub>7</sub>,o2] is set
the Arrows of A . ( the of F . (c<sub>7</sub>,o2)) is set
(B,A,F,o2) is Element of the carrier of A
the of F . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
the of F . [o2,o2] is set
( the of F . (o2,o2)) `1 is set
(B,A,F,c₇) is Element of the carrier of A
the of F . (c₇,c₇) is Element of [: the carrier of A, the carrier of A:]
the of F . [c₇,c₇] is set
( the of F . (c₇,c₇)) `1 is set
the Arrows of A . ((B,A,F,o2),(B,A,F,c<sub>7</sub>)) is set
[(B,A,F,o2),(B,A,F,c<sub>7</sub>)] is V15() set
{(B,A,F,o2),(B,A,F,c<sub>7</sub>)} is set
{(B,A,F,o2)} is set
{{(B,A,F,o2),(B,A,F,c<sub>7</sub>)},{(B,A,F,o2)}} is set
the Arrows of A . [(B,A,F,o2),(B,A,F,c<sub>7</sub>)] is set
<^(B,A,F,o2),(B,A,F,c<sub>7</sub>)^> is set
the Arrows of B . [c<sub>7</sub>,o2] is set
[:( the Arrows of B . [c<sub>7</sub>,o2]),(( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o2]):] is Relation-like set
bool [:( the Arrows of B . [c<sub>7</sub>,o2]),(( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o2]):] is non empty set
proj1 (B,A,(A,B,A),c<sub>7</sub>,o2) is set
the Arrows of B . (c<sub>7</sub>,o2) is set
the of (A,B,A) . (c<sub>7</sub>,o2) is Element of [: the carrier of A, the carrier of A:]
the of (A,B,A) . [c<sub>7</sub>,o2] is set
(G "") . ( the of (A,B,A) . (c<sub>7</sub>,o2)) is Relation-like ( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2)) -defined the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2)) -valued Function-like quasi_total Element of bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2))):]
( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2)) is set
the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2)) is set
[:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2))):] is Relation-like set
bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o2))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o2))):] is non empty set
(G "") . [(B,A,F,o2),(B,A,F,c<sub>7</sub>)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)) " is Relation-like Function-like set
f is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
(B,A,(A,B,A),c<sub>7</sub>,o2) * (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)) is Relation-like Function-like set
((B,A,(A,B,A),c<sub>7</sub>,o2) * (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))) . o3 is set
proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)) is set
id (proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))) is Relation-like proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)) -defined proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)) -valued Function-like one-to-one V14( proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))) quasi_total Element of bool [:(proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))),(proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))):]
[:(proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))),(proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))):] is Relation-like set
bool [:(proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))),(proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>))):] is non empty set
(id (proj2 (A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)))) . o3 is set
id (proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)) is Relation-like proj1 (B,A,(A,B,A),c<sub>7</sub>,o2) -defined proj1 (B,A,(A,B,A),c<sub>7</sub>,o2) -valued Function-like one-to-one V14( proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)) quasi_total Element of bool [:(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)):]
[:(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)):] is Relation-like set
bool [:(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)),(proj1 (B,A,(A,B,A),c<sub>7</sub>,o2)):] is non empty set
(id (proj1 (B,A,(A,B,A),c<sub>7</sub>,o2))) . o3 is set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] 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 carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A " is Relation-like Function-like set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of (A,B,A), the Arrows of B, the Arrows of A)
G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
G "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
( the of A ") * (G "") is Relation-like Function-like Function-yielding V37() set
c<sub>7</sub> is Element of the carrier of B
o2 is Element of the carrier of B
<^c<sub>7</sub>,o2^> is set
o3 is Element of the carrier of B
<^o2,o3^> is set
(B,A,(A,B,A),c<sub>7</sub>) is Element of the carrier of A
the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of A, the carrier of A:]
[c<sub>7</sub>,c<sub>7</sub>] is V15() set
{c<sub>7</sub>,c<sub>7</sub>} is set
{c<sub>7</sub>} is set
{{c<sub>7</sub>,c<sub>7</sub>},{c<sub>7</sub>}} is set
the of (A,B,A) . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
(B,A,(A,B,A),o2) is Element of the carrier of A
the of (A,B,A) . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the of (A,B,A) . [o2,o2] is set
( the of (A,B,A) . (o2,o2)) `1 is set
<^(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)^> is set
(B,A,(A,B,A),o3) is Element of the carrier of A
the of (A,B,A) . (o3,o3) is Element of [: the carrier of A, the carrier of A:]
[o3,o3] is V15() set
{o3,o3} is set
{o3} is set
{{o3,o3},{o3}} is set
the of (A,B,A) . [o3,o3] is set
( the of (A,B,A) . (o3,o3)) `1 is set
<^(B,A,(A,B,A),o2),(B,A,(A,B,A),o3)^> is set
(B,A,(A,B,A),c₇,o2) is Relation-like Function-like set
the of (A,B,A) . (c₇,o2) is set
[c₇,o2] is V15() set
{c₇,o2} is set
{{c₇,o2},{c₇}} is set
the of (A,B,A) . [c₇,o2] is Relation-like Function-like set
(B,A,(A,B,A),o2,o3) is Relation-like Function-like set
the of (A,B,A) . (o2,o3) is set
[o2,o3] is V15() set
{o2,o3} is set
{{o2,o3},{o2}} is set
the of (A,B,A) . [o2,o3] is Relation-like Function-like set
(B,A,(A,B,A),c₇,o3) is Relation-like Function-like set
the of (A,B,A) . (c₇,o3) is set
[c₇,o3] is V15() set
{c₇,o3} is set
{{c₇,o3},{c₇}} is set
the of (A,B,A) . [c₇,o3] is Relation-like Function-like set
F is (B,A) (B,A) (B,A)
(B,A,F,c₇) is Element of the carrier of A
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of F . (c₇,c₇) is Element of [: the carrier of A, the carrier of A:]
the of F . [c₇,c₇] is set
( the of F . (c₇,c₇)) `1 is set
(B,A,F,o2) is Element of the carrier of A
the of F . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
the of F . [o2,o2] is set
( the of F . (o2,o2)) `1 is set
<^(B,A,F,c₇),(B,A,F,o2)^> is set
(B,A,F,o3) is Element of the carrier of A
the of F . (o3,o3) is Element of [: the carrier of A, the carrier of A:]
the of F . [o3,o3] is set
( the of F . (o3,o3)) `1 is set
<^(B,A,F,o2),(B,A,F,o3)^> is set
<^c<sub>7</sub>,o3^> is set
<^(B,A,F,c<sub>7</sub>),(B,A,F,o3)^> is set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)) is Element of the carrier of B
the of A . ((B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)) is Element of [: the carrier of B, the carrier of B:]
[(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)] is V15() set
{(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)} is set
{(B,A,(A,B,A),c<sub>7</sub>)} is set
{{(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)},{(B,A,(A,B,A),c<sub>7</sub>)}} is set
the of A . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>)] is set
( the of A . ((B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),c<sub>7</sub>))) `1 is set
(A,B,A,(B,A,(A,B,A),o3)) is Element of the carrier of B
the of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),o3)) is Element of [: the carrier of B, the carrier of B:]
[(B,A,(A,B,A),o3),(B,A,(A,B,A),o3)] is V15() set
{(B,A,(A,B,A),o3),(B,A,(A,B,A),o3)} is set
{(B,A,(A,B,A),o3)} is set
{{(B,A,(A,B,A),o3),(B,A,(A,B,A),o3)},{(B,A,(A,B,A),o3)}} is set
the of A . [(B,A,(A,B,A),o3),(B,A,(A,B,A),o3)] is set
( the of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),o3))) `1 is set
<^(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o3))^> is set
f is Element of <^c<sub>7</sub>,o2^>
(B,A,(A,B,A),c<sub>7</sub>,o2) . f is set
g is Element of <^o2,o3^>
(B,A,(A,B,A),o2,o3) . g is set
g * f is Element of <^c<sub>7</sub>,o3^>
(B,A,(A,B,A),c<sub>7</sub>,o3) . (g * f) is set
K is (B,A) (B,A)
(B,A,K,c<sub>7</sub>,o2,f) is Element of <^(B,A,K,c<sub>7</sub>),(B,A,K,o2)^>
(B,A,K,c<sub>7</sub>) is Element of the carrier of A
the of K is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of K . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of A, the carrier of A:]
the of K . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of K . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
(B,A,K,o2) is Element of the carrier of A
the of K . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
the of K . [o2,o2] is set
( the of K . (o2,o2)) `1 is set
<^(B,A,K,c<sub>7</sub>),(B,A,K,o2)^> is set
(B,A,K,c<sub>7</sub>,o2) is Relation-like <^c<sub>7</sub>,o2^> -defined <^(B,A,K,c<sub>7</sub>),(B,A,K,o2)^> -valued Function-like quasi_total Element of bool [:<^c<sub>7</sub>,o2^>,<^(B,A,K,c<sub>7</sub>),(B,A,K,o2)^>:]
[:<^c<sub>7</sub>,o2^>,<^(B,A,K,c<sub>7</sub>),(B,A,K,o2)^>:] is Relation-like set
bool [:<^c<sub>7</sub>,o2^>,<^(B,A,K,c<sub>7</sub>),(B,A,K,o2)^>:] is non empty set
the of K is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of K, the Arrows of B, the Arrows of A)
the of K . (c<sub>7</sub>,o2) is set
the of K . [c<sub>7</sub>,o2] is Relation-like Function-like set
(B,A,K,c<sub>7</sub>,o2) . f is set
(B,A,K,o2,o3,g) is Element of <^(B,A,K,o2),(B,A,K,o3)^>
(B,A,K,o3) is Element of the carrier of A
the of K . (o3,o3) is Element of [: the carrier of A, the carrier of A:]
the of K . [o3,o3] is set
( the of K . (o3,o3)) `1 is set
<^(B,A,K,o2),(B,A,K,o3)^> is set
(B,A,K,o2,o3) is Relation-like <^o2,o3^> -defined <^(B,A,K,o2),(B,A,K,o3)^> -valued Function-like quasi_total Element of bool [:<^o2,o3^>,<^(B,A,K,o2),(B,A,K,o3)^>:]
[:<^o2,o3^>,<^(B,A,K,o2),(B,A,K,o3)^>:] is Relation-like set
bool [:<^o2,o3^>,<^(B,A,K,o2),(B,A,K,o3)^>:] is non empty set
the of K . (o2,o3) is set
the of K . [o2,o3] is Relation-like Function-like set
(B,A,K,o2,o3) . g is set
f9 is Element of <^(B,A,(A,B,A),c₇),(B,A,(A,B,A),o2)^>
g9 is Element of <^(B,A,(A,B,A),o2),(B,A,(A,B,A),o3)^>
g9 * f9 is Element of <^(B,A,(A,B,A),c₇),(B,A,(A,B,A),o3)^>
<^(B,A,(A,B,A),c₇),(B,A,(A,B,A),o3)^> is set
(A,B,A,(B,A,(A,B,A),o2)) is Element of the carrier of B
the of A . ((B,A,(A,B,A),o2),(B,A,(A,B,A),o2)) is Element of [: the carrier of B, the carrier of B:]
[(B,A,(A,B,A),o2),(B,A,(A,B,A),o2)] is V15() set
{(B,A,(A,B,A),o2),(B,A,(A,B,A),o2)} is set
{(B,A,(A,B,A),o2)} is set
{{(B,A,(A,B,A),o2),(B,A,(A,B,A),o2)},{(B,A,(A,B,A),o2)}} is set
the of A . [(B,A,(A,B,A),o2),(B,A,(A,B,A),o2)] is set
( the of A . ((B,A,(A,B,A),o2),(B,A,(A,B,A),o2))) `1 is set
<^(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o2))^> is set
<^(A,B,A,(B,A,(A,B,A),o2)),(A,B,A,(B,A,(A,B,A),o3))^> is set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) is set
[(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)] is V15() set
{(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)} is set
{{(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)},{(B,A,(A,B,A),c<sub>7</sub>)}} is set
the of A . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o2)) . f9 is set
(A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),o3)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),o2),(B,A,(A,B,A),o3)) is set
[(B,A,(A,B,A),o2),(B,A,(A,B,A),o3)] is V15() set
{(B,A,(A,B,A),o2),(B,A,(A,B,A),o3)} is set
{{(B,A,(A,B,A),o2),(B,A,(A,B,A),o3)},{(B,A,(A,B,A),o2)}} is set
the of A . [(B,A,(A,B,A),o2),(B,A,(A,B,A),o3)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),o3)) . g9 is set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)) is set
[(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)] is V15() set
{(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)} is set
{{(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)},{(B,A,(A,B,A),c<sub>7</sub>)}} is set
the of A . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)) . (g9 * f9) is set
g99 is Element of <^(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o2))^>
f99 is Element of <^(A,B,A,(B,A,(A,B,A),o2)),(A,B,A,(B,A,(A,B,A),o3))^>
f99 * g99 is Element of <^(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o3))^>
dom the of (A,B,A) is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
dom the of A 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
dom the of A 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:]
( the of A * the Arrows of B) . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)] is set
the of A . ((B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)) is Element of [: the carrier of B, the carrier of B:]
the of A . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)] is set
the Arrows of B . ( the of A . ((B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3))) is set
the Arrows of B . ((A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o3))) is set
[(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o3))] is V15() set
{(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o3))} is set
{(A,B,A,(B,A,(A,B,A),c<sub>7</sub>))} is set
{{(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o3))},{(A,B,A,(B,A,(A,B,A),c<sub>7</sub>))}} is set
the Arrows of B . [(A,B,A,(B,A,(A,B,A),c<sub>7</sub>)),(A,B,A,(B,A,(A,B,A),o3))] is set
the Arrows of A . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)] is set
[:( the Arrows of A . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)]),(( the of A * the Arrows of B) . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)]):] is Relation-like set
bool [:( the Arrows of A . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)]),(( the of A * the Arrows of B) . [(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)]):] is non empty set
proj1 (A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)) is set
the Arrows of A . ((B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)) is set
the of (A,B,A) * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o3] is set
the of F . (c<sub>7</sub>,o3) is Element of [: the carrier of A, the carrier of A:]
the of F . [c<sub>7</sub>,o3] is set
the Arrows of A . ( the of F . (c<sub>7</sub>,o3)) is set
the Arrows of B . [c<sub>7</sub>,o3] is set
[:( the Arrows of B . [c<sub>7</sub>,o3]),(( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o3]):] is Relation-like set
bool [:( the Arrows of B . [c<sub>7</sub>,o3]),(( the of (A,B,A) * the Arrows of A) . [c<sub>7</sub>,o3]):] is non empty set
proj1 (B,A,(A,B,A),c<sub>7</sub>,o3) is set
the Arrows of B . (c<sub>7</sub>,o3) is set
the of (A,B,A) . (c<sub>7</sub>,o3) is Element of [: the carrier of A, the carrier of A:]
the of (A,B,A) . [c<sub>7</sub>,o3] is set
(G "") . ( the of (A,B,A) . (c<sub>7</sub>,o3)) is Relation-like ( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o3)) -defined the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o3)) -valued Function-like quasi_total Element of bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o3))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o3))):]
( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o3)) is set
the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o3)) is set
[:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o3))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o3))):] is Relation-like set
bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c<sub>7</sub>,o3))),( the Arrows of A . ( the of (A,B,A) . (c<sub>7</sub>,o3))):] is non empty set
[(B,A,F,c<sub>7</sub>),(B,A,F,o3)] is V15() set
{(B,A,F,c<sub>7</sub>),(B,A,F,o3)} is set
{(B,A,F,c<sub>7</sub>)} is set
{{(B,A,F,c<sub>7</sub>),(B,A,F,o3)},{(B,A,F,c<sub>7</sub>)}} is set
(G "") . [(B,A,F,c<sub>7</sub>),(B,A,F,o3)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),c<sub>7</sub>),(B,A,(A,B,A),o3)) " is Relation-like Function-like set
o2 is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
(B,A,B,F,A) is (B,B) (B,B) (B,B)
the of (B,A,B,F,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) 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 of A * the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
( the of A ") * the of A is Relation-like [: the carrier of B, the carrier of B:] -valued Function-like set
rng the of A is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
id (rng the of A) is Relation-like rng the of A -defined rng the of A -valued Function-like one-to-one non empty V14( rng the of A) quasi_total Element of bool [:(rng the of A),(rng the of A):]
[:(rng the of A),(rng the of A):] is Relation-like non empty set
bool [:(rng the of A),(rng the of A):] is non empty set
id (dom the of (A,B,A)) is Relation-like dom the of (A,B,A) -defined dom the of (A,B,A) -valued Function-like one-to-one non empty V14( dom the of (A,B,A)) quasi_total Element of bool [:(dom the of (A,B,A)),(dom the of (A,B,A)):]
[:(dom the of (A,B,A)),(dom the of (A,B,A)):] is Relation-like non empty set
bool [:(dom the of (A,B,A)),(dom the of (A,B,A)):] is non empty set
id [: the carrier of B, the carrier 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 one-to-one non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
the of (B,A,B,F,A) . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of B, the carrier of B:]
the of (B,A,B,F,A) . [c<sub>7</sub>,c<sub>7</sub>] is set
(B,B,(B,A,B,F,A),c<sub>7</sub>) is Element of the carrier of B
( the of (B,A,B,F,A) . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
the of (B,A,B,F,A) . (o2,o2) is Element of [: the carrier of B, the carrier of B:]
the of (B,A,B,F,A) . [o2,o2] is set
(B,B,(B,A,B,F,A),o2) is Element of the carrier of B
( the of (B,A,B,F,A) . (o2,o2)) `1 is set
the of (B,A,B,F,A) . (o3,o3) is Element of [: the carrier of B, the carrier of B:]
the of (B,A,B,F,A) . [o3,o3] is set
(B,B,(B,A,B,F,A),o3) is Element of the carrier of B
( the of (B,A,B,F,A) . (o3,o3)) `1 is set
proj2 (B,A,(A,B,A),c₇,o3) is set
(A,B,A,(B,A,(A,B,A),c₇),(B,A,(A,B,A),o3)) . ((B,A,(A,B,A),c₇,o3) . (g * f)) is set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the carrier of B is non empty set
[: the carrier of B, the carrier of B:] 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 carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
the of A " is Relation-like Function-like set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of B is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
the of A * the Arrows of B is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:], the of A, the Arrows of A, the Arrows of B)
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of (A,B,A), the Arrows of B, the Arrows of A)
G is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
G "" is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the of A * the Arrows of B, the Arrows of A
( the of A ") * (G "") is Relation-like Function-like Function-yielding V37() set
c₇ is Element of the carrier of B
o2 is Element of the carrier of B
<^c₇,o2^> is set
o3 is Element of the carrier of B
<^o2,o3^> is set
(B,A,(A,B,A),o2) is Element of the carrier of A
the of (A,B,A) . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
[o2,o2] is V15() set
{o2,o2} is set
{o2} is set
{{o2,o2},{o2}} is set
the of (A,B,A) . [o2,o2] is set
( the of (A,B,A) . (o2,o2)) `1 is set
(B,A,(A,B,A),c<sub>7</sub>) is Element of the carrier of A
the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of A, the carrier of A:]
[c<sub>7</sub>,c<sub>7</sub>] is V15() set
{c<sub>7</sub>,c<sub>7</sub>} is set
{c<sub>7</sub>} is set
{{c<sub>7</sub>,c<sub>7</sub>},{c<sub>7</sub>}} is set
the of (A,B,A) . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of (A,B,A) . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
<^(B,A,(A,B,A),o2),(B,A,(A,B,A),c₇)^> is set
(B,A,(A,B,A),o3) is Element of the carrier of A
the of (A,B,A) . (o3,o3) is Element of [: the carrier of A, the carrier of A:]
[o3,o3] is V15() set
{o3,o3} is set
{o3} is set
{{o3,o3},{o3}} is set
the of (A,B,A) . [o3,o3] is set
( the of (A,B,A) . (o3,o3)) `1 is set
<^(B,A,(A,B,A),o3),(B,A,(A,B,A),o2)^> is set
(B,A,(A,B,A),c<sub>7</sub>,o2) is Relation-like Function-like set
the of (A,B,A) . (c<sub>7</sub>,o2) is set
[c<sub>7</sub>,o2] is V15() set
{c<sub>7</sub>,o2} is set
{{c<sub>7</sub>,o2},{c<sub>7</sub>}} is set
the of (A,B,A) . [c<sub>7</sub>,o2] is Relation-like Function-like set
(B,A,(A,B,A),o2,o3) is Relation-like Function-like set
the of (A,B,A) . (o2,o3) is set
[o2,o3] is V15() set
{o2,o3} is set
{{o2,o3},{o2}} is set
the of (A,B,A) . [o2,o3] is Relation-like Function-like set
(B,A,(A,B,A),c<sub>7</sub>,o3) is Relation-like Function-like set
the of (A,B,A) . (c<sub>7</sub>,o3) is set
[c<sub>7</sub>,o3] is V15() set
{c<sub>7</sub>,o3} is set
{{c<sub>7</sub>,o3},{c<sub>7</sub>}} is set
the of (A,B,A) . [c<sub>7</sub>,o3] is Relation-like Function-like set
F is (B,A) (B,A) (B,A)
(B,A,F,o2) is Element of the carrier of A
the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of F . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
the of F . [o2,o2] is set
( the of F . (o2,o2)) `1 is set
(B,A,F,c₇) is Element of the carrier of A
the of F . (c₇,c₇) is Element of [: the carrier of A, the carrier of A:]
the of F . [c₇,c₇] is set
( the of F . (c₇,c₇)) `1 is set
<^(B,A,F,o2),(B,A,F,c<sub>7</sub>)^> is set
(B,A,F,o3) is Element of the carrier of A
the of F . (o3,o3) is Element of [: the carrier of A, the carrier of A:]
the of F . [o3,o3] is set
( the of F . (o3,o3)) `1 is set
<^(B,A,F,o3),(B,A,F,o2)^> is set
<^c₇,o3^> is set
<^(B,A,F,o3),(B,A,F,c₇)^> is set
(A,B,A,(B,A,(A,B,A),c₇)) is Element of the carrier of B
the of A . ((B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)) is Element of [: the carrier of B, the carrier of B:]
[(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)] is V15() set
{(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)} is set
{(B,A,(A,B,A),c₇)} is set
{{(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)},{(B,A,(A,B,A),c₇)}} is set
the of A . [(B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇)] is set
( the of A . ((B,A,(A,B,A),c₇),(B,A,(A,B,A),c₇))) `1 is set
(A,B,A,(B,A,(A,B,A),o3)) is Element of the carrier of B
the of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),o3)) is Element of [: the carrier of B, the carrier of B:]
[(B,A,(A,B,A),o3),(B,A,(A,B,A),o3)] is V15() set
{(B,A,(A,B,A),o3),(B,A,(A,B,A),o3)} is set
{(B,A,(A,B,A),o3)} is set
{{(B,A,(A,B,A),o3),(B,A,(A,B,A),o3)},{(B,A,(A,B,A),o3)}} is set
the of A . [(B,A,(A,B,A),o3),(B,A,(A,B,A),o3)] is set
( the of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),o3))) `1 is set
<^(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o3))^> is set
f is Element of <^c₇,o2^>
(B,A,(A,B,A),c₇,o2) . f is set
g is Element of <^o2,o3^>
(B,A,(A,B,A),o2,o3) . g is set
g * f is Element of <^c₇,o3^>
(B,A,(A,B,A),c₇,o3) . (g * f) is set
K is (B,A) (B,A)
(B,A,K,c₇,o2,f) is Element of <^(B,A,K,o2),(B,A,K,c₇)^>
(B,A,K,o2) is Element of the carrier of A
the of K is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
the of K . (o2,o2) is Element of [: the carrier of A, the carrier of A:]
the of K . [o2,o2] is set
( the of K . (o2,o2)) `1 is set
(B,A,K,c<sub>7</sub>) is Element of the carrier of A
the of K . (c<sub>7</sub>,c<sub>7</sub>) is Element of [: the carrier of A, the carrier of A:]
the of K . [c<sub>7</sub>,c<sub>7</sub>] is set
( the of K . (c<sub>7</sub>,c<sub>7</sub>)) `1 is set
<^(B,A,K,o2),(B,A,K,c₇)^> is set
(B,A,K,c₇,o2) is Relation-like <^c₇,o2^> -defined <^(B,A,K,o2),(B,A,K,c₇)^> -valued Function-like quasi_total Element of bool [:<^c₇,o2^>,<^(B,A,K,o2),(B,A,K,c₇)^>:]
[:<^c₇,o2^>,<^(B,A,K,o2),(B,A,K,c₇)^>:] is Relation-like set
bool [:<^c₇,o2^>,<^(B,A,K,o2),(B,A,K,c₇)^>:] is non empty set
the of K is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) Function-yielding V37() ([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:], the of K, the Arrows of B, the Arrows of A)
the of K . (c₇,o2) is set
the of K . [c₇,o2] is Relation-like Function-like set
(B,A,K,c₇,o2) . f is set
(B,A,K,o2,o3,g) is Element of <^(B,A,K,o3),(B,A,K,o2)^>
(B,A,K,o3) is Element of the carrier of A
the of K . (o3,o3) is Element of [: the carrier of A, the carrier of A:]
the of K . [o3,o3] is set
( the of K . (o3,o3)) `1 is set
<^(B,A,K,o3),(B,A,K,o2)^> is set
(B,A,K,o2,o3) is Relation-like <^o2,o3^> -defined <^(B,A,K,o3),(B,A,K,o2)^> -valued Function-like quasi_total Element of bool [:<^o2,o3^>,<^(B,A,K,o3),(B,A,K,o2)^>:]
[:<^o2,o3^>,<^(B,A,K,o3),(B,A,K,o2)^>:] is Relation-like set
bool [:<^o2,o3^>,<^(B,A,K,o3),(B,A,K,o2)^>:] is non empty set
the of K . (o2,o3) is set
the of K . [o2,o3] is Relation-like Function-like set
(B,A,K,o2,o3) . g is set
f9 is Element of <^(B,A,(A,B,A),o2),(B,A,(A,B,A),c<sub>7</sub>)^>
g9 is Element of <^(B,A,(A,B,A),o3),(B,A,(A,B,A),o2)^>
f9 * g9 is Element of <^(B,A,(A,B,A),o3),(B,A,(A,B,A),c<sub>7</sub>)^>
<^(B,A,(A,B,A),o3),(B,A,(A,B,A),c<sub>7</sub>)^> is set
(A,B,A,(B,A,(A,B,A),o2)) is Element of the carrier of B
the of A . ((B,A,(A,B,A),o2),(B,A,(A,B,A),o2)) is Element of [: the carrier of B, the carrier of B:]
[(B,A,(A,B,A),o2),(B,A,(A,B,A),o2)] is V15() set
{(B,A,(A,B,A),o2),(B,A,(A,B,A),o2)} is set
{(B,A,(A,B,A),o2)} is set
{{(B,A,(A,B,A),o2),(B,A,(A,B,A),o2)},{(B,A,(A,B,A),o2)}} is set
the of A . [(B,A,(A,B,A),o2),(B,A,(A,B,A),o2)] is set
( the of A . ((B,A,(A,B,A),o2),(B,A,(A,B,A),o2))) `1 is set
<^(A,B,A,(B,A,(A,B,A),o2)),(A,B,A,(B,A,(A,B,A),o3))^> is set
<^(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o2))^> is set
(A,B,A,(B,A,(A,B,A),o3),(B,A,(A,B,A),o2)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),o2)) is set
[(B,A,(A,B,A),o3),(B,A,(A,B,A),o2)] is V15() set
{(B,A,(A,B,A),o3),(B,A,(A,B,A),o2)} is set
{{(B,A,(A,B,A),o3),(B,A,(A,B,A),o2)},{(B,A,(A,B,A),o3)}} is set
the of A . [(B,A,(A,B,A),o3),(B,A,(A,B,A),o2)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),o3),(B,A,(A,B,A),o2)) . g9 is set
(A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c₇)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),o2),(B,A,(A,B,A),c₇)) is set
[(B,A,(A,B,A),o2),(B,A,(A,B,A),c₇)] is V15() set
{(B,A,(A,B,A),o2),(B,A,(A,B,A),c₇)} is set
{{(B,A,(A,B,A),o2),(B,A,(A,B,A),c₇)},{(B,A,(A,B,A),o2)}} is set
the of A . [(B,A,(A,B,A),o2),(B,A,(A,B,A),c₇)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),o2),(B,A,(A,B,A),c₇)) . f9 is set
(A,B,A,(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)) is Relation-like Function-like set
the of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)) is set
[(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)] is V15() set
{(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)} is set
{{(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)},{(B,A,(A,B,A),o3)}} is set
the of A . [(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)) . (f9 * g9) is set
g99 is Element of <^(A,B,A,(B,A,(A,B,A),o2)),(A,B,A,(B,A,(A,B,A),o3))^>
f99 is Element of <^(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o2))^>
g99 * f99 is Element of <^(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o3))^>
dom the of (A,B,A) is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
dom the of A 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
dom the of A 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:]
( the of A * the Arrows of B) . [(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)] is set
the of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)) is Element of [: the carrier of B, the carrier of B:]
the of A . [(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)] is set
the Arrows of B . ( the of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),c₇))) is set
the Arrows of B . ((A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o3))) is set
[(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o3))] is V15() set
{(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o3))} is set
{(A,B,A,(B,A,(A,B,A),c₇))} is set
{{(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o3))},{(A,B,A,(B,A,(A,B,A),c₇))}} is set
the Arrows of B . [(A,B,A,(B,A,(A,B,A),c₇)),(A,B,A,(B,A,(A,B,A),o3))] is set
the Arrows of A . [(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)] is set
[:( the Arrows of A . [(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)]),(( the of A * the Arrows of B) . [(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)]):] is Relation-like set
bool [:( the Arrows of A . [(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)]),(( the of A * the Arrows of B) . [(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)]):] is non empty set
proj1 (A,B,A,(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)) is set
the Arrows of A . ((B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)) is set
the of (A,B,A) * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like non empty V14([: the carrier of B, the carrier of B:]) set
( the of (A,B,A) * the Arrows of A) . [c₇,o3] is set
the of F . (c₇,o3) is Element of [: the carrier of A, the carrier of A:]
the of F . [c₇,o3] is set
the Arrows of A . ( the of F . (c₇,o3)) is set
the Arrows of B . [c₇,o3] is set
[:( the Arrows of B . [c₇,o3]),(( the of (A,B,A) * the Arrows of A) . [c₇,o3]):] is Relation-like set
bool [:( the Arrows of B . [c₇,o3]),(( the of (A,B,A) * the Arrows of A) . [c₇,o3]):] is non empty set
proj1 (B,A,(A,B,A),c₇,o3) is set
the Arrows of B . (c₇,o3) is set
the of (A,B,A) . (c₇,o3) is Element of [: the carrier of A, the carrier of A:]
the of (A,B,A) . [c₇,o3] is set
(G "") . ( the of (A,B,A) . (c₇,o3)) is Relation-like ( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,o3)) -defined the Arrows of A . ( the of (A,B,A) . (c₇,o3)) -valued Function-like quasi_total Element of bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,o3))),( the Arrows of A . ( the of (A,B,A) . (c₇,o3))):]
( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,o3)) is set
the Arrows of A . ( the of (A,B,A) . (c₇,o3)) is set
[:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,o3))),( the Arrows of A . ( the of (A,B,A) . (c₇,o3))):] is Relation-like set
bool [:(( the of A * the Arrows of B) . ( the of (A,B,A) . (c₇,o3))),( the Arrows of A . ( the of (A,B,A) . (c₇,o3))):] is non empty set
[(B,A,F,o3),(B,A,F,c₇)] is V15() set
{(B,A,F,o3),(B,A,F,c₇)} is set
{(B,A,F,o3)} is set
{{(B,A,F,o3),(B,A,F,c₇)},{(B,A,F,o3)}} is set
(G "") . [(B,A,F,o3),(B,A,F,c₇)] is Relation-like Function-like set
(A,B,A,(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)) " is Relation-like Function-like set
o2 is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the of A * the Arrows of B
(B,A,B,F,A) is (B,B) (B,B) (B,B)
the of (B,A,B,F,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) 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 of A * the of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
( the of A ") * the of A is Relation-like [: the carrier of B, the carrier of B:] -valued Function-like set
rng the of A is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
id (rng the of A) is Relation-like rng the of A -defined rng the of A -valued Function-like one-to-one non empty V14( rng the of A) quasi_total Element of bool [:(rng the of A),(rng the of A):]
[:(rng the of A),(rng the of A):] is Relation-like non empty set
bool [:(rng the of A),(rng the of A):] is non empty set
id (dom the of (A,B,A)) is Relation-like dom the of (A,B,A) -defined dom the of (A,B,A) -valued Function-like one-to-one non empty V14( dom the of (A,B,A)) quasi_total Element of bool [:(dom the of (A,B,A)),(dom the of (A,B,A)):]
[:(dom the of (A,B,A)),(dom the of (A,B,A)):] is Relation-like non empty set
bool [:(dom the of (A,B,A)),(dom the of (A,B,A)):] is non empty set
id [: the carrier of B, the carrier 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 one-to-one non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]:]
the of (B,A,B,F,A) . (c₇,c₇) is Element of [: the carrier of B, the carrier of B:]
the of (B,A,B,F,A) . [c₇,c₇] is set
(B,B,(B,A,B,F,A),c₇) is Element of the carrier of B
( the of (B,A,B,F,A) . (c₇,c₇)) `1 is set
the of (B,A,B,F,A) . (o2,o2) is Element of [: the carrier of B, the carrier of B:]
the of (B,A,B,F,A) . [o2,o2] is set
(B,B,(B,A,B,F,A),o2) is Element of the carrier of B
( the of (B,A,B,F,A) . (o2,o2)) `1 is set
the of (B,A,B,F,A) . (o3,o3) is Element of [: the carrier of B, the carrier of B:]
the of (B,A,B,F,A) . [o3,o3] is set
(B,B,(B,A,B,F,A),o3) is Element of the carrier of B
( the of (B,A,B,F,A) . (o3,o3)) `1 is set
proj2 (B,A,(A,B,A),c₇,o3) is set
(A,B,A,(B,A,(A,B,A),o3),(B,A,(A,B,A),c₇)) . ((B,A,(A,B,A),c₇,o3) . (g * f)) is set
A is 1-sorted
B is non empty 1-sorted
A is (A,B)
the carrier of A is set
the carrier of B is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: the carrier of A, the carrier of A:] is Relation-like set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
[: the carrier of A, the carrier of B:] is Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
the of A .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
id the carrier of B is Relation-like the carrier of B -defined the carrier of B -valued Function-like one-to-one non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of B:]
B is Relation-like the carrier of A -defined the carrier of B -valued Function-like V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
A is 1-sorted
B is non empty 1-sorted
A is (A,B)
the carrier of A is set
the carrier of B is non empty set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: the carrier of A, the carrier of A:] is Relation-like set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
[: the carrier of A, the carrier of B:] is Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
B is Relation-like the carrier of A -defined the carrier of B -valued Function-like V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:B,B:]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:B,B:]) .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
[:B,B:] .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
the of A .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
id the carrier of B is Relation-like the carrier of B -defined the carrier of B -valued Function-like one-to-one non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of B:]
A is 1-sorted
B is 1-sorted
A is (A,B)
the carrier of A is set
the carrier of B is set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: the carrier of A, the carrier of A:] is Relation-like set
[: the carrier of B, the carrier of B:] is Relation-like set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
[: the carrier of A, the carrier of B:] is Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
B 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:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
id the carrier of B is Relation-like the carrier of B -defined the carrier of B -valued Function-like one-to-one V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
the of A .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
A is 1-sorted
B is 1-sorted
A is (A,B)
the carrier of A is set
the carrier of B is set
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
[: the carrier of A, the carrier of A:] is Relation-like set
[: the carrier of B, the carrier of B:] is Relation-like set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is non empty set
[: the carrier of A, the carrier of B:] is Relation-like set
bool [: the carrier of A, the carrier of B:] is non empty set
B 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:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:B,B:]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
the of A .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
[:B,B:] .: (id the carrier of A) is Relation-like the carrier of B -defined the carrier of B -valued Element of bool [: the carrier of B, the carrier of B:]
id the carrier of B is Relation-like the carrier of B -defined the carrier of B -valued Function-like one-to-one V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of B:]
A is non empty transitive with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
A is (A,B)
B is (A,B) (A,B) (A,B)
A is non empty transitive with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
A is (A,B)
B is (A,B) (A,B) (A,B)
A is non empty transitive with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
A is (A,B)
A is non empty transitive with_units reflexive AltCatStr
B is non empty with_units reflexive AltCatStr
A is (A,B)
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
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 B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] 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
B is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
B " is Relation-like Function-like set
proj1 (B ") is set
rng B is non empty Element of bool the carrier of B
bool the carrier of B is non empty set
proj2 (B ") is set
dom B is non empty Element of bool the carrier of A
bool the carrier of A is non empty set
rng [:B,B:] is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
[:(rng B),(rng B):] is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
[: 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
F is Relation-like the carrier of B -defined the carrier of A -valued Function-like non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of A:]
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[:F,F:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:B,B:] " is Relation-like Function-like set
B is (B,A)
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
A is (A,B) (A,B) (A,B)
(A,B,A) is (B,A) (B,A)
the of A is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
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 B is non empty set
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:] 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
B is Relation-like the carrier of A -defined the carrier of B -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of B:]
[:B,B:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
( the carrier of A, the carrier of A,[: the carrier of B, the carrier of B:],[:B,B:]) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:]
B " is Relation-like Function-like set
proj1 (B ") is set
rng B is non empty Element of bool the carrier of B
bool the carrier of B is non empty set
proj2 (B ") is set
dom B is non empty Element of bool the carrier of A
bool the carrier of A is non empty set
rng [:B,B:] is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
bool [: the carrier of B, the carrier of B:] is non empty set
[:(rng B),(rng B):] is Relation-like the carrier of B -defined the carrier of B -valued non empty Element of bool [: the carrier of B, the carrier of B:]
[: 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
F is Relation-like the carrier of B -defined the carrier of A -valued Function-like non empty V14( the carrier of B) quasi_total Element of bool [: the carrier of B, the carrier of A:]
the of (A,B,A) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:] is non empty set
[:F,F:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
( the carrier of B, the carrier of B,[: the carrier of A, the carrier of A:],[:F,F:]) is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) quasi_total Element of bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:]
[:B,B:] " is Relation-like Function-like set
the of A " is Relation-like Function-like set
B is (B,A)
A is non empty transitive with_units reflexive AltCatStr
(A) is (A,A) (A,A) (A,A) (A,A) (A,A) (A,A) (A,A) (A,A) (A,A)
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F is (A,B)
(A,B,F) is (B,A) (B,A)
G is (B,A)
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F is (A,B)
(A,B,F) is (B,A) (B,A)
G is (B,A)