K156() is Element of bool K152()
K152() is set
bool K152() is non empty set
K118() is set
bool K118() is non empty set
bool K156() is non empty set
{} is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty V36() V37() set
1 is non empty set
{{},1} is non empty set
the non empty transitive V129() with_units reflexive AltCatStr is non empty transitive V129() with_units reflexive AltCatStr
A is non empty reflexive AltCatStr
B is SubCatStr of A
A is non empty reflexive AltCatStr
B is non empty reflexive AltCatStr
G is non empty reflexive SubCatStr of A
C is feasible FunctorStr over A,B
C | G is FunctorStr over G,B
incl G is reflexive feasible strict Covariant FunctorStr over G,A
C * (incl G) is feasible strict FunctorStr over G,B
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 A -valued Function-like V14(A) quasi_total Element of bool [:A,A:]
rng B is set
A is non empty set
bool A is non empty set
B is non empty Element of bool A
bool B is non empty set
C is non empty Element of bool A
incl C is Relation-like C -defined A -valued C -valued Function-like one-to-one non empty V14(C) quasi_total onto Element of bool [:C,A:]
[:C,A:] is Relation-like non empty set
bool [:C,A:] is non empty set
incl B is Relation-like B -defined A -valued B -valued Function-like one-to-one non empty V14(B) quasi_total onto Element of bool [:B,A:]
[:B,A:] is Relation-like non empty set
bool [:B,A:] is non empty set
G is non empty Element of bool B
incl G is Relation-like G -defined B -valued G -valued Function-like one-to-one non empty V14(G) quasi_total onto Element of bool [:G,B:]
[:G,B:] is Relation-like non empty set
bool [:G,B:] is non empty set
(incl B) * (incl G) is Relation-like G -defined A -valued Function-like one-to-one non empty V14(G) quasi_total Element of bool [:G,A:]
[:G,A:] is Relation-like non empty set
bool [:G,A:] is non empty set
B /\ G is Element of bool B
id (B /\ G) is Relation-like B /\ G -defined B /\ G -valued Function-like one-to-one V14(B /\ G) quasi_total onto bijective Element of bool [:(B /\ G),(B /\ G):]
[:(B /\ G),(B /\ G):] is Relation-like set
bool [:(B /\ G),(B /\ G):] is non empty set
A is set
B is set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
[:B,A:] is Relation-like set
bool [:B,A:] is non empty set
C is Relation-like A -defined B -valued Function-like quasi_total Element of bool [:A,B:]
C " is Relation-like Function-like set
rng C is set
A is set
B is set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
C is non empty set
[:B,C:] is Relation-like set
bool [:B,C:] is non empty set
[:A,C:] is Relation-like set
bool [:A,C:] is non empty set
G is Relation-like A -defined B -valued Function-like quasi_total Element of bool [:A,B:]
F is Relation-like B -defined C -valued Function-like V14(B) quasi_total Element of bool [:B,C:]
F * G is Relation-like A -defined C -valued Function-like Element of bool [:A,C:]
rng F is set
GI is Relation-like A -defined C -valued Function-like V14(A) quasi_total Element of bool [:A,C:]
rng G is set
rng (F * G) is set
A is non empty reflexive AltCatStr
B is non empty reflexive SubCatStr of A
incl B is reflexive feasible strict Covariant FunctorStr over B,A
C is non empty SubCatStr of A
incl C is reflexive feasible strict Covariant FunctorStr over C,A
G is non empty SubCatStr of B
incl G is reflexive feasible strict Covariant FunctorStr over G,B
(incl B) * (incl G) is reflexive feasible strict Covariant FunctorStr over G,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 G is non empty set
[: the carrier of G, the carrier of G:] is Relation-like non empty set
the MorphMap of (incl C) is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() MSUnTrans of the ObjectMap of (incl C), the Arrows of C, the Arrows of A
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] 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 ObjectMap of (incl C) is Relation-like [: the carrier of C, the carrier of C:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of C, the carrier of C:]) quasi_total Element of bool [:[: the carrier of C, the carrier of C:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of C, the carrier of C:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:],[: the carrier of A, the carrier of A:]:] is non empty set
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) 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 MorphMap of (incl G) is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty V14([: the carrier of G, the carrier of G:]) V36() V37() MSUnTrans of the ObjectMap of (incl G), the Arrows of G, the Arrows of B
the ObjectMap of (incl G) is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:],[: the carrier of B, the carrier of B:]:]
[:[: the carrier of G, the carrier of G:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of B, the carrier of B:]:] is non empty set
the Arrows of G is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty V14([: the carrier of G, the carrier of G:]) 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 MorphMap of (incl 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:]) V36() V37() MSUnTrans of the ObjectMap of (incl B), the Arrows of B, the Arrows of A
the ObjectMap of (incl 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
the ObjectMap of (incl G) * the MorphMap of (incl B) is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty V14([: the carrier of G, the carrier of G:]) V36() V37() set
( the ObjectMap of (incl G) * the MorphMap of (incl B)) ** the MorphMap of (incl G) is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty V14([: the carrier of G, the carrier of G:]) V36() V37() set
dom the MorphMap of (incl G) is non empty set
dom ( the ObjectMap of (incl G) * the MorphMap of (incl B)) is non empty set
CA is set
the MorphMap of (incl C) . CA is Relation-like Function-like set
(( the ObjectMap of (incl G) * the MorphMap of (incl B)) ** the MorphMap of (incl G)) . CA is Relation-like Function-like set
id the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) V36() V37() ManySortedFunction of the Arrows of C, the Arrows of C
(id the Arrows of C) . CA is Relation-like Function-like set
dom (( the ObjectMap of (incl G) * the MorphMap of (incl B)) ** the MorphMap of (incl G)) is non empty set
(dom the MorphMap of (incl G)) /\ (dom ( the ObjectMap of (incl G) * the MorphMap of (incl B))) is set
id [: the carrier of G, the carrier of G:] is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of G, the carrier of G:] -valued Function-like one-to-one non empty V14([: the carrier of G, the carrier of G:]) quasi_total onto bijective Element of bool [:[: the carrier of G, the carrier of G:],[: the carrier of G, the carrier of G:]:]
[:[: the carrier of G, the carrier of G:],[: the carrier of G, the carrier of G:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of G, the carrier of G:]:] is non empty set
(id [: the carrier of G, the carrier of G:]) * the MorphMap of (incl B) is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like V36() V37() set
dom ((id [: the carrier of G, the carrier of G:]) * the MorphMap of (incl B)) is set
dom the MorphMap of (incl B) is non empty set
(dom the MorphMap of (incl B)) /\ [: the carrier of G, the carrier of G:] is Relation-like set
[: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:] is Relation-like set
dom (id [: the carrier of G, the carrier of G:]) is Relation-like non empty set
the Arrows of G . CA is set
the Arrows of B . CA is set
( the ObjectMap of (incl G) * the MorphMap of (incl B)) . CA is Relation-like Function-like set
((id [: the carrier of G, the carrier of G:]) * the MorphMap of (incl B)) . CA is Relation-like Function-like set
(id [: the carrier of G, the carrier of G:]) . CA is set
the MorphMap of (incl B) . ((id [: the carrier of G, the carrier of G:]) . CA) is Relation-like Function-like set
the MorphMap of (incl B) . CA is Relation-like Function-like set
id 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:]) V36() V37() ManySortedFunction of the Arrows of B, the Arrows of B
(id the Arrows of B) . CA is Relation-like Function-like set
the MorphMap of (incl G) . CA is Relation-like Function-like set
id the Arrows of G is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty V14([: the carrier of G, the carrier of G:]) V36() V37() ManySortedFunction of the Arrows of G, the Arrows of G
(id the Arrows of G) . CA is Relation-like Function-like set
( the MorphMap of (incl G) . CA) * ( the MorphMap of (incl B) . CA) is Relation-like Function-like set
id ( the Arrows of G . CA) is Relation-like the Arrows of G . CA -defined the Arrows of G . CA -valued Function-like one-to-one V14( the Arrows of G . CA) quasi_total onto bijective Element of bool [:( the Arrows of G . CA),( the Arrows of G . CA):]
[:( the Arrows of G . CA),( the Arrows of G . CA):] is Relation-like set
bool [:( the Arrows of G . CA),( the Arrows of G . CA):] is non empty set
(id ( the Arrows of G . CA)) * ((id the Arrows of B) . CA) is Relation-like the Arrows of G . CA -defined Function-like set
id ( the Arrows of B . CA) is Relation-like the Arrows of B . CA -defined the Arrows of B . CA -valued Function-like one-to-one V14( the Arrows of B . CA) quasi_total onto bijective Element of bool [:( the Arrows of B . CA),( the Arrows of B . CA):]
[:( the Arrows of B . CA),( the Arrows of B . CA):] is Relation-like set
bool [:( the Arrows of B . CA),( the Arrows of B . CA):] is non empty set
(id ( the Arrows of B . CA)) * (id ( the Arrows of G . CA)) is Relation-like the Arrows of G . CA -defined the Arrows of B . CA -valued Function-like one-to-one Element of bool [:( the Arrows of G . CA),( the Arrows of B . CA):]
[:( the Arrows of G . CA),( the Arrows of B . CA):] is Relation-like set
bool [:( the Arrows of G . CA),( the Arrows of B . CA):] is non empty set
( the Arrows of B . CA) /\ ( the Arrows of G . CA) is set
id (( the Arrows of B . CA) /\ ( the Arrows of G . CA)) is Relation-like ( the Arrows of B . CA) /\ ( the Arrows of G . CA) -defined ( the Arrows of B . CA) /\ ( the Arrows of G . CA) -valued Function-like one-to-one V14(( the Arrows of B . CA) /\ ( the Arrows of G . CA)) quasi_total onto bijective Element of bool [:(( the Arrows of B . CA) /\ ( the Arrows of G . CA)),(( the Arrows of B . CA) /\ ( the Arrows of G . CA)):]
[:(( the Arrows of B . CA) /\ ( the Arrows of G . CA)),(( the Arrows of B . CA) /\ ( the Arrows of G . CA)):] is Relation-like set
bool [:(( the Arrows of B . CA) /\ ( the Arrows of G . CA)),(( the Arrows of B . CA) /\ ( the Arrows of G . CA)):] is non empty set
id [: the carrier of G, the carrier of G:] is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of G, the carrier of G:] -valued Function-like one-to-one non empty V14([: the carrier of G, the carrier of G:]) quasi_total onto bijective Element of bool [:[: the carrier of G, the carrier of G:],[: the carrier of G, the carrier of G:]:]
[:[: the carrier of G, the carrier of G:],[: the carrier of G, the carrier of G:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of G, the carrier of G:]:] is non empty set
[: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:] is Relation-like set
id ([: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:]) is Relation-like [: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:] -defined [: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:] -valued Function-like one-to-one V14([: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:]) quasi_total onto bijective Element of bool [:([: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:]),([: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:]):]
[:([: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:]),([: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:]):] is Relation-like set
bool [:([: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:]),([: the carrier of B, the carrier of B:] /\ [: the carrier of G, the carrier of G:]):] 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 onto bijective 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:]) * (id [: the carrier of G, the carrier of G:]) is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of B, the carrier of B:] -valued Function-like one-to-one Element of bool [:[: the carrier of G, the carrier of G:],[: the carrier of B, the carrier of B:]:]
(id [: the carrier of B, the carrier of B:]) * the ObjectMap of (incl G) is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:],[: the carrier of B, the carrier of B:]:]
the ObjectMap of (incl B) * the ObjectMap of (incl G) is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of G, the carrier of G:]) quasi_total Element of bool [:[: the carrier of G, the carrier of G:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of G, the carrier of G:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of A, the carrier of A:]:] is non empty set
A is non empty AltCatStr
B is non empty AltCatStr
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
C is FunctorStr over A,B
the ObjectMap of C 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 MorphMap of C 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:]) V36() V37() MSUnTrans of the ObjectMap of C, 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
A is non empty AltGraph
B is non empty reflexive AltGraph
C is non empty reflexive AltGraph
G is feasible FunctorStr over A,B
F is FunctorStr over B,C
F * G is strict FunctorStr over A,C
the ObjectMap 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 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 ObjectMap of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
[:[: the carrier of B, the carrier of B:],[: the carrier of C, the carrier of C:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of C, the carrier of C:]:] is non empty set
the ObjectMap of (F * G) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of C, the carrier of C:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of C, the carrier of C:]:] is non empty set
the ObjectMap of F * the ObjectMap of G is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
A is non empty AltGraph
B is non empty reflexive AltGraph
C is non empty reflexive AltGraph
G is feasible FunctorStr over A,B
F is FunctorStr over B,C
F * G is strict FunctorStr over A,C
the MorphMap 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:]) V36() V37() MSUnTrans of the ObjectMap of F, the Arrows of B, the Arrows of C
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 C is non empty set
[: the carrier of C, the carrier of C:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
[:[: the carrier of B, the carrier of B:],[: the carrier of C, the carrier of C:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of C, the carrier of C:]:] 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 Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the MorphMap 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:]) V36() V37() MSUnTrans of the ObjectMap of G, the Arrows of A, the Arrows 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 ObjectMap 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 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 MorphMap of (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:]) V36() V37() MSUnTrans of the ObjectMap of (F * G), the Arrows of A, the Arrows of C
the ObjectMap of (F * G) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of C, the carrier of C:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of C, the carrier of C:]:] is non empty set
CB 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:]) V36() V37() set
CA 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:]:]
CA * the MorphMap 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:]) V36() V37() set
(CA * the MorphMap of F) ** the MorphMap 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:]) V36() V37() set
OGI is set
CB . OGI is Relation-like Function-like set
dom ((CA * the MorphMap of F) ** the MorphMap of G) is non empty set
the MorphMap of G . OGI is Relation-like Function-like set
(CA * the MorphMap of F) . OGI is Relation-like Function-like set
( the MorphMap of G . OGI) * ((CA * the MorphMap of F) . OGI) is Relation-like Function-like set
CA . OGI is set
the MorphMap of F . (CA . OGI) is Relation-like Function-like set
( the MorphMap of G . OGI) * ( the MorphMap of F . (CA . OGI)) is Relation-like Function-like set
A is non empty AltGraph
B is non empty reflexive AltGraph
C is non empty reflexive AltGraph
G is feasible FunctorStr over A,B
F is FunctorStr over B,C
F * G is strict FunctorStr over A,C
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] 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 B, the carrier of B:],[: the carrier of C, the carrier of C:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of C, the carrier of C:]:] is non empty set
the ObjectMap of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
MF is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
rng MF 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 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 ObjectMap 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:]:]
CB 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:]:]
rng CB is Relation-like non empty set
MF * CB is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of C, the carrier of C:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of C, the carrier of C:]:] is non empty set
rng (MF * CB) is Relation-like non empty set
the ObjectMap of (F * G) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
A is non empty AltGraph
B is non empty reflexive AltGraph
C is non empty reflexive AltGraph
G is feasible FunctorStr over A,B
F is FunctorStr over B,C
F * G is strict FunctorStr over A,C
the carrier of C is non empty set
[: the carrier of C, the carrier of C:] 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 is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of 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 ObjectMap 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 carrier of B, the carrier of B:],[: the carrier of C, the carrier of C:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of C, the carrier of C:]:] is non empty set
the ObjectMap of F is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
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 ObjectMap of G * 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 MorphMap 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:]) V36() V37() MSUnTrans of the ObjectMap of G, the Arrows of A, the Arrows of B
CA 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:]) V36() V37() ManySortedFunction of the Arrows of A, the ObjectMap of G * the Arrows of B
the Arrows of C is Relation-like [: the carrier of C, the carrier of C:] -defined Function-like non empty V14([: the carrier of C, the carrier of C:]) set
the ObjectMap of F * the Arrows of C 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 MorphMap 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:]) V36() V37() MSUnTrans of the ObjectMap of F, the Arrows of B, the Arrows of C
OGI 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:]) V36() V37() ManySortedFunction of the Arrows of B, the ObjectMap of F * the Arrows of C
the ObjectMap of (F * G) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of C, the carrier of C:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of C, the carrier of C:]:] is non empty set
the ObjectMap of (F * G) * the Arrows of C 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 MorphMap of (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:]) V36() V37() MSUnTrans of the ObjectMap of (F * G), the Arrows of A, the Arrows of C
CC 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:]) V36() V37() ManySortedFunction of the Arrows of A, the ObjectMap of (F * G) * the Arrows of C
OG 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:]:]
OG * OGI 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:]) V36() V37() set
(OG * OGI) ** CA 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:]) V36() V37() set
OF is set
CC . OF is Relation-like Function-like set
rng (CC . OF) is set
( the ObjectMap of (F * G) * the Arrows of C) . OF is set
OG . OF is set
the Arrows of B . (OG . OF) is set
( the ObjectMap of F * the Arrows of C) . (OG . OF) is set
[:( the Arrows of B . (OG . OF)),(( the ObjectMap of F * the Arrows of C) . (OG . OF)):] is Relation-like set
bool [:( the Arrows of B . (OG . OF)),(( the ObjectMap of F * the Arrows of C) . (OG . OF)):] is non empty set
OGI . (OG . OF) is Relation-like Function-like set
CA . OF is Relation-like Function-like set
(CA . OF) * (OGI . (OG . OF)) is Relation-like Function-like set
rng ((CA . OF) * (OGI . (OG . OF))) is set
rng (OGI . (OG . OF)) is set
OFI is Relation-like the Arrows of B . (OG . OF) -defined ( the ObjectMap of F * the Arrows of C) . (OG . OF) -valued Function-like quasi_total Element of bool [:( the Arrows of B . (OG . OF)),(( the ObjectMap of F * the Arrows of C) . (OG . OF)):]
rng OFI is set
(CA . OF) * {} is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty V36() V37() set
rng ((CA . OF) * {}) is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty trivial V36() V37() set
OFI is Relation-like the Arrows of B . (OG . OF) -defined ( the ObjectMap of F * the Arrows of C) . (OG . OF) -valued Function-like quasi_total Element of bool [:( the Arrows of B . (OG . OF)),(( the ObjectMap of F * the Arrows of C) . (OG . OF)):]
rng OFI is set
dom OFI is set
OG * 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
(OG * the Arrows of B) . OF is set
rng (CA . OF) is set
OFI is Relation-like the Arrows of B . (OG . OF) -defined ( the ObjectMap of F * the Arrows of C) . (OG . OF) -valued Function-like quasi_total Element of bool [:( the Arrows of B . (OG . OF)),(( the ObjectMap of F * the Arrows of C) . (OG . OF)):]
rng OFI is set
dom ((OG * OGI) ** CA) is non empty set
(OG * OGI) . OF is Relation-like Function-like set
(CA . OF) * ((OG * OGI) . OF) is Relation-like Function-like set
rng ((CA . OF) * ((OG * OGI) . OF)) is set
CB is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
CB . (OG . OF) is set
the Arrows of C . (CB . (OG . OF)) is set
CB * OG is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of C, the carrier of C:] -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 C, the carrier of C:]:]
(CB * OG) . OF is set
the Arrows of C . ((CB * OG) . OF) is set
the ObjectMap of (F * G) . OF is set
the Arrows of C . ( the ObjectMap of (F * G) . OF) is set
CC 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:]) V36() V37() ManySortedFunction of the Arrows of A, the ObjectMap of (F * G) * the Arrows of C
A is non empty AltGraph
B is non empty reflexive AltGraph
C is non empty reflexive AltGraph
G is feasible FunctorStr over A,B
F is FunctorStr over B,C
F * G is strict FunctorStr over A,C
A is non empty AltGraph
B is non empty reflexive AltGraph
C is non empty reflexive AltGraph
G is feasible FunctorStr over A,B
F is FunctorStr over B,C
F * G is strict FunctorStr over A,C
A is non empty AltGraph
B is non empty reflexive AltGraph
C is non empty reflexive AltGraph
G is feasible FunctorStr over A,B
F is FunctorStr over B,C
F * G is strict FunctorStr over A,C
A is non empty reflexive AltCatStr
B is non empty reflexive AltCatStr
C is non empty reflexive SubCatStr of A
G is non empty SubCatStr of A
F is non empty SubCatStr of C
GI is FunctorStr over A,B
GI | G is FunctorStr over G,B
incl G is reflexive feasible strict Covariant FunctorStr over G,A
GI * (incl G) is strict FunctorStr over G,B
GI | C is FunctorStr over C,B
incl C is reflexive feasible strict Covariant FunctorStr over C,A
GI * (incl C) is strict FunctorStr over C,B
(GI | C) | F is FunctorStr over F,B
incl F is reflexive feasible strict Covariant FunctorStr over F,C
(GI | C) * (incl F) is strict FunctorStr over F,B
(incl C) * (incl F) is reflexive feasible strict Covariant FunctorStr over F,A
GI * ((incl C) * (incl F)) is strict FunctorStr over F,B
A is non empty AltCatStr
B is non empty SubCatStr of A
incl B is reflexive feasible strict Covariant FunctorStr over B,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 ObjectMap of (incl 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
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 MorphMap of (incl 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:]) V36() V37() MSUnTrans of the ObjectMap of (incl B), the Arrows of B, the Arrows 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 ObjectMap of (incl B) * 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
G is non empty set
[:[: the carrier of B, the carrier of B:],G:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],G:] is non empty set
GI is Relation-like [: the carrier of B, the carrier of B:] -defined G -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:],G:]
F is Relation-like G -defined Function-like non empty V14(G) set
GI * 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:]) set
dom the Arrows of A is non empty set
(dom the Arrows of A) /\ [: the carrier of B, the carrier of B:] is Relation-like set
C 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:]) V36() V37() ManySortedFunction of the Arrows of B, the ObjectMap of (incl B) * the Arrows of A
F is set
C . F is Relation-like Function-like set
rng (C . F) is set
( the ObjectMap of (incl B) * the Arrows of A) . F is set
the Arrows of A || the carrier of B is set
the Arrows of A | [: the carrier of B, the carrier of B:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -defined Function-like set
the Arrows of B . F is set
the Arrows of A . F is set
id 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:]) V36() V37() ManySortedFunction of the Arrows of B, the Arrows of B
(id the Arrows of B) . F is Relation-like Function-like set
rng ((id the Arrows of B) . F) is set
id ( the Arrows of B . F) is Relation-like the Arrows of B . F -defined the Arrows of B . F -valued Function-like one-to-one V14( the Arrows of B . F) quasi_total onto bijective Element of bool [:( the Arrows of B . F),( the Arrows of B . F):]
[:( 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
rng (id ( the Arrows of B . 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 onto bijective 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:]) * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like set
((id [: the carrier of B, the carrier of B:]) * the Arrows of A) . F is set
the Arrows of A | [: the carrier of B, the carrier of B:] is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of A, the carrier of A:] -defined Function-like set
dom ( the Arrows of A | [: the carrier of B, the carrier of B:]) is set
the Arrows of A || the carrier of B is set
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:]) set
F is set
G . F is set
the Arrows of B . F is set
GI is set
FI 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:]) V36() V37() ManySortedFunction of the Arrows of B, the ObjectMap of (incl B) * the Arrows of A
id 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:]) V36() V37() ManySortedFunction of the Arrows of B, the Arrows of B
(id the Arrows of B) . F is Relation-like Function-like set
rng ((id the Arrows of B) . F) is set
( the ObjectMap of (incl B) * the Arrows of A) . 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 onto bijective 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:]) * the Arrows of A is Relation-like [: the carrier of B, the carrier of B:] -defined Function-like set
((id [: the carrier of B, the carrier of B:]) * the Arrows of A) . F is set
the Arrows of A . F is set
MF is set
OG is set
[MF,OG] is set
{MF,OG} is non empty set
{MF} is non empty set
{{MF,OG},{MF}} is non empty set
G . (MF,OG) is set
G . [MF,OG] is set
the Arrows of A . (MF,OG) is set
the Arrows of A . [MF,OG] is set
id ( the Arrows of B . F) is Relation-like the Arrows of B . F -defined the Arrows of B . F -valued Function-like one-to-one V14( the Arrows of B . F) quasi_total onto bijective Element of bool [:( the Arrows of B . F),( the Arrows of B . F):]
[:( 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
rng (id ( the Arrows of B . F)) is set
F is set
the Arrows of B . F is set
G . F is set
GI is set
FI is set
[GI,FI] is set
{GI,FI} is non empty set
{GI} is non empty set
{{GI,FI},{GI}} is non empty set
G . (GI,FI) is set
G . [GI,FI] is set
the Arrows of A . (GI,FI) is set
the Arrows of A . [GI,FI] is set
MF is set
the Arrows of B . (GI,FI) is set
the Arrows of B . [GI,FI] is set
A is non empty AltCatStr
B is non empty AltCatStr
the carrier of A is non empty set
C is reflexive Covariant FunctorStr over A,B
[: 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 ObjectMap of C 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
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 ObjectMap of C * 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 MorphMap of C 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:]) V36() V37() MSUnTrans of the ObjectMap of C, the Arrows 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:]) V36() V37() ManySortedFunction of the Arrows of A, the ObjectMap of C * the Arrows of B
GI is Element of the carrier of A
FI is Element of the carrier of A
[GI,FI] is set
{GI,FI} is non empty set
{GI} is non empty set
{{GI,FI},{GI}} is non empty set
dom the ObjectMap of C is Relation-like non empty set
F . [GI,FI] is Relation-like Function-like set
rng (F . [GI,FI]) is set
( the ObjectMap of C * the Arrows of B) . [GI,FI] is set
Morph-Map (C,GI,FI) is Relation-like <^GI,FI^> -defined <^(C . GI),(C . FI)^> -valued Function-like quasi_total Element of bool [:<^GI,FI^>,<^(C . GI),(C . FI)^>:]
<^GI,FI^> is set
C . GI is Element of the carrier of B
the ObjectMap of C . (GI,GI) is Element of [: the carrier of B, the carrier of B:]
[GI,GI] is set
{GI,GI} is non empty set
{{GI,GI},{GI}} is non empty set
the ObjectMap of C . [GI,GI] is set
K40(( the ObjectMap of C . (GI,GI))) is set
C . FI is Element of the carrier of B
the ObjectMap of C . (FI,FI) is Element of [: the carrier of B, the carrier of B:]
[FI,FI] is set
{FI,FI} is non empty set
{FI} is non empty set
{{FI,FI},{FI}} is non empty set
the ObjectMap of C . [FI,FI] is set
K40(( the ObjectMap of C . (FI,FI))) is set
<^(C . GI),(C . FI)^> is set
[:<^GI,FI^>,<^(C . GI),(C . FI)^>:] is Relation-like set
bool [:<^GI,FI^>,<^(C . GI),(C . FI)^>:] is non empty set
the MorphMap of C . (GI,FI) is set
the MorphMap of C . [GI,FI] is Relation-like Function-like set
rng (Morph-Map (C,GI,FI)) is set
the ObjectMap of C . (GI,FI) is Element of [: the carrier of B, the carrier of B:]
the ObjectMap of C . [GI,FI] is set
the Arrows of B . ( the ObjectMap of C . (GI,FI)) is set
the Arrows of B . ((C . GI),(C . FI)) is set
[(C . GI),(C . FI)] is set
{(C . GI),(C . FI)} is non empty set
{(C . GI)} is non empty set
{{(C . GI),(C . FI)},{(C . GI)}} is non empty set
the Arrows of B . [(C . GI),(C . FI)] is set
GI is non empty set
[:[: the carrier of A, the carrier of A:],GI:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],GI:] is non empty set
MF is Relation-like [: the carrier of A, the carrier of A:] -defined GI -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:],GI:]
FI is Relation-like GI -defined Function-like non empty V14(GI) set
MF * FI 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
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:]) V36() V37() ManySortedFunction of the Arrows of A, the ObjectMap of C * the Arrows of B
GI is set
F . GI is Relation-like Function-like set
rng (F . GI) is set
( the ObjectMap of C * the Arrows of B) . GI is set
FI is set
MF is set
[FI,MF] is set
{FI,MF} is non empty set
{FI} is non empty set
{{FI,MF},{FI}} is non empty set
OG is Element of the carrier of A
CB is Element of the carrier of A
[OG,CB] is set
{OG,CB} is non empty set
{OG} is non empty set
{{OG,CB},{OG}} is non empty set
C . OG is Element of the carrier of B
the ObjectMap of C . (OG,OG) is Element of [: the carrier of B, the carrier of B:]
[OG,OG] is set
{OG,OG} is non empty set
{{OG,OG},{OG}} is non empty set
the ObjectMap of C . [OG,OG] is set
K40(( the ObjectMap of C . (OG,OG))) is set
C . CB is Element of the carrier of B
the ObjectMap of C . (CB,CB) is Element of [: the carrier of B, the carrier of B:]
[CB,CB] is set
{CB,CB} is non empty set
{CB} is non empty set
{{CB,CB},{CB}} is non empty set
the ObjectMap of C . [CB,CB] is set
K40(( the ObjectMap of C . (CB,CB))) is set
<^(C . OG),(C . CB)^> is set
Morph-Map (C,OG,CB) is Relation-like <^OG,CB^> -defined <^(C . OG),(C . CB)^> -valued Function-like quasi_total Element of bool [:<^OG,CB^>,<^(C . OG),(C . CB)^>:]
<^OG,CB^> is set
[:<^OG,CB^>,<^(C . OG),(C . CB)^>:] is Relation-like set
bool [:<^OG,CB^>,<^(C . OG),(C . CB)^>:] is non empty set
the MorphMap of C . (OG,CB) is set
the MorphMap of C . [OG,CB] is Relation-like Function-like set
rng (Morph-Map (C,OG,CB)) is set
the Arrows of B . ((C . OG),(C . CB)) is set
[(C . OG),(C . CB)] is set
{(C . OG),(C . CB)} is non empty set
{(C . OG)} is non empty set
{{(C . OG),(C . CB)},{(C . OG)}} is non empty set
the Arrows of B . [(C . OG),(C . CB)] is set
the ObjectMap of C . (OG,CB) is Element of [: the carrier of B, the carrier of B:]
the ObjectMap of C . [OG,CB] is set
the Arrows of B . ( the ObjectMap of C . (OG,CB)) is set
( the ObjectMap of C * the Arrows of B) . (OG,CB) is set
( the ObjectMap of C * the Arrows of B) . [OG,CB] is set
A is non empty AltCatStr
B is non empty AltCatStr
the carrier of A is non empty set
C is reflexive Covariant FunctorStr over A,B
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the MorphMap of C 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:]) V36() V37() MSUnTrans of the ObjectMap of C, 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 ObjectMap of C 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
F is Element of the carrier of A
GI is Element of the carrier of A
[F,GI] is set
{F,GI} is non empty set
{F} is non empty set
{{F,GI},{F}} is non empty set
dom the MorphMap of C is non empty set
Morph-Map (C,F,GI) is Relation-like <^F,GI^> -defined <^(C . F),(C . GI)^> -valued Function-like quasi_total Element of bool [:<^F,GI^>,<^(C . F),(C . GI)^>:]
<^F,GI^> is set
C . F is Element of the carrier of B
the ObjectMap of C . (F,F) is Element of [: the carrier of B, the carrier of B:]
[F,F] is set
{F,F} is non empty set
{{F,F},{F}} is non empty set
the ObjectMap of C . [F,F] is set
K40(( the ObjectMap of C . (F,F))) is set
C . GI is Element of the carrier of B
the ObjectMap of C . (GI,GI) is Element of [: the carrier of B, the carrier of B:]
[GI,GI] is set
{GI,GI} is non empty set
{GI} is non empty set
{{GI,GI},{GI}} is non empty set
the ObjectMap of C . [GI,GI] is set
K40(( the ObjectMap of C . (GI,GI))) is set
<^(C . F),(C . GI)^> is set
[:<^F,GI^>,<^(C . F),(C . GI)^>:] is Relation-like set
bool [:<^F,GI^>,<^(C . F),(C . GI)^>:] is non empty set
the MorphMap of C . (F,GI) is set
the MorphMap of C . [F,GI] is Relation-like Function-like set
F is set
the MorphMap of C . F is Relation-like Function-like set
GI is Relation-like Function-like set
FI is set
MF is set
[FI,MF] is set
{FI,MF} is non empty set
{FI} is non empty set
{{FI,MF},{FI}} is non empty set
OG is Element of the carrier of A
CB is Element of the carrier of A
the MorphMap of C . (OG,CB) is set
[OG,CB] is set
{OG,CB} is non empty set
{OG} is non empty set
{{OG,CB},{OG}} is non empty set
the MorphMap of C . [OG,CB] is Relation-like Function-like set
Morph-Map (C,OG,CB) is Relation-like <^OG,CB^> -defined <^(C . OG),(C . CB)^> -valued Function-like quasi_total Element of bool [:<^OG,CB^>,<^(C . OG),(C . CB)^>:]
<^OG,CB^> is set
C . OG is Element of the carrier of B
the ObjectMap of C . (OG,OG) is Element of [: the carrier of B, the carrier of B:]
[OG,OG] is set
{OG,OG} is non empty set
{{OG,OG},{OG}} is non empty set
the ObjectMap of C . [OG,OG] is set
K40(( the ObjectMap of C . (OG,OG))) is set
C . CB is Element of the carrier of B
the ObjectMap of C . (CB,CB) is Element of [: the carrier of B, the carrier of B:]
[CB,CB] is set
{CB,CB} is non empty set
{CB} is non empty set
{{CB,CB},{CB}} is non empty set
the ObjectMap of C . [CB,CB] is set
K40(( the ObjectMap of C . (CB,CB))) is set
<^(C . OG),(C . CB)^> is set
[:<^OG,CB^>,<^(C . OG),(C . CB)^>:] is Relation-like set
bool [:<^OG,CB^>,<^(C . OG),(C . CB)^>:] is non empty set
A is non empty transitive with_units reflexive AltCatStr
id A is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A,A
(id A) " is strict FunctorStr over 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 ObjectMap of (id 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 ObjectMap of (id 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 MorphMap of (id 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:]) V36() V37() MSUnTrans of the ObjectMap of (id A), the Arrows of A, the Arrows of A
the MorphMap of ((id 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:]) V36() V37() MSUnTrans of the ObjectMap of ((id A) "), the Arrows of A, the Arrows of A
the ObjectMap of ((id 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 ObjectMap of (id A) " is Relation-like Function-like set
C 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:]) V36() V37() ManySortedFunction of the Arrows of A, the ObjectMap of (id A) * the Arrows of A
C "" 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:]) V36() V37() ManySortedFunction of the ObjectMap of (id A) * the Arrows of A, the Arrows of A
( the ObjectMap of (id A) ") * (C "") is Relation-like Function-like V36() V37() 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:]) V36() V37() ManySortedFunction of the Arrows of A, the Arrows of A
G is set
(id the Arrows of A) . G is Relation-like Function-like set
the Arrows of A . G is set
id ( the Arrows of A . G) is Relation-like the Arrows of A . G -defined the Arrows of A . G -valued Function-like one-to-one V14( the Arrows of A . G) quasi_total onto bijective Element of bool [:( the Arrows of A . G),( the Arrows of A . G):]
[:( the Arrows of A . G),( the Arrows of A . G):] is Relation-like set
bool [:( the Arrows of A . G),( the Arrows of A . G):] is non empty set
dom the Arrows of A is non empty set
(dom the Arrows of A) /\ [: the carrier of A, the carrier of A:] is Relation-like set
G is set
C . G is Relation-like Function-like set
rng (C . G) is set
( the ObjectMap of (id A) * the Arrows of A) . G is set
(id the Arrows of A) . G is Relation-like Function-like set
rng ((id the Arrows of A) . G) is set
the Arrows of A . G is set
id ( the Arrows of A . G) is Relation-like the Arrows of A . G -defined the Arrows of A . G -valued Function-like one-to-one V14( the Arrows of A . G) quasi_total onto bijective Element of bool [:( the Arrows of A . G),( the Arrows of A . G):]
[:( the Arrows of A . G),( the Arrows of A . G):] is Relation-like set
bool [:( the Arrows of A . G),( the Arrows of A . G):] is non empty set
rng (id ( the Arrows of A . G)) 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 onto bijective 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:]) * 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
((id [: the carrier of A, the carrier of A:]) * the Arrows of A) . G is set
G is set
(C "") . G is Relation-like Function-like set
C . G is Relation-like Function-like set
the MorphMap of (id A) . G is Relation-like Function-like set
( the MorphMap of (id A) . G) " is Relation-like Function-like set
(id the Arrows of A) . G is Relation-like Function-like set
((id the Arrows of A) . G) " is Relation-like Function-like set
the Arrows of A . G is set
id ( the Arrows of A . G) is Relation-like the Arrows of A . G -defined the Arrows of A . G -valued Function-like one-to-one V14( the Arrows of A . G) quasi_total onto bijective Element of bool [:( the Arrows of A . G),( the Arrows of A . G):]
[:( the Arrows of A . G),( the Arrows of A . G):] is Relation-like set
bool [:( the Arrows of A . G),( the Arrows of A . G):] is non empty set
(id ( the Arrows of A . G)) " is Relation-like the Arrows of A . G -defined the Arrows of A . G -valued Function-like one-to-one V14( the Arrows of A . G) quasi_total onto bijective Element of bool [:( the Arrows of A . G),( the Arrows of A . G):]
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 onto bijective 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:]) * the MorphMap of (id 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:]) V36() V37() set
dom the MorphMap of (id A) is non empty set
(dom the MorphMap of (id A)) /\ [: the carrier of A, the carrier of A:] is Relation-like set
G is set
((id [: the carrier of A, the carrier of A:]) * the MorphMap of (id A)) . G is Relation-like Function-like set
the MorphMap of (id A) . G is Relation-like Function-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 non empty V14([: the carrier of A, the carrier of A:]) quasi_total onto bijective Element of bool [:[: the carrier of A, the carrier of A:],[: 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
id B is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of B,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
F is feasible FunctorStr over A,B
F " is strict FunctorStr over B,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 ObjectMap of F is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of B, the carrier of B:] -valued