:: FUNCTOR3 semantic presentation

K125() is M2( bool K121())
K121() is set
bool K121() is non empty set
K87() is set
bool K87() is non empty set
bool K125() is non empty 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 non empty set
the non empty transitive strict associative with_units reflexive AltCatStr is non empty transitive strict associative with_units reflexive AltCatStr
A is non empty transitive AltCatStr
B is non empty with_units reflexive AltCatStr
the carrier of B is non empty set
the M2( the carrier of B) is M2( the carrier of B)
idm the M2( the carrier of B) is retraction coretraction mono epi M2(<^ the M2( the carrier of B), the M2( the carrier of B)^>)
<^ the M2( the carrier of B), the M2( the carrier of B)^> is non empty set
A --> (idm the M2( the carrier of B)) is reflexive feasible strict Covariant Contravariant comp-preserving comp-reversing FunctorStr over A,B
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 M2( the carrier of B) is M2( the carrier of B)
idm the M2( the carrier of B) is retraction coretraction mono epi M2(<^ the M2( the carrier of B), the M2( the carrier of B)^>)
<^ the M2( the carrier of B), the M2( the carrier of B)^> is non empty set
A --> (idm the M2( the carrier of B)) is reflexive feasible strict Covariant Contravariant id-preserving comp-preserving comp-reversing FunctorStr over A,B
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 M2( the carrier of B) is M2( the carrier of B)
idm the M2( the carrier of B) is retraction coretraction mono epi M2(<^ the M2( the carrier of B), the M2( the carrier of B)^>)
<^ the M2( the carrier of B), the M2( the carrier of B)^> is non empty set
A --> (idm the M2( the carrier of B)) is reflexive feasible strict Covariant Contravariant id-preserving comp-preserving comp-reversing FunctorStr over A,B
F2 is feasible id-preserving Functor of A,B
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is M2( the carrier of A)
F1 is M2( the carrier of A)
<^B,F1^> is set
a is M2( the carrier of A)
<^F1,a^> is set
F2 is M2( the carrier of A)
<^B,F2^> is set
<^F2,a^> is set
idm F1 is retraction coretraction iso mono epi M2(<^F1,F1^>)
<^F1,F1^> is non empty set
idm F2 is retraction coretraction iso mono epi M2(<^F2,F2^>)
<^F2,F2^> is non empty set
<^F1,B^> is set
<^a,F2^> is set
e is M2(<^B,F1^>)
e " is M2(<^F1,B^>)
e * (e ") is M2(<^F1,F1^>)
e1 is M2(<^F1,a^>)
e1 * e is M2(<^B,a^>)
<^B,a^> is set
k is M2(<^B,F2^>)
k * (e ") is M2(<^F1,F2^>)
<^F1,F2^> is set
a is M2(<^F2,a^>)
a * k is M2(<^B,a^>)
a " is M2(<^a,F2^>)
(a ") * a is M2(<^F2,F2^>)
(a ") * e1 is M2(<^F1,F2^>)
e1 * (idm F1) is M2(<^F1,a^>)
(e1 * e) * (e ") is M2(<^F1,a^>)
a * (k * (e ")) is M2(<^F1,a^>)
(a ") * (a * (k * (e "))) is M2(<^F1,F2^>)
((a ") * a) * (k * (e ")) is M2(<^F1,F2^>)
A is non empty transitive AltCatStr
the carrier of A is non empty set
B is non empty with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Covariant FunctorStr over A,B
F2 is FunctorStr over B,F1
F2 * a is strict FunctorStr over A,F1
e is M2( the carrier of A)
e1 is M2( the carrier of A)
Morph-Map ((F2 * a),e,e1) is Relation-like Function-like set
the MorphMap of (F2 * 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() MSUnTrans of the ObjectMap of (F2 * a), the Arrows of A, the Arrows of F1
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] 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 F1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined Function-like non empty V14([: the carrier of F1, the carrier of F1:]) set
the MorphMap of (F2 * a) . (e,e1) is set
[e,e1] is set
the MorphMap of (F2 * a) . [e,e1] is Relation-like Function-like set
Morph-Map (a,e,e1) is Relation-like <^e,e1^> -defined <^(a . e),(a . e1)^> -valued Function-like V18(<^e,e1^>,<^(a . e),(a . e1)^>) M2( bool [:<^e,e1^>,<^(a . e),(a . e1)^>:])
<^e,e1^> is set
a . e is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
a . e1 is M2( the carrier of B)
the ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
[e1,e1] is set
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
<^(a . e),(a . e1)^> is set
[:<^e,e1^>,<^(a . e),(a . e1)^>:] is Relation-like set
bool [:<^e,e1^>,<^(a . e),(a . e1)^>:] is non empty set
the MorphMap 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() MSUnTrans of the ObjectMap of a, 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 MorphMap of a . (e,e1) is set
the MorphMap of a . [e,e1] is Relation-like Function-like set
Morph-Map (F2,(a . e),(a . e1)) is Relation-like Function-like set
the MorphMap of F2 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() MSUnTrans of the ObjectMap of F2, the Arrows of B, the Arrows of F1
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the MorphMap of F2 . ((a . e),(a . e1)) is set
[(a . e),(a . e1)] is set
the MorphMap of F2 . [(a . e),(a . e1)] is Relation-like Function-like set
(Morph-Map (a,e,e1)) (#) (Morph-Map (F2,(a . e),(a . e1))) is Relation-like <^e,e1^> -defined Function-like set
dom the MorphMap of F2 is non empty set
rng the ObjectMap of a is Relation-like the carrier of B -defined the carrier of B -valued non empty M2( bool [: the carrier of B, the carrier of B:])
bool [: the carrier of B, the carrier of B:] is non empty set
the ObjectMap of a (#) the MorphMap of F2 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 ObjectMap of a (#) the MorphMap of F2) is non empty set
dom the ObjectMap of a is Relation-like non empty set
( the ObjectMap of a (#) the MorphMap of F2) . [e,e1] is Relation-like Function-like set
the ObjectMap of a . (e,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e1] is set
the MorphMap of F2 . ( the ObjectMap of a . (e,e1)) is Relation-like Function-like set
dom the MorphMap of a is non empty set
(dom ( the ObjectMap of a (#) the MorphMap of F2)) /\ (dom the MorphMap of a) is set
( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap 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() set
dom (( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) is non empty set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . (e,e1) is set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . [e,e1] is Relation-like Function-like set
A is non empty transitive AltCatStr
the carrier of A is non empty set
B is non empty with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Contravariant FunctorStr over A,B
F2 is FunctorStr over B,F1
F2 * a is strict FunctorStr over A,F1
e is M2( the carrier of A)
e1 is M2( the carrier of A)
Morph-Map ((F2 * a),e,e1) is Relation-like Function-like set
the MorphMap of (F2 * 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() MSUnTrans of the ObjectMap of (F2 * a), the Arrows of A, the Arrows of F1
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] 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 F1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined Function-like non empty V14([: the carrier of F1, the carrier of F1:]) set
the MorphMap of (F2 * a) . (e,e1) is set
[e,e1] is set
the MorphMap of (F2 * a) . [e,e1] is Relation-like Function-like set
Morph-Map (a,e,e1) is Relation-like <^e,e1^> -defined <^(a . e1),(a . e)^> -valued Function-like V18(<^e,e1^>,<^(a . e1),(a . e)^>) M2( bool [:<^e,e1^>,<^(a . e1),(a . e)^>:])
<^e,e1^> is set
a . e1 is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
[e1,e1] is set
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
a . e is M2( the carrier of B)
the ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
<^(a . e1),(a . e)^> is set
[:<^e,e1^>,<^(a . e1),(a . e)^>:] is Relation-like set
bool [:<^e,e1^>,<^(a . e1),(a . e)^>:] is non empty set
the MorphMap 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() MSUnTrans of the ObjectMap of a, 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 MorphMap of a . (e,e1) is set
the MorphMap of a . [e,e1] is Relation-like Function-like set
Morph-Map (F2,(a . e1),(a . e)) is Relation-like Function-like set
the MorphMap of F2 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() MSUnTrans of the ObjectMap of F2, the Arrows of B, the Arrows of F1
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the MorphMap of F2 . ((a . e1),(a . e)) is set
[(a . e1),(a . e)] is set
the MorphMap of F2 . [(a . e1),(a . e)] is Relation-like Function-like set
(Morph-Map (a,e,e1)) (#) (Morph-Map (F2,(a . e1),(a . e))) is Relation-like <^e,e1^> -defined Function-like set
dom the MorphMap of F2 is non empty set
rng the ObjectMap of a is Relation-like the carrier of B -defined the carrier of B -valued non empty M2( bool [: the carrier of B, the carrier of B:])
bool [: the carrier of B, the carrier of B:] is non empty set
the ObjectMap of a (#) the MorphMap of F2 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 ObjectMap of a (#) the MorphMap of F2) is non empty set
dom the ObjectMap of a is Relation-like non empty set
( the ObjectMap of a (#) the MorphMap of F2) . [e,e1] is Relation-like Function-like set
the ObjectMap of a . (e,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e1] is set
the MorphMap of F2 . ( the ObjectMap of a . (e,e1)) is Relation-like Function-like set
dom the MorphMap of a is non empty set
(dom ( the ObjectMap of a (#) the MorphMap of F2)) /\ (dom the MorphMap of a) is set
( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap 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() set
dom (( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) is non empty set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . (e,e1) is set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . [e,e1] is Relation-like Function-like set
A is set
B is non empty set
[:A,B:] is Relation-like set
bool [:A,B:] is non empty set
F1 is Relation-like A -defined B -valued Function-like V14(A) V18(A,B) M2( bool [:A,B:])
a is Relation-like A -defined Function-like V14(A) set
F2 is Relation-like B -defined Function-like non empty V14(B) set
F1 (#) F2 is Relation-like A -defined Function-like V14(A) set
id F2 is Relation-like B -defined Function-like non empty V14(B) Function-yielding V37() ManySortedFunction of F2,F2
F1 (#) (id F2) is Relation-like A -defined Function-like V14(A) Function-yielding V37() set
e is Relation-like A -defined Function-like V14(A) Function-yielding V37() ManySortedFunction of a,F1 (#) F2
(F1 (#) (id F2)) ** e is Relation-like A -defined Function-like V14(A) Function-yielding V37() set
e1 is set
(F1 (#) F2) . e1 is set
F1 . e1 is set
F2 . (F1 . e1) is set
(F1 (#) (id F2)) . e1 is Relation-like Function-like set
(id F2) . (F1 . e1) is Relation-like Function-like set
id ((F1 (#) F2) . e1) is Relation-like (F1 (#) F2) . e1 -defined (F1 (#) F2) . e1 -valued Function-like one-to-one V14((F1 (#) F2) . e1) V18((F1 (#) F2) . e1,(F1 (#) F2) . e1) M2( bool [:((F1 (#) F2) . e1),((F1 (#) F2) . e1):])
[:((F1 (#) F2) . e1),((F1 (#) F2) . e1):] is Relation-like set
bool [:((F1 (#) F2) . e1),((F1 (#) F2) . e1):] is non empty set
e1 is set
(F1 (#) (id F2)) . e1 is Relation-like Function-like set
(F1 (#) F2) . e1 is set
[:((F1 (#) F2) . e1),((F1 (#) F2) . e1):] is Relation-like set
bool [:((F1 (#) F2) . e1),((F1 (#) F2) . e1):] is non empty set
id ((F1 (#) F2) . e1) is Relation-like (F1 (#) F2) . e1 -defined (F1 (#) F2) . e1 -valued Function-like one-to-one V14((F1 (#) F2) . e1) V18((F1 (#) F2) . e1,(F1 (#) F2) . e1) M2( bool [:((F1 (#) F2) . e1),((F1 (#) F2) . e1):])
e1 is set
e . e1 is Relation-like Function-like set
a . e1 is set
(F1 (#) F2) . e1 is set
[:(a . e1),((F1 (#) F2) . e1):] is Relation-like set
bool [:(a . e1),((F1 (#) F2) . e1):] is non empty set
(F1 (#) (id F2)) . e1 is Relation-like Function-like set
F1 . e1 is set
(id F2) . (F1 . e1) is Relation-like Function-like set
F2 . (F1 . e1) is set
id (F2 . (F1 . e1)) is Relation-like F2 . (F1 . e1) -defined F2 . (F1 . e1) -valued Function-like one-to-one V14(F2 . (F1 . e1)) V18(F2 . (F1 . e1),F2 . (F1 . e1)) M2( bool [:(F2 . (F1 . e1)),(F2 . (F1 . e1)):])
[:(F2 . (F1 . e1)),(F2 . (F1 . e1)):] is Relation-like set
bool [:(F2 . (F1 . e1)),(F2 . (F1 . e1)):] is non empty set
((F1 (#) (id F2)) ** e) . e1 is Relation-like Function-like set
id ((F1 (#) F2) . e1) is Relation-like (F1 (#) F2) . e1 -defined (F1 (#) F2) . e1 -valued Function-like one-to-one V14((F1 (#) F2) . e1) V18((F1 (#) F2) . e1,(F1 (#) F2) . e1) M2( bool [:((F1 (#) F2) . e1),((F1 (#) F2) . e1):])
[:((F1 (#) F2) . e1),((F1 (#) F2) . e1):] is Relation-like set
bool [:((F1 (#) F2) . e1),((F1 (#) F2) . e1):] is non empty set
(e . e1) (#) (id ((F1 (#) F2) . e1)) is Relation-like (F1 (#) F2) . e1 -valued Function-like set
A is non empty transitive AltCatStr
B is non empty with_units reflexive AltCatStr
id B is reflexive feasible strict Covariant V165(B,B) FunctorStr over B,B
F1 is feasible FunctorStr over A,B
(id B) * F1 is feasible strict FunctorStr over A,B
the ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 MorphMap of F1 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() MSUnTrans of the ObjectMap of F1, 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
FunctorStr(# the ObjectMap of F1, the MorphMap of F1 #) is strict FunctorStr over A,B
the ObjectMap of ((id B) * F1) 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (id B) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of (id B) * the ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F1 (#) 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 ((id B) * F1) 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() MSUnTrans of the ObjectMap of ((id B) * F1), the Arrows of A, the Arrows of B
the MorphMap of (id 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() MSUnTrans of the ObjectMap of (id B), the Arrows of B, the Arrows of B
the ObjectMap of F1 (#) the MorphMap of (id 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
( the ObjectMap of F1 (#) the MorphMap of (id B)) ** the MorphMap of F1 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
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:]) Function-yielding V37() ManySortedFunction of the Arrows of B, the Arrows of B
the ObjectMap of F1 (#) (id 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:]) Function-yielding V37() set
( the ObjectMap of F1 (#) (id the Arrows of B)) ** the MorphMap of F1 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
A is non empty transitive with_units reflexive AltCatStr
id A is reflexive feasible strict Covariant id-preserving comp-preserving covariant V165(A,A) Functor of A,A
B is non empty with_units reflexive AltCatStr
F1 is feasible FunctorStr over A,B
F1 * (id A) is feasible strict FunctorStr over A,B
the ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 MorphMap of F1 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() MSUnTrans of the ObjectMap of F1, 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
FunctorStr(# the ObjectMap of F1, the MorphMap of F1 #) is strict FunctorStr over A,B
the ObjectMap of (F1 * (id 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]) M2( 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 F1 * the ObjectMap of (id 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of F1 * (id [: the carrier of A, the carrier 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F1 (#) 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 (F1 * (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:]) Function-yielding V37() MSUnTrans of the ObjectMap of (F1 * (id A)), the Arrows of A, the Arrows of B
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:]) Function-yielding V37() MSUnTrans of the ObjectMap of (id A), the Arrows of A, the Arrows of A
the ObjectMap of (id A) (#) the MorphMap of F1 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 ObjectMap of (id A) (#) the MorphMap of F1) ** 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:]) Function-yielding V37() set
(id [: the carrier of A, the carrier of A:]) (#) the MorphMap of F1 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
((id [: the carrier of A, the carrier of A:]) (#) the MorphMap of F1) ** 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:]) Function-yielding V37() set
the MorphMap of F1 ** 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:]) Function-yielding 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:]) Function-yielding V37() ManySortedFunction of the Arrows of A, the Arrows of A
the MorphMap of F1 ** (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() set
A is non empty AltCatStr
the carrier of A is non empty set
B is non empty reflexive AltCatStr
F1 is non empty reflexive AltCatStr
a is reflexive feasible Covariant FunctorStr over A,B
F2 is reflexive feasible Covariant FunctorStr over B,F1
F2 * a is reflexive feasible strict Covariant FunctorStr over A,F1
e is M2( the carrier of A)
a . e is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
e1 is M2( the carrier of A)
<^e,e1^> is set
a . e1 is M2( the carrier of B)
the ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
[e1,e1] is set
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
k is M2(<^e,e1^>)
(F2 * a) . k is M2(<^((F2 * a) . e),((F2 * a) . e1)^>)
(F2 * a) . e is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (F2 * a) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (F2 * a) . [e,e] is set
K40(( the ObjectMap of (F2 * a) . (e,e))) is set
(F2 * a) . e1 is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e1,e1) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (F2 * a) . [e1,e1] is set
K40(( the ObjectMap of (F2 * a) . (e1,e1))) is set
<^((F2 * a) . e),((F2 * a) . e1)^> is set
a . k is M2(<^(a . e),(a . e1)^>)
<^(a . e),(a . e1)^> is set
F2 . (a . k) is M2(<^(F2 . (a . e)),(F2 . (a . e1))^>)
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
F2 . (a . e1) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . e1),(a . e1)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e1),(a . e1)] is set
the ObjectMap of F2 . [(a . e1),(a . e1)] is set
K40(( the ObjectMap of F2 . ((a . e1),(a . e1)))) is set
<^(F2 . (a . e)),(F2 . (a . e1))^> is set
the MorphMap 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() MSUnTrans of the ObjectMap 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 MorphMap of a . (e,e1) is set
[e,e1] is set
the MorphMap of a . [e,e1] is Relation-like Function-like set
the MorphMap of F2 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() MSUnTrans of the ObjectMap of F2, the Arrows of B, the Arrows of F1
the Arrows of F1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined Function-like non empty V14([: the carrier of F1, the carrier of F1:]) set
the ObjectMap of a (#) the MorphMap of F2 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 ObjectMap of a (#) the MorphMap of F2) ** the MorphMap 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() set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . (e,e1) is set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . [e,e1] is Relation-like Function-like set
( the ObjectMap of a (#) the MorphMap of F2) . (e,e1) is set
( the ObjectMap of a (#) the MorphMap of F2) . [e,e1] is Relation-like Function-like set
dom (( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) is non empty set
dom ( the ObjectMap of a (#) the MorphMap of F2) is non empty set
dom the MorphMap of a is non empty set
(dom ( the ObjectMap of a (#) the MorphMap of F2)) /\ (dom the MorphMap of a) is set
[: the carrier of A, the carrier of A:] /\ (dom the MorphMap of a) is Relation-like set
[: the carrier of A, the carrier of A:] /\ [: the carrier of A, the carrier of A:] is Relation-like set
dom the ObjectMap of a is Relation-like non empty set
Morph-Map (a,e,e1) is Relation-like <^e,e1^> -defined <^(a . e),(a . e1)^> -valued Function-like V18(<^e,e1^>,<^(a . e),(a . e1)^>) M2( bool [:<^e,e1^>,<^(a . e),(a . e1)^>:])
[:<^e,e1^>,<^(a . e),(a . e1)^>:] is Relation-like set
bool [:<^e,e1^>,<^(a . e),(a . e1)^>:] is non empty set
dom (Morph-Map (a,e,e1)) is set
Morph-Map ((F2 * a),e,e1) is Relation-like <^e,e1^> -defined <^((F2 * a) . e),((F2 * a) . e1)^> -valued Function-like V18(<^e,e1^>,<^((F2 * a) . e),((F2 * a) . e1)^>) M2( bool [:<^e,e1^>,<^((F2 * a) . e),((F2 * a) . e1)^>:])
[:<^e,e1^>,<^((F2 * a) . e),((F2 * a) . e1)^>:] is Relation-like set
bool [:<^e,e1^>,<^((F2 * a) . e),((F2 * a) . e1)^>:] is non empty set
the MorphMap of (F2 * 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() MSUnTrans of the ObjectMap of (F2 * a), the Arrows of A, the Arrows of F1
the MorphMap of (F2 * a) . (e,e1) is set
the MorphMap of (F2 * a) . [e,e1] is Relation-like Function-like set
(Morph-Map ((F2 * a),e,e1)) . k is set
G1t is Relation-like Function-like set
G1t . k is set
sF2 is Relation-like Function-like set
fa is Relation-like Function-like set
sF2 (#) fa is Relation-like Function-like set
(sF2 (#) fa) . k is set
(Morph-Map (a,e,e1)) . k is set
fa . ((Morph-Map (a,e,e1)) . k) is set
fa . (a . k) is set
the ObjectMap of a . (e,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e1] is set
the MorphMap of F2 . ( the ObjectMap of a . (e,e1)) is Relation-like Function-like set
( the MorphMap of F2 . ( the ObjectMap of a . (e,e1))) . (a . k) is set
Morph-Map (F2,(a . e),(a . e1)) is Relation-like <^(a . e),(a . e1)^> -defined <^(F2 . (a . e)),(F2 . (a . e1))^> -valued Function-like V18(<^(a . e),(a . e1)^>,<^(F2 . (a . e)),(F2 . (a . e1))^>) M2( bool [:<^(a . e),(a . e1)^>,<^(F2 . (a . e)),(F2 . (a . e1))^>:])
[:<^(a . e),(a . e1)^>,<^(F2 . (a . e)),(F2 . (a . e1))^>:] is Relation-like set
bool [:<^(a . e),(a . e1)^>,<^(F2 . (a . e)),(F2 . (a . e1))^>:] is non empty set
the MorphMap of F2 . ((a . e),(a . e1)) is set
[(a . e),(a . e1)] is set
the MorphMap of F2 . [(a . e),(a . e1)] is Relation-like Function-like set
(Morph-Map (F2,(a . e),(a . e1))) . (a . k) is set
A is non empty AltCatStr
the carrier of A is non empty set
B is non empty reflexive AltCatStr
F1 is non empty reflexive AltCatStr
a is reflexive feasible Contravariant FunctorStr over A,B
F2 is reflexive feasible Contravariant FunctorStr over B,F1
F2 * a is reflexive feasible strict Covariant FunctorStr over A,F1
e is M2( the carrier of A)
a . e is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
e1 is M2( the carrier of A)
<^e,e1^> is set
a . e1 is M2( the carrier of B)
the ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
[e1,e1] is set
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
k is M2(<^e,e1^>)
(F2 * a) . k is M2(<^((F2 * a) . e),((F2 * a) . e1)^>)
(F2 * a) . e is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (F2 * a) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (F2 * a) . [e,e] is set
K40(( the ObjectMap of (F2 * a) . (e,e))) is set
(F2 * a) . e1 is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e1,e1) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (F2 * a) . [e1,e1] is set
K40(( the ObjectMap of (F2 * a) . (e1,e1))) is set
<^((F2 * a) . e),((F2 * a) . e1)^> is set
a . k is M2(<^(a . e1),(a . e)^>)
<^(a . e1),(a . e)^> is set
F2 . (a . k) is M2(<^(F2 . (a . e)),(F2 . (a . e1))^>)
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
F2 . (a . e1) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . e1),(a . e1)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e1),(a . e1)] is set
the ObjectMap of F2 . [(a . e1),(a . e1)] is set
K40(( the ObjectMap of F2 . ((a . e1),(a . e1)))) is set
<^(F2 . (a . e)),(F2 . (a . e1))^> is set
the MorphMap 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() MSUnTrans of the ObjectMap 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 MorphMap of a . (e,e1) is set
[e,e1] is set
the MorphMap of a . [e,e1] is Relation-like Function-like set
the MorphMap of F2 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() MSUnTrans of the ObjectMap of F2, the Arrows of B, the Arrows of F1
the Arrows of F1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined Function-like non empty V14([: the carrier of F1, the carrier of F1:]) set
the ObjectMap of a (#) the MorphMap of F2 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 ObjectMap of a (#) the MorphMap of F2) ** the MorphMap 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() set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . (e,e1) is set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . [e,e1] is Relation-like Function-like set
( the ObjectMap of a (#) the MorphMap of F2) . (e,e1) is set
( the ObjectMap of a (#) the MorphMap of F2) . [e,e1] is Relation-like Function-like set
dom (( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) is non empty set
dom ( the ObjectMap of a (#) the MorphMap of F2) is non empty set
dom the MorphMap of a is non empty set
(dom ( the ObjectMap of a (#) the MorphMap of F2)) /\ (dom the MorphMap of a) is set
[: the carrier of A, the carrier of A:] /\ (dom the MorphMap of a) is Relation-like set
[: the carrier of A, the carrier of A:] /\ [: the carrier of A, the carrier of A:] is Relation-like set
dom the ObjectMap of a is Relation-like non empty set
Morph-Map (a,e,e1) is Relation-like <^e,e1^> -defined <^(a . e1),(a . e)^> -valued Function-like V18(<^e,e1^>,<^(a . e1),(a . e)^>) M2( bool [:<^e,e1^>,<^(a . e1),(a . e)^>:])
[:<^e,e1^>,<^(a . e1),(a . e)^>:] is Relation-like set
bool [:<^e,e1^>,<^(a . e1),(a . e)^>:] is non empty set
dom (Morph-Map (a,e,e1)) is set
Morph-Map ((F2 * a),e,e1) is Relation-like <^e,e1^> -defined <^((F2 * a) . e),((F2 * a) . e1)^> -valued Function-like V18(<^e,e1^>,<^((F2 * a) . e),((F2 * a) . e1)^>) M2( bool [:<^e,e1^>,<^((F2 * a) . e),((F2 * a) . e1)^>:])
[:<^e,e1^>,<^((F2 * a) . e),((F2 * a) . e1)^>:] is Relation-like set
bool [:<^e,e1^>,<^((F2 * a) . e),((F2 * a) . e1)^>:] is non empty set
the MorphMap of (F2 * 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() MSUnTrans of the ObjectMap of (F2 * a), the Arrows of A, the Arrows of F1
the MorphMap of (F2 * a) . (e,e1) is set
the MorphMap of (F2 * a) . [e,e1] is Relation-like Function-like set
(Morph-Map ((F2 * a),e,e1)) . k is set
G1t is Relation-like Function-like set
G1t . k is set
sF2 is Relation-like Function-like set
fa is Relation-like Function-like set
sF2 (#) fa is Relation-like Function-like set
(sF2 (#) fa) . k is set
(Morph-Map (a,e,e1)) . k is set
fa . ((Morph-Map (a,e,e1)) . k) is set
fa . (a . k) is set
the ObjectMap of a . (e,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e1] is set
the MorphMap of F2 . ( the ObjectMap of a . (e,e1)) is Relation-like Function-like set
( the MorphMap of F2 . ( the ObjectMap of a . (e,e1))) . (a . k) is set
Morph-Map (F2,(a . e1),(a . e)) is Relation-like <^(a . e1),(a . e)^> -defined <^(F2 . (a . e)),(F2 . (a . e1))^> -valued Function-like V18(<^(a . e1),(a . e)^>,<^(F2 . (a . e)),(F2 . (a . e1))^>) M2( bool [:<^(a . e1),(a . e)^>,<^(F2 . (a . e)),(F2 . (a . e1))^>:])
[:<^(a . e1),(a . e)^>,<^(F2 . (a . e)),(F2 . (a . e1))^>:] is Relation-like set
bool [:<^(a . e1),(a . e)^>,<^(F2 . (a . e)),(F2 . (a . e1))^>:] is non empty set
the MorphMap of F2 . ((a . e1),(a . e)) is set
[(a . e1),(a . e)] is set
the MorphMap of F2 . [(a . e1),(a . e)] is Relation-like Function-like set
(Morph-Map (F2,(a . e1),(a . e))) . (a . k) is set
A is non empty AltCatStr
the carrier of A is non empty set
B is non empty reflexive AltCatStr
F1 is non empty reflexive AltCatStr
a is reflexive feasible Covariant FunctorStr over A,B
F2 is reflexive feasible Contravariant FunctorStr over B,F1
F2 * a is reflexive feasible strict Contravariant FunctorStr over A,F1
e is M2( the carrier of A)
a . e is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
e1 is M2( the carrier of A)
<^e,e1^> is set
a . e1 is M2( the carrier of B)
the ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
[e1,e1] is set
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
k is M2(<^e,e1^>)
(F2 * a) . k is M2(<^((F2 * a) . e1),((F2 * a) . e)^>)
(F2 * a) . e1 is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (F2 * a) . (e1,e1) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (F2 * a) . [e1,e1] is set
K40(( the ObjectMap of (F2 * a) . (e1,e1))) is set
(F2 * a) . e is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (F2 * a) . [e,e] is set
K40(( the ObjectMap of (F2 * a) . (e,e))) is set
<^((F2 * a) . e1),((F2 * a) . e)^> is set
a . k is M2(<^(a . e),(a . e1)^>)
<^(a . e),(a . e1)^> is set
F2 . (a . k) is M2(<^(F2 . (a . e1)),(F2 . (a . e))^>)
F2 . (a . e1) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e1),(a . e1)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e1),(a . e1)] is set
the ObjectMap of F2 . [(a . e1),(a . e1)] is set
K40(( the ObjectMap of F2 . ((a . e1),(a . e1)))) is set
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
<^(F2 . (a . e1)),(F2 . (a . e))^> is set
the MorphMap 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() MSUnTrans of the ObjectMap 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 MorphMap of a . (e,e1) is set
[e,e1] is set
the MorphMap of a . [e,e1] is Relation-like Function-like set
the MorphMap of F2 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() MSUnTrans of the ObjectMap of F2, the Arrows of B, the Arrows of F1
the Arrows of F1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined Function-like non empty V14([: the carrier of F1, the carrier of F1:]) set
the ObjectMap of a (#) the MorphMap of F2 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 ObjectMap of a (#) the MorphMap of F2) ** the MorphMap 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() set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . (e,e1) is set
(( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) . [e,e1] is Relation-like Function-like set
( the ObjectMap of a (#) the MorphMap of F2) . (e,e1) is set
( the ObjectMap of a (#) the MorphMap of F2) . [e,e1] is Relation-like Function-like set
dom (( the ObjectMap of a (#) the MorphMap of F2) ** the MorphMap of a) is non empty set
dom ( the ObjectMap of a (#) the MorphMap of F2) is non empty set
dom the MorphMap of a is non empty set
(dom ( the ObjectMap of a (#) the MorphMap of F2)) /\ (dom the MorphMap of a) is set
[: the carrier of A, the carrier of A:] /\ (dom the MorphMap of a) is Relation-like set
[: the carrier of A, the carrier of A:] /\ [: the carrier of A, the carrier of A:] is Relation-like set
dom the ObjectMap of a is Relation-like non empty set
Morph-Map (a,e,e1) is Relation-like <^e,e1^> -defined <^(a . e),(a . e1)^> -valued Function-like V18(<^e,e1^>,<^(a . e),(a . e1)^>) M2( bool [:<^e,e1^>,<^(a . e),(a . e1)^>:])
[:<^e,e1^>,<^(a . e),(a . e1)^>:] is Relation-like set
bool [:<^e,e1^>,<^(a . e),(a . e1)^>:] is non empty set
dom (Morph-Map (a,e,e1)) is set
Morph-Map ((F2 * a),e,e1) is Relation-like <^e,e1^> -defined <^((F2 * a) . e1),((F2 * a) . e)^> -valued Function-like V18(<^e,e1^>,<^((F2 * a) . e1),((F2 * a) . e)^>) M2( bool [:<^e,e1^>,<^((F2 * a) . e1),((F2 * a) . e)^>:])
[:<^e,e1^>,<^((F2 * a) . e1),((F2 * a) . e)^>:] is Relation-like set
bool [:<^e,e1^>,<^((F2 * a) . e1),((F2 * a) . e)^>:] is non empty set
the MorphMap of (F2 * 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() MSUnTrans of the ObjectMap of (F2 * a), the Arrows of A, the Arrows of F1
the MorphMap of (F2 * a) . (e,e1) is set
the MorphMap of (F2 * a) . [e,e1] is Relation-like Function-like set
(Morph-Map ((F2 * a),e,e1)) . k is set
G1t is Relation-like Function-like set
G1t . k is set
sF2 is Relation-like Function-like set
fa is Relation-like Function-like set
sF2 (#) fa is Relation-like Function-like set
(sF2 (#) fa) . k is set
(Morph-Map (a,e,e1)) . k is set
fa . ((Morph-Map (a,e,e1)) . k) is set
fa . (a . k) is set
the ObjectMap of a . (e,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e1] is set
the MorphMap of F2 . ( the ObjectMap of a . (e,e1)) is Relation-like Function-like set
( the MorphMap of F2 . ( the ObjectMap of a . (e,e1))) . (a . k) is set
Morph-Map (F2,(a . e),(a . e1)) is Relation-like <^(a . e),(a . e1)^> -defined <^(F2 . (a . e1)),(F2 . (a . e))^> -valued Function-like V18(<^(a . e),(a . e1)^>,<^(F2 . (a . e1)),(F2 . (a . e))^>) M2( bool [:<^(a . e),(a . e1)^>,<^(F2 . (a . e1)),(F2 . (a . e))^>:])
[:<^(a . e),(a . e1)^>,<^(F2 . (a . e1)),(F2 . (a . e))^>:] is Relation-like set
bool [:<^(a . e),(a . e1)^>,<^(F2 . (a . e1)),(F2 . (a . e))^>:] is non empty set
the MorphMap of F2 . ((a . e),(a . e1)) is set
[(a . e),(a . e1)] is set
the MorphMap of F2 . [(a . e),(a . e1)] is Relation-like Function-like set
(Morph-Map (F2,(a . e),(a . e1))) . (a . k) is set
A is non empty AltCatStr
the carrier of A is non empty set
B is non empty reflexive AltCatStr
F1 is non empty reflexive AltCatStr
a is reflexive feasible Covariant FunctorStr over F1,B
F2 is reflexive feasible Contravariant FunctorStr over A,F1
a * F2 is reflexive feasible strict Contravariant FunctorStr over A,B
e is M2( the carrier of A)
F2 . e is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of F2 is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . (e,e) is M2([: the carrier of F1, the carrier of F1:])
[e,e] is set
the ObjectMap of F2 . [e,e] is set
K40(( the ObjectMap of F2 . (e,e))) is set
e1 is M2( the carrier of A)
<^e,e1^> is set
F2 . e1 is M2( the carrier of F1)
the ObjectMap of F2 . (e1,e1) is M2([: the carrier of F1, the carrier of F1:])
[e1,e1] is set
the ObjectMap of F2 . [e1,e1] is set
K40(( the ObjectMap of F2 . (e1,e1))) is set
k is M2(<^e,e1^>)
(a * F2) . k is M2(<^((a * F2) . e1),((a * F2) . e)^>)
(a * F2) . e1 is M2( 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 ObjectMap of (a * F2) 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of (a * F2) . (e1,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (a * F2) . [e1,e1] is set
K40(( the ObjectMap of (a * F2) . (e1,e1))) is set
(a * F2) . e is M2( the carrier of B)
the ObjectMap of (a * F2) . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (a * F2) . [e,e] is set
K40(( the ObjectMap of (a * F2) . (e,e))) is set
<^((a * F2) . e1),((a * F2) . e)^> is set
F2 . k is M2(<^(F2 . e1),(F2 . e)^>)
<^(F2 . e1),(F2 . e)^> is set
a . (F2 . k) is M2(<^(a . (F2 . e1)),(a . (F2 . e))^>)
a . (F2 . e1) is M2( the carrier of B)
the ObjectMap of a is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is non empty set
the ObjectMap of a . ((F2 . e1),(F2 . e1)) is M2([: the carrier of B, the carrier of B:])
[(F2 . e1),(F2 . e1)] is set
the ObjectMap of a . [(F2 . e1),(F2 . e1)] is set
K40(( the ObjectMap of a . ((F2 . e1),(F2 . e1)))) is set
a . (F2 . e) is M2( the carrier of B)
the ObjectMap of a . ((F2 . e),(F2 . e)) is M2([: the carrier of B, the carrier of B:])
[(F2 . e),(F2 . e)] is set
the ObjectMap of a . [(F2 . e),(F2 . e)] is set
K40(( the ObjectMap of a . ((F2 . e),(F2 . e)))) is set
<^(a . (F2 . e1)),(a . (F2 . e))^> is set
the MorphMap of F2 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() MSUnTrans of the ObjectMap of F2, the Arrows of A, the Arrows of F1
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 F1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined Function-like non empty V14([: the carrier of F1, the carrier of F1:]) set
the MorphMap of F2 . (e,e1) is set
[e,e1] is set
the MorphMap of F2 . [e,e1] is Relation-like Function-like set
the MorphMap of a is Relation-like [: the carrier of F1, the carrier of F1:] -defined Function-like non empty V14([: the carrier of F1, the carrier of F1:]) Function-yielding V37() MSUnTrans of the ObjectMap of a, the Arrows of F1, 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 ObjectMap of F2 (#) the MorphMap 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() set
( the ObjectMap of F2 (#) the MorphMap of a) ** the MorphMap of F2 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 ObjectMap of F2 (#) the MorphMap of a) ** the MorphMap of F2) . (e,e1) is set
(( the ObjectMap of F2 (#) the MorphMap of a) ** the MorphMap of F2) . [e,e1] is Relation-like Function-like set
( the ObjectMap of F2 (#) the MorphMap of a) . (e,e1) is set
( the ObjectMap of F2 (#) the MorphMap of a) . [e,e1] is Relation-like Function-like set
dom (( the ObjectMap of F2 (#) the MorphMap of a) ** the MorphMap of F2) is non empty set
dom ( the ObjectMap of F2 (#) the MorphMap of a) is non empty set
dom the MorphMap of F2 is non empty set
(dom ( the ObjectMap of F2 (#) the MorphMap of a)) /\ (dom the MorphMap of F2) is set
[: the carrier of A, the carrier of A:] /\ (dom the MorphMap of F2) is Relation-like set
[: the carrier of A, the carrier of A:] /\ [: the carrier of A, the carrier of A:] is Relation-like set
dom the ObjectMap of F2 is Relation-like non empty set
Morph-Map (F2,e,e1) is Relation-like <^e,e1^> -defined <^(F2 . e1),(F2 . e)^> -valued Function-like V18(<^e,e1^>,<^(F2 . e1),(F2 . e)^>) M2( bool [:<^e,e1^>,<^(F2 . e1),(F2 . e)^>:])
[:<^e,e1^>,<^(F2 . e1),(F2 . e)^>:] is Relation-like set
bool [:<^e,e1^>,<^(F2 . e1),(F2 . e)^>:] is non empty set
dom (Morph-Map (F2,e,e1)) is set
Morph-Map ((a * F2),e,e1) is Relation-like <^e,e1^> -defined <^((a * F2) . e1),((a * F2) . e)^> -valued Function-like V18(<^e,e1^>,<^((a * F2) . e1),((a * F2) . e)^>) M2( bool [:<^e,e1^>,<^((a * F2) . e1),((a * F2) . e)^>:])
[:<^e,e1^>,<^((a * F2) . e1),((a * F2) . e)^>:] is Relation-like set
bool [:<^e,e1^>,<^((a * F2) . e1),((a * F2) . e)^>:] is non empty set
the MorphMap of (a * F2) 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() MSUnTrans of the ObjectMap of (a * F2), the Arrows of A, the Arrows of B
the MorphMap of (a * F2) . (e,e1) is set
the MorphMap of (a * F2) . [e,e1] is Relation-like Function-like set
(Morph-Map ((a * F2),e,e1)) . k is set
G1t is Relation-like Function-like set
G1t . k is set
sF2 is Relation-like Function-like set
fa is Relation-like Function-like set
sF2 (#) fa is Relation-like Function-like set
(sF2 (#) fa) . k is set
(Morph-Map (F2,e,e1)) . k is set
fa . ((Morph-Map (F2,e,e1)) . k) is set
fa . (F2 . k) is set
the ObjectMap of F2 . (e,e1) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [e,e1] is set
the MorphMap of a . ( the ObjectMap of F2 . (e,e1)) is Relation-like Function-like set
( the MorphMap of a . ( the ObjectMap of F2 . (e,e1))) . (F2 . k) is set
Morph-Map (a,(F2 . e1),(F2 . e)) is Relation-like <^(F2 . e1),(F2 . e)^> -defined <^(a . (F2 . e1)),(a . (F2 . e))^> -valued Function-like V18(<^(F2 . e1),(F2 . e)^>,<^(a . (F2 . e1)),(a . (F2 . e))^>) M2( bool [:<^(F2 . e1),(F2 . e)^>,<^(a . (F2 . e1)),(a . (F2 . e))^>:])
[:<^(F2 . e1),(F2 . e)^>,<^(a . (F2 . e1)),(a . (F2 . e))^>:] is Relation-like set
bool [:<^(F2 . e1),(F2 . e)^>,<^(a . (F2 . e1)),(a . (F2 . e))^>:] is non empty set
the MorphMap of a . ((F2 . e1),(F2 . e)) is set
[(F2 . e1),(F2 . e)] is set
the MorphMap of a . [(F2 . e1),(F2 . e)] is Relation-like Function-like set
(Morph-Map (a,(F2 . e1),(F2 . e))) . (F2 . k) is set
A is non empty transitive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Covariant comp-preserving FunctorStr over A,B
F2 is reflexive feasible Covariant comp-preserving FunctorStr over B,F1
F2 * a is reflexive feasible strict Covariant FunctorStr over A,F1
the carrier of A is non empty set
e is M2( the carrier of A)
e1 is M2( the carrier of A)
<^e,e1^> is set
k is M2( the carrier of A)
<^e1,k^> is set
(F2 * a) . e is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (F2 * a) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
[e,e] is set
the ObjectMap of (F2 * a) . [e,e] is set
K40(( the ObjectMap of (F2 * a) . (e,e))) is set
(F2 * a) . e1 is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e1,e1) is M2([: the carrier of F1, the carrier of F1:])
[e1,e1] is set
the ObjectMap of (F2 * a) . [e1,e1] is set
K40(( the ObjectMap of (F2 * a) . (e1,e1))) is set
(F2 * a) . k is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (k,k) is M2([: the carrier of F1, the carrier of F1:])
[k,k] is set
the ObjectMap of (F2 * a) . [k,k] is set
K40(( the ObjectMap of (F2 * a) . (k,k))) is set
a . e is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
a . e1 is M2( the carrier of B)
the ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
<^(a . e),(a . e1)^> is set
a . k is M2( the carrier of B)
the ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
<^(a . e1),(a . k)^> is set
a is M2(<^e,e1^>)
(F2 * a) . a is M2(<^((F2 * a) . e),((F2 * a) . e1)^>)
<^((F2 * a) . e),((F2 * a) . e1)^> is set
sF2 is M2(<^e1,k^>)
sF2 * a is M2(<^e,k^>)
<^e,k^> is set
(F2 * a) . (sF2 * a) is M2(<^((F2 * a) . e),((F2 * a) . k)^>)
<^((F2 * a) . e),((F2 * a) . k)^> is set
(F2 * a) . sF2 is M2(<^((F2 * a) . e1),((F2 * a) . k)^>)
<^((F2 * a) . e1),((F2 * a) . k)^> is set
((F2 * a) . sF2) * ((F2 * a) . a) is M2(<^((F2 * a) . e),((F2 * a) . k)^>)
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
F2 . (a . k) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . k),(a . k)) is M2([: the carrier of F1, the carrier of F1:])
[(a . k),(a . k)] is set
the ObjectMap of F2 . [(a . k),(a . k)] is set
K40(( the ObjectMap of F2 . ((a . k),(a . k)))) is set
F2 . (a . e1) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . e1),(a . e1)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e1),(a . e1)] is set
the ObjectMap of F2 . [(a . e1),(a . e1)] is set
K40(( the ObjectMap of F2 . ((a . e1),(a . e1)))) is set
<^(F2 . (a . e1)),(F2 . (a . k))^> is set
a . (sF2 * a) is M2(<^(a . e),(a . k)^>)
<^(a . e),(a . k)^> is set
F2 . (a . (sF2 * a)) is M2(<^(F2 . (a . e)),(F2 . (a . k))^>)
<^(F2 . (a . e)),(F2 . (a . k))^> is set
a . a is M2(<^(a . e),(a . e1)^>)
a . sF2 is M2(<^(a . e1),(a . k)^>)
(a . sF2) * (a . a) is M2(<^(a . e),(a . k)^>)
F2 . ((a . sF2) * (a . a)) is M2(<^(F2 . (a . e)),(F2 . (a . k))^>)
F2 . (a . a) is M2(<^(F2 . (a . e)),(F2 . (a . e1))^>)
<^(F2 . (a . e)),(F2 . (a . e1))^> is set
F2 . (a . sF2) is M2(<^(F2 . (a . e1)),(F2 . (a . k))^>)
(F2 . (a . sF2)) * (F2 . (a . a)) is M2(<^(F2 . (a . e)),(F2 . (a . k))^>)
G1t is M2(<^(F2 . (a . e1)),(F2 . (a . k))^>)
G1t * (F2 . (a . a)) is M2(<^(F2 . (a . e)),(F2 . (a . k))^>)
A is non empty transitive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Contravariant comp-reversing FunctorStr over A,B
F2 is reflexive feasible Contravariant comp-reversing FunctorStr over B,F1
F2 * a is reflexive feasible strict Covariant FunctorStr over A,F1
the carrier of A is non empty set
e is M2( the carrier of A)
e1 is M2( the carrier of A)
<^e,e1^> is set
k is M2( the carrier of A)
<^e1,k^> is set
(F2 * a) . e is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (F2 * a) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
[e,e] is set
the ObjectMap of (F2 * a) . [e,e] is set
K40(( the ObjectMap of (F2 * a) . (e,e))) is set
(F2 * a) . e1 is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e1,e1) is M2([: the carrier of F1, the carrier of F1:])
[e1,e1] is set
the ObjectMap of (F2 * a) . [e1,e1] is set
K40(( the ObjectMap of (F2 * a) . (e1,e1))) is set
(F2 * a) . k is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (k,k) is M2([: the carrier of F1, the carrier of F1:])
[k,k] is set
the ObjectMap of (F2 * a) . [k,k] is set
K40(( the ObjectMap of (F2 * a) . (k,k))) is set
a . e1 is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
a . e is M2( the carrier of B)
the ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
<^(a . e1),(a . e)^> is set
a . k is M2( the carrier of B)
the ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
<^(a . k),(a . e1)^> is set
a is M2(<^e,e1^>)
(F2 * a) . a is M2(<^((F2 * a) . e),((F2 * a) . e1)^>)
<^((F2 * a) . e),((F2 * a) . e1)^> is set
sF2 is M2(<^e1,k^>)
sF2 * a is M2(<^e,k^>)
<^e,k^> is set
(F2 * a) . (sF2 * a) is M2(<^((F2 * a) . e),((F2 * a) . k)^>)
<^((F2 * a) . e),((F2 * a) . k)^> is set
(F2 * a) . sF2 is M2(<^((F2 * a) . e1),((F2 * a) . k)^>)
<^((F2 * a) . e1),((F2 * a) . k)^> is set
((F2 * a) . sF2) * ((F2 * a) . a) is M2(<^((F2 * a) . e),((F2 * a) . k)^>)
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
F2 . (a . k) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . k),(a . k)) is M2([: the carrier of F1, the carrier of F1:])
[(a . k),(a . k)] is set
the ObjectMap of F2 . [(a . k),(a . k)] is set
K40(( the ObjectMap of F2 . ((a . k),(a . k)))) is set
F2 . (a . e1) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . e1),(a . e1)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e1),(a . e1)] is set
the ObjectMap of F2 . [(a . e1),(a . e1)] is set
K40(( the ObjectMap of F2 . ((a . e1),(a . e1)))) is set
<^(F2 . (a . e1)),(F2 . (a . k))^> is set
a . (sF2 * a) is M2(<^(a . k),(a . e)^>)
<^(a . k),(a . e)^> is set
F2 . (a . (sF2 * a)) is M2(<^(F2 . (a . e)),(F2 . (a . k))^>)
<^(F2 . (a . e)),(F2 . (a . k))^> is set
a . sF2 is M2(<^(a . k),(a . e1)^>)
a . a is M2(<^(a . e1),(a . e)^>)
(a . a) * (a . sF2) is M2(<^(a . k),(a . e)^>)
F2 . ((a . a) * (a . sF2)) is M2(<^(F2 . (a . e)),(F2 . (a . k))^>)
F2 . (a . a) is M2(<^(F2 . (a . e)),(F2 . (a . e1))^>)
<^(F2 . (a . e)),(F2 . (a . e1))^> is set
F2 . (a . sF2) is M2(<^(F2 . (a . e1)),(F2 . (a . k))^>)
(F2 . (a . sF2)) * (F2 . (a . a)) is M2(<^(F2 . (a . e)),(F2 . (a . k))^>)
G1t is M2(<^(F2 . (a . e1)),(F2 . (a . k))^>)
G1t * (F2 . (a . a)) is M2(<^(F2 . (a . e)),(F2 . (a . k))^>)
A is non empty transitive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Covariant comp-preserving FunctorStr over A,B
F2 is reflexive feasible Contravariant comp-reversing FunctorStr over B,F1
F2 * a is reflexive feasible strict Contravariant FunctorStr over A,F1
the carrier of A is non empty set
e is M2( the carrier of A)
e1 is M2( the carrier of A)
<^e,e1^> is set
k is M2( the carrier of A)
<^e1,k^> is set
(F2 * a) . k is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (F2 * a) . (k,k) is M2([: the carrier of F1, the carrier of F1:])
[k,k] is set
the ObjectMap of (F2 * a) . [k,k] is set
K40(( the ObjectMap of (F2 * a) . (k,k))) is set
(F2 * a) . e1 is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e1,e1) is M2([: the carrier of F1, the carrier of F1:])
[e1,e1] is set
the ObjectMap of (F2 * a) . [e1,e1] is set
K40(( the ObjectMap of (F2 * a) . (e1,e1))) is set
(F2 * a) . e is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
[e,e] is set
the ObjectMap of (F2 * a) . [e,e] is set
K40(( the ObjectMap of (F2 * a) . (e,e))) is set
a . e is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
a . e1 is M2( the carrier of B)
the ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
<^(a . e),(a . e1)^> is set
a . k is M2( the carrier of B)
the ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
<^(a . e1),(a . k)^> is set
a is M2(<^e,e1^>)
(F2 * a) . a is M2(<^((F2 * a) . e1),((F2 * a) . e)^>)
<^((F2 * a) . e1),((F2 * a) . e)^> is set
sF2 is M2(<^e1,k^>)
sF2 * a is M2(<^e,k^>)
<^e,k^> is set
(F2 * a) . (sF2 * a) is M2(<^((F2 * a) . k),((F2 * a) . e)^>)
<^((F2 * a) . k),((F2 * a) . e)^> is set
(F2 * a) . sF2 is M2(<^((F2 * a) . k),((F2 * a) . e1)^>)
<^((F2 * a) . k),((F2 * a) . e1)^> is set
((F2 * a) . a) * ((F2 * a) . sF2) is M2(<^((F2 * a) . k),((F2 * a) . e)^>)
F2 . (a . e1) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e1),(a . e1)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e1),(a . e1)] is set
the ObjectMap of F2 . [(a . e1),(a . e1)] is set
K40(( the ObjectMap of F2 . ((a . e1),(a . e1)))) is set
F2 . (a . k) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . k),(a . k)) is M2([: the carrier of F1, the carrier of F1:])
[(a . k),(a . k)] is set
the ObjectMap of F2 . [(a . k),(a . k)] is set
K40(( the ObjectMap of F2 . ((a . k),(a . k)))) is set
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
<^(F2 . (a . e1)),(F2 . (a . e))^> is set
a . (sF2 * a) is M2(<^(a . e),(a . k)^>)
<^(a . e),(a . k)^> is set
F2 . (a . (sF2 * a)) is M2(<^(F2 . (a . k)),(F2 . (a . e))^>)
<^(F2 . (a . k)),(F2 . (a . e))^> is set
a . a is M2(<^(a . e),(a . e1)^>)
a . sF2 is M2(<^(a . e1),(a . k)^>)
(a . sF2) * (a . a) is M2(<^(a . e),(a . k)^>)
F2 . ((a . sF2) * (a . a)) is M2(<^(F2 . (a . k)),(F2 . (a . e))^>)
F2 . (a . sF2) is M2(<^(F2 . (a . k)),(F2 . (a . e1))^>)
<^(F2 . (a . k)),(F2 . (a . e1))^> is set
F2 . (a . a) is M2(<^(F2 . (a . e1)),(F2 . (a . e))^>)
(F2 . (a . a)) * (F2 . (a . sF2)) is M2(<^(F2 . (a . k)),(F2 . (a . e))^>)
G1t is M2(<^(F2 . (a . e1)),(F2 . (a . e))^>)
G1t * (F2 . (a . sF2)) is M2(<^(F2 . (a . k)),(F2 . (a . e))^>)
A is non empty transitive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Contravariant comp-reversing FunctorStr over A,B
F2 is reflexive feasible Covariant comp-preserving FunctorStr over B,F1
F2 * a is reflexive feasible strict Contravariant FunctorStr over A,F1
the carrier of A is non empty set
e is M2( the carrier of A)
e1 is M2( the carrier of A)
<^e,e1^> is set
k is M2( the carrier of A)
<^e1,k^> is set
(F2 * a) . k is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (F2 * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (F2 * a) . (k,k) is M2([: the carrier of F1, the carrier of F1:])
[k,k] is set
the ObjectMap of (F2 * a) . [k,k] is set
K40(( the ObjectMap of (F2 * a) . (k,k))) is set
(F2 * a) . e1 is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e1,e1) is M2([: the carrier of F1, the carrier of F1:])
[e1,e1] is set
the ObjectMap of (F2 * a) . [e1,e1] is set
K40(( the ObjectMap of (F2 * a) . (e1,e1))) is set
(F2 * a) . e is M2( the carrier of F1)
the ObjectMap of (F2 * a) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
[e,e] is set
the ObjectMap of (F2 * a) . [e,e] is set
K40(( the ObjectMap of (F2 * a) . (e,e))) is set
a . e1 is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
a . e is M2( the carrier of B)
the ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
<^(a . e1),(a . e)^> is set
a . k is M2( the carrier of B)
the ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
<^(a . k),(a . e1)^> is set
a is M2(<^e,e1^>)
(F2 * a) . a is M2(<^((F2 * a) . e1),((F2 * a) . e)^>)
<^((F2 * a) . e1),((F2 * a) . e)^> is set
sF2 is M2(<^e1,k^>)
sF2 * a is M2(<^e,k^>)
<^e,k^> is set
(F2 * a) . (sF2 * a) is M2(<^((F2 * a) . k),((F2 * a) . e)^>)
<^((F2 * a) . k),((F2 * a) . e)^> is set
(F2 * a) . sF2 is M2(<^((F2 * a) . k),((F2 * a) . e1)^>)
<^((F2 * a) . k),((F2 * a) . e1)^> is set
((F2 * a) . a) * ((F2 * a) . sF2) is M2(<^((F2 * a) . k),((F2 * a) . e)^>)
F2 . (a . e1) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e1),(a . e1)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e1),(a . e1)] is set
the ObjectMap of F2 . [(a . e1),(a . e1)] is set
K40(( the ObjectMap of F2 . ((a . e1),(a . e1)))) is set
F2 . (a . k) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . k),(a . k)) is M2([: the carrier of F1, the carrier of F1:])
[(a . k),(a . k)] is set
the ObjectMap of F2 . [(a . k),(a . k)] is set
K40(( the ObjectMap of F2 . ((a . k),(a . k)))) is set
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
<^(F2 . (a . e1)),(F2 . (a . e))^> is set
a . (sF2 * a) is M2(<^(a . k),(a . e)^>)
<^(a . k),(a . e)^> is set
F2 . (a . (sF2 * a)) is M2(<^(F2 . (a . k)),(F2 . (a . e))^>)
<^(F2 . (a . k)),(F2 . (a . e))^> is set
a . sF2 is M2(<^(a . k),(a . e1)^>)
a . a is M2(<^(a . e1),(a . e)^>)
(a . a) * (a . sF2) is M2(<^(a . k),(a . e)^>)
F2 . ((a . a) * (a . sF2)) is M2(<^(F2 . (a . k)),(F2 . (a . e))^>)
F2 . (a . sF2) is M2(<^(F2 . (a . k)),(F2 . (a . e1))^>)
<^(F2 . (a . k)),(F2 . (a . e1))^> is set
F2 . (a . a) is M2(<^(F2 . (a . e1)),(F2 . (a . e))^>)
(F2 . (a . a)) * (F2 . (a . sF2)) is M2(<^(F2 . (a . k)),(F2 . (a . e))^>)
G1t is M2(<^(F2 . (a . e1)),(F2 . (a . e))^>)
G1t * (F2 . (a . sF2)) is M2(<^(F2 . (a . k)),(F2 . (a . e))^>)
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
F2 * a is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over A,F1
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A,B
F2 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of B,F1
F2 * a is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over A,F1
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of B,F1
F2 * a is reflexive feasible strict Contravariant id-preserving comp-reversing FunctorStr over A,F1
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty with_units reflexive AltCatStr
a is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
F2 * a is reflexive feasible strict Contravariant id-preserving comp-reversing FunctorStr over A,F1
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
the carrier of A is non empty set
the carrier of B is non empty set
k is M2( the carrier of A)
(A,B,F1,a,e) . k is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,a,e) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,e) . (k,k) is M2([: the carrier of F1, the carrier of F1:])
[k,k] is set
the ObjectMap of (A,B,F1,a,e) . [k,k] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (k,k))) is set
(A,B,F1,F2,e1) . k is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e1) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,F2,e1) . (k,k) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e1) . [k,k] is set
K40(( the ObjectMap of (A,B,F1,F2,e1) . (k,k))) is set
<^((A,B,F1,a,e) . k),((A,B,F1,F2,e1) . k)^> is set
a . k is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
F2 . k is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [k,k] is set
K40(( the ObjectMap of F2 . (k,k))) is set
<^(a . k),(F2 . k)^> is set
e . (a . k) is M2( the carrier of F1)
the ObjectMap of e is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of e . ((a . k),(a . k)) is M2([: the carrier of F1, the carrier of F1:])
[(a . k),(a . k)] is set
the ObjectMap of e . [(a . k),(a . k)] is set
K40(( the ObjectMap of e . ((a . k),(a . k)))) is set
e . (F2 . k) is M2( the carrier of F1)
the ObjectMap of e . ((F2 . k),(F2 . k)) is M2([: the carrier of F1, the carrier of F1:])
[(F2 . k),(F2 . k)] is set
the ObjectMap of e . [(F2 . k),(F2 . k)] is set
K40(( the ObjectMap of e . ((F2 . k),(F2 . k)))) is set
<^(e . (a . k)),(e . (F2 . k))^> is set
e1 . (F2 . k) is M2( the carrier of F1)
the ObjectMap of e1 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of e1 . ((F2 . k),(F2 . k)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e1 . [(F2 . k),(F2 . k)] is set
K40(( the ObjectMap of e1 . ((F2 . k),(F2 . k)))) is set
<^(e . (F2 . k)),(e1 . (F2 . k))^> is set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F1 is non empty transitive with_units reflexive AltCatStr
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of a,F2
a is set
sF2 is M2( the carrier of A)
a . sF2 is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
[sF2,sF2] is set
the ObjectMap of a . [sF2,sF2] is set
K40(( the ObjectMap of a . (sF2,sF2))) is set
F2 . sF2 is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [sF2,sF2] is set
K40(( the ObjectMap of F2 . (sF2,sF2))) is set
e ! sF2 is M2(<^(a . sF2),(F2 . sF2)^>)
<^(a . sF2),(F2 . sF2)^> is set
e1 . (e ! sF2) is M2(<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^>)
e1 . (a . sF2) is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of e1 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of e1 . ((a . sF2),(a . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(a . sF2),(a . sF2)] is set
the ObjectMap of e1 . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of e1 . ((a . sF2),(a . sF2)))) is set
e1 . (F2 . sF2) is M2( the carrier of F1)
the ObjectMap of e1 . ((F2 . sF2),(F2 . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(F2 . sF2),(F2 . sF2)] is set
the ObjectMap of e1 . [(F2 . sF2),(F2 . sF2)] is set
K40(( the ObjectMap of e1 . ((F2 . sF2),(F2 . sF2)))) is set
<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^> is set
a is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) set
sF2 is M2( the carrier of A)
a . sF2 is set
(A,B,F1,a,e1) . sF2 is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,a,e1) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,e1) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
[sF2,sF2] is set
the ObjectMap of (A,B,F1,a,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,a,e1) . (sF2,sF2))) is set
(A,B,F1,F2,e1) . sF2 is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e1) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,F2,e1) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,F2,e1) . (sF2,sF2))) is set
<^((A,B,F1,a,e1) . sF2),((A,B,F1,F2,e1) . sF2)^> is set
a . sF2 is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [sF2,sF2] is set
K40(( the ObjectMap of a . (sF2,sF2))) is set
e1 . (a . sF2) is M2( the carrier of F1)
the ObjectMap of e1 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of e1 . ((a . sF2),(a . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(a . sF2),(a . sF2)] is set
the ObjectMap of e1 . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of e1 . ((a . sF2),(a . sF2)))) is set
G1t is M2( the carrier of A)
a . G1t is M2( the carrier of B)
the ObjectMap of a . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
[G1t,G1t] is set
the ObjectMap of a . [G1t,G1t] is set
K40(( the ObjectMap of a . (G1t,G1t))) is set
F2 . G1t is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [G1t,G1t] is set
K40(( the ObjectMap of F2 . (G1t,G1t))) is set
e ! G1t is M2(<^(a . G1t),(F2 . G1t)^>)
<^(a . G1t),(F2 . G1t)^> is set
e1 . (e ! G1t) is M2(<^(e1 . (a . G1t)),(e1 . (F2 . G1t))^>)
e1 . (a . G1t) is M2( the carrier of F1)
the ObjectMap of e1 . ((a . G1t),(a . G1t)) is M2([: the carrier of F1, the carrier of F1:])
[(a . G1t),(a . G1t)] is set
the ObjectMap of e1 . [(a . G1t),(a . G1t)] is set
K40(( the ObjectMap of e1 . ((a . G1t),(a . G1t)))) is set
e1 . (F2 . G1t) is M2( the carrier of F1)
the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of F1, the carrier of F1:])
[(F2 . G1t),(F2 . G1t)] is set
the ObjectMap of e1 . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)))) is set
<^(e1 . (a . G1t)),(e1 . (F2 . G1t))^> is set
sF2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,e1)
G1t is M2( the carrier of A)
sF2 . G1t is set
a . G1t is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
[G1t,G1t] is set
the ObjectMap of a . [G1t,G1t] is set
K40(( the ObjectMap of a . (G1t,G1t))) is set
F2 . G1t is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [G1t,G1t] is set
K40(( the ObjectMap of F2 . (G1t,G1t))) is set
e ! G1t is M2(<^(a . G1t),(F2 . G1t)^>)
<^(a . G1t),(F2 . G1t)^> is set
e1 . (e ! G1t) is M2(<^(e1 . (a . G1t)),(e1 . (F2 . G1t))^>)
e1 . (a . G1t) is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of e1 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of e1 . ((a . G1t),(a . G1t)) is M2([: the carrier of F1, the carrier of F1:])
[(a . G1t),(a . G1t)] is set
the ObjectMap of e1 . [(a . G1t),(a . G1t)] is set
K40(( the ObjectMap of e1 . ((a . G1t),(a . G1t)))) is set
e1 . (F2 . G1t) is M2( the carrier of F1)
the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of F1, the carrier of F1:])
[(F2 . G1t),(F2 . G1t)] is set
the ObjectMap of e1 . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)))) is set
<^(e1 . (a . G1t)),(e1 . (F2 . G1t))^> is set
fa is M2( the carrier of A)
a . fa is M2( the carrier of B)
the ObjectMap of a . (fa,fa) is M2([: the carrier of B, the carrier of B:])
[fa,fa] is set
the ObjectMap of a . [fa,fa] is set
K40(( the ObjectMap of a . (fa,fa))) is set
F2 . fa is M2( the carrier of B)
the ObjectMap of F2 . (fa,fa) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [fa,fa] is set
K40(( the ObjectMap of F2 . (fa,fa))) is set
e ! fa is M2(<^(a . fa),(F2 . fa)^>)
<^(a . fa),(F2 . fa)^> is set
e1 . (e ! fa) is M2(<^(e1 . (a . fa)),(e1 . (F2 . fa))^>)
e1 . (a . fa) is M2( the carrier of F1)
the ObjectMap of e1 . ((a . fa),(a . fa)) is M2([: the carrier of F1, the carrier of F1:])
[(a . fa),(a . fa)] is set
the ObjectMap of e1 . [(a . fa),(a . fa)] is set
K40(( the ObjectMap of e1 . ((a . fa),(a . fa)))) is set
e1 . (F2 . fa) is M2( the carrier of F1)
the ObjectMap of e1 . ((F2 . fa),(F2 . fa)) is M2([: the carrier of F1, the carrier of F1:])
[(F2 . fa),(F2 . fa)] is set
the ObjectMap of e1 . [(F2 . fa),(F2 . fa)] is set
K40(( the ObjectMap of e1 . ((F2 . fa),(F2 . fa)))) is set
<^(e1 . (a . fa)),(e1 . (F2 . fa))^> is set
k is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,e1)
a is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,e1)
sF2 is M2( the carrier of A)
k ! sF2 is M2(<^((A,B,F1,a,e1) . sF2),((A,B,F1,F2,e1) . sF2)^>)
(A,B,F1,a,e1) . sF2 is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,a,e1) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,e1) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
[sF2,sF2] is set
the ObjectMap of (A,B,F1,a,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,a,e1) . (sF2,sF2))) is set
(A,B,F1,F2,e1) . sF2 is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e1) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,F2,e1) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,F2,e1) . (sF2,sF2))) is set
<^((A,B,F1,a,e1) . sF2),((A,B,F1,F2,e1) . sF2)^> is set
k . sF2 is set
a . sF2 is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [sF2,sF2] is set
K40(( the ObjectMap of a . (sF2,sF2))) is set
F2 . sF2 is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [sF2,sF2] is set
K40(( the ObjectMap of F2 . (sF2,sF2))) is set
e ! sF2 is M2(<^(a . sF2),(F2 . sF2)^>)
<^(a . sF2),(F2 . sF2)^> is set
e1 . (e ! sF2) is M2(<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^>)
e1 . (a . sF2) is M2( the carrier of F1)
the ObjectMap of e1 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of e1 . ((a . sF2),(a . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(a . sF2),(a . sF2)] is set
the ObjectMap of e1 . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of e1 . ((a . sF2),(a . sF2)))) is set
e1 . (F2 . sF2) is M2( the carrier of F1)
the ObjectMap of e1 . ((F2 . sF2),(F2 . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(F2 . sF2),(F2 . sF2)] is set
the ObjectMap of e1 . [(F2 . sF2),(F2 . sF2)] is set
K40(( the ObjectMap of e1 . ((F2 . sF2),(F2 . sF2)))) is set
<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^> is set
a . sF2 is set
a ! sF2 is M2(<^((A,B,F1,a,e1) . sF2),((A,B,F1,F2,e1) . sF2)^>)
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
the carrier of F1 is non empty set
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,B
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
(F1,B,A,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,A
(F1,B,A,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,A
e1 is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of a,F2
(F1,B,A,a,F2,e1,e) is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of (F1,B,A,a,e),(F1,B,A,F2,e)
k is M2( the carrier of F1)
(F1,B,A,a,F2,e1,e) ! k is M2(<^((F1,B,A,a,e) . k),((F1,B,A,F2,e) . k)^>)
(F1,B,A,a,e) . k is M2( 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 ObjectMap of (F1,B,A,a,e) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
[:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is non empty set
the ObjectMap of (F1,B,A,a,e) . (k,k) is M2([: the carrier of A, the carrier of A:])
[k,k] is set
the ObjectMap of (F1,B,A,a,e) . [k,k] is set
K40(( the ObjectMap of (F1,B,A,a,e) . (k,k))) is set
(F1,B,A,F2,e) . k is M2( the carrier of A)
the ObjectMap of (F1,B,A,F2,e) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (F1,B,A,F2,e) . (k,k) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (F1,B,A,F2,e) . [k,k] is set
K40(( the ObjectMap of (F1,B,A,F2,e) . (k,k))) is set
<^((F1,B,A,a,e) . k),((F1,B,A,F2,e) . k)^> is set
a . k is M2( 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 ObjectMap of a is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is non empty set
the ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
F2 . k is M2( the carrier of B)
the ObjectMap of F2 is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [k,k] is set
K40(( the ObjectMap of F2 . (k,k))) is set
e1 ! k is M2(<^(a . k),(F2 . k)^>)
<^(a . k),(F2 . k)^> is set
e . (e1 ! k) is M2(<^(e . (a . k)),(e . (F2 . k))^>)
e . (a . k) is M2( the carrier of A)
the ObjectMap of e 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 e . ((a . k),(a . k)) is M2([: the carrier of A, the carrier of A:])
[(a . k),(a . k)] is set
the ObjectMap of e . [(a . k),(a . k)] is set
K40(( the ObjectMap of e . ((a . k),(a . k)))) is set
e . (F2 . k) is M2( the carrier of A)
the ObjectMap of e . ((F2 . k),(F2 . k)) is M2([: the carrier of A, the carrier of A:])
[(F2 . k),(F2 . k)] is set
the ObjectMap of e . [(F2 . k),(F2 . k)] is set
K40(( the ObjectMap of e . ((F2 . k),(F2 . k)))) is set
<^(e . (a . k)),(e . (F2 . k))^> is set
(F1,B,A,a,F2,e1,e) . k is set
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
A is non empty transitive with_units reflexive AltCatStr
the carrier of B is non empty set
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
the carrier of A is non empty set
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
(A,B,F1,e,a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,e,F2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e1 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of a,F2
a is set
sF2 is M2( the carrier of A)
e . sF2 is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap of e 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of e . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
[sF2,sF2] is set
the ObjectMap of e . [sF2,sF2] is set
K40(( the ObjectMap of e . (sF2,sF2))) is set
e1 ! (e . sF2) is M2(<^(a . (e . sF2)),(F2 . (e . sF2))^>)
a . (e . sF2) is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of a is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of a . ((e . sF2),(e . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(e . sF2),(e . sF2)] is set
the ObjectMap of a . [(e . sF2),(e . sF2)] is set
K40(( the ObjectMap of a . ((e . sF2),(e . sF2)))) is set
F2 . (e . sF2) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of F2 . ((e . sF2),(e . sF2)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [(e . sF2),(e . sF2)] is set
K40(( the ObjectMap of F2 . ((e . sF2),(e . sF2)))) is set
<^(a . (e . sF2)),(F2 . (e . sF2))^> is set
a is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) set
sF2 is M2( the carrier of A)
a . sF2 is set
(A,B,F1,e,a) . sF2 is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,e,a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,e,a) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
[sF2,sF2] is set
the ObjectMap of (A,B,F1,e,a) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,e,a) . (sF2,sF2))) is set
(A,B,F1,e,F2) . sF2 is M2( the carrier of F1)
the ObjectMap of (A,B,F1,e,F2) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,e,F2) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,e,F2) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,e,F2) . (sF2,sF2))) is set
<^((A,B,F1,e,a) . sF2),((A,B,F1,e,F2) . sF2)^> is set
e . sF2 is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap of e 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of e . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of e . [sF2,sF2] is set
K40(( the ObjectMap of e . (sF2,sF2))) is set
a . (e . sF2) is M2( the carrier of F1)
the ObjectMap of a is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of a . ((e . sF2),(e . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(e . sF2),(e . sF2)] is set
the ObjectMap of a . [(e . sF2),(e . sF2)] is set
K40(( the ObjectMap of a . ((e . sF2),(e . sF2)))) is set
G1t is M2( the carrier of A)
e . G1t is M2( the carrier of B)
the ObjectMap of e . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
[G1t,G1t] is set
the ObjectMap of e . [G1t,G1t] is set
K40(( the ObjectMap of e . (G1t,G1t))) is set
e1 ! (e . G1t) is M2(<^(a . (e . G1t)),(F2 . (e . G1t))^>)
a . (e . G1t) is M2( the carrier of F1)
the ObjectMap of a . ((e . G1t),(e . G1t)) is M2([: the carrier of F1, the carrier of F1:])
[(e . G1t),(e . G1t)] is set
the ObjectMap of a . [(e . G1t),(e . G1t)] is set
K40(( the ObjectMap of a . ((e . G1t),(e . G1t)))) is set
F2 . (e . G1t) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of F2 . ((e . G1t),(e . G1t)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [(e . G1t),(e . G1t)] is set
K40(( the ObjectMap of F2 . ((e . G1t),(e . G1t)))) is set
<^(a . (e . G1t)),(F2 . (e . G1t))^> is set
sF2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,e,a),(A,B,F1,e,F2)
G1t is M2( the carrier of A)
sF2 . G1t is set
e . G1t is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap of e 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of e . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
[G1t,G1t] is set
the ObjectMap of e . [G1t,G1t] is set
K40(( the ObjectMap of e . (G1t,G1t))) is set
e1 ! (e . G1t) is M2(<^(a . (e . G1t)),(F2 . (e . G1t))^>)
a . (e . G1t) is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of a is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of a . ((e . G1t),(e . G1t)) is M2([: the carrier of F1, the carrier of F1:])
[(e . G1t),(e . G1t)] is set
the ObjectMap of a . [(e . G1t),(e . G1t)] is set
K40(( the ObjectMap of a . ((e . G1t),(e . G1t)))) is set
F2 . (e . G1t) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of F2 . ((e . G1t),(e . G1t)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [(e . G1t),(e . G1t)] is set
K40(( the ObjectMap of F2 . ((e . G1t),(e . G1t)))) is set
<^(a . (e . G1t)),(F2 . (e . G1t))^> is set
fa is M2( the carrier of A)
e . fa is M2( the carrier of B)
the ObjectMap of e . (fa,fa) is M2([: the carrier of B, the carrier of B:])
[fa,fa] is set
the ObjectMap of e . [fa,fa] is set
K40(( the ObjectMap of e . (fa,fa))) is set
e1 ! (e . fa) is M2(<^(a . (e . fa)),(F2 . (e . fa))^>)
a . (e . fa) is M2( the carrier of F1)
the ObjectMap of a . ((e . fa),(e . fa)) is M2([: the carrier of F1, the carrier of F1:])
[(e . fa),(e . fa)] is set
the ObjectMap of a . [(e . fa),(e . fa)] is set
K40(( the ObjectMap of a . ((e . fa),(e . fa)))) is set
F2 . (e . fa) is M2( the carrier of F1)
the ObjectMap of F2 . ((e . fa),(e . fa)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [(e . fa),(e . fa)] is set
K40(( the ObjectMap of F2 . ((e . fa),(e . fa)))) is set
<^(a . (e . fa)),(F2 . (e . fa))^> is set
k is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,e,a),(A,B,F1,e,F2)
a is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,e,a),(A,B,F1,e,F2)
sF2 is M2( the carrier of A)
k ! sF2 is M2(<^((A,B,F1,e,a) . sF2),((A,B,F1,e,F2) . sF2)^>)
(A,B,F1,e,a) . sF2 is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,e,a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,e,a) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
[sF2,sF2] is set
the ObjectMap of (A,B,F1,e,a) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,e,a) . (sF2,sF2))) is set
(A,B,F1,e,F2) . sF2 is M2( the carrier of F1)
the ObjectMap of (A,B,F1,e,F2) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,e,F2) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,e,F2) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,e,F2) . (sF2,sF2))) is set
<^((A,B,F1,e,a) . sF2),((A,B,F1,e,F2) . sF2)^> is set
k . sF2 is set
e . sF2 is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap of e 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of e . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of e . [sF2,sF2] is set
K40(( the ObjectMap of e . (sF2,sF2))) is set
e1 ! (e . sF2) is M2(<^(a . (e . sF2)),(F2 . (e . sF2))^>)
a . (e . sF2) is M2( the carrier of F1)
the ObjectMap of a is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of a . ((e . sF2),(e . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(e . sF2),(e . sF2)] is set
the ObjectMap of a . [(e . sF2),(e . sF2)] is set
K40(( the ObjectMap of a . ((e . sF2),(e . sF2)))) is set
F2 . (e . sF2) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of F2 . ((e . sF2),(e . sF2)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [(e . sF2),(e . sF2)] is set
K40(( the ObjectMap of F2 . ((e . sF2),(e . sF2)))) is set
<^(a . (e . sF2)),(F2 . (e . sF2))^> is set
a . sF2 is set
a ! sF2 is M2(<^((A,B,F1,e,a) . sF2),((A,B,F1,e,F2) . sF2)^>)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
the carrier of F1 is non empty set
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,A
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
(F1,A,B,a,F2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,B
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
(F1,A,B,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,B
e1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F2,e
(F1,A,B,F2,e,a,e1) is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of (F1,A,B,a,F2),(F1,A,B,a,e)
k is M2( the carrier of F1)
(F1,A,B,F2,e,a,e1) ! k is M2(<^((F1,A,B,a,F2) . k),((F1,A,B,a,e) . k)^>)
(F1,A,B,a,F2) . k is M2( 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 ObjectMap of (F1,A,B,a,F2) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
[:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is non empty set
the ObjectMap of (F1,A,B,a,F2) . (k,k) is M2([: the carrier of B, the carrier of B:])
[k,k] is set
the ObjectMap of (F1,A,B,a,F2) . [k,k] is set
K40(( the ObjectMap of (F1,A,B,a,F2) . (k,k))) is set
(F1,A,B,a,e) . k is M2( the carrier of B)
the ObjectMap of (F1,A,B,a,e) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (F1,A,B,a,e) . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (F1,A,B,a,e) . [k,k] is set
K40(( the ObjectMap of (F1,A,B,a,e) . (k,k))) is set
<^((F1,A,B,a,F2) . k),((F1,A,B,a,e) . k)^> is set
a . k is M2( the carrier of A)
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the ObjectMap of a is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is non empty set
the ObjectMap of a . (k,k) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
e1 ! (a . k) is M2(<^(F2 . (a . k)),(e . (a . k))^>)
F2 . (a . k) is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F2 . ((a . k),(a . k)) is M2([: the carrier of B, the carrier of B:])
[(a . k),(a . k)] is set
the ObjectMap of F2 . [(a . k),(a . k)] is set
K40(( the ObjectMap of F2 . ((a . k),(a . k)))) is set
e . (a . k) is M2( the carrier of B)
the ObjectMap of e 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of e . ((a . k),(a . k)) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of e . [(a . k),(a . k)] is set
K40(( the ObjectMap of e . ((a . k),(a . k)))) is set
<^(F2 . (a . k)),(e . (a . k))^> is set
(F1,A,B,F2,e,a,e1) . k 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
F1 is non empty transitive with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,A
(B,F1,A,a,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,F1,A,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,F1,A,e,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
k is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of a,F2
(B,F1,A,a,F2,k,e1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e1),(B,F1,A,F2,e1)
a is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of F2,e
a `*` k is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of a,e
(B,F1,A,a,e,(a `*` k),e1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e1),(B,F1,A,e,e1)
(B,F1,A,F2,e,a,e1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,F2,e1),(B,F1,A,e,e1)
(B,F1,A,F2,e,a,e1) `*` (B,F1,A,a,F2,k,e1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e1),(B,F1,A,e,e1)
sF2 is M2( the carrier of B)
F2 . sF2 is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
[sF2,sF2] is set
the ObjectMap of F2 . [sF2,sF2] is set
K40(( the ObjectMap of F2 . (sF2,sF2))) is set
e1 . (F2 . sF2) is M2( 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 ObjectMap of e1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is non empty set
the ObjectMap of e1 . ((F2 . sF2),(F2 . sF2)) is M2([: the carrier of A, the carrier of A:])
[(F2 . sF2),(F2 . sF2)] is set
the ObjectMap of e1 . [(F2 . sF2),(F2 . sF2)] is set
K40(( the ObjectMap of e1 . ((F2 . sF2),(F2 . sF2)))) is set
(B,F1,A,F2,e1) . sF2 is M2( the carrier of A)
the ObjectMap of (B,F1,A,F2,e1) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 (B,F1,A,F2,e1) . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,F2,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (B,F1,A,F2,e1) . (sF2,sF2))) is set
e . sF2 is M2( the carrier of F1)
the ObjectMap of e is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of e . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e . [sF2,sF2] is set
K40(( the ObjectMap of e . (sF2,sF2))) is set
e1 . (e . sF2) is M2( the carrier of A)
the ObjectMap of e1 . ((e . sF2),(e . sF2)) is M2([: the carrier of A, the carrier of A:])
[(e . sF2),(e . sF2)] is set
the ObjectMap of e1 . [(e . sF2),(e . sF2)] is set
K40(( the ObjectMap of e1 . ((e . sF2),(e . sF2)))) is set
(B,F1,A,e,e1) . sF2 is M2( the carrier of A)
the ObjectMap of (B,F1,A,e,e1) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (B,F1,A,e,e1) . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,e,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (B,F1,A,e,e1) . (sF2,sF2))) is set
a . sF2 is M2( the carrier of F1)
the ObjectMap of a is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of a . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of a . [sF2,sF2] is set
K40(( the ObjectMap of a . (sF2,sF2))) is set
e1 . (a . sF2) is M2( the carrier of A)
the ObjectMap of e1 . ((a . sF2),(a . sF2)) is M2([: the carrier of A, the carrier of A:])
[(a . sF2),(a . sF2)] is set
the ObjectMap of e1 . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of e1 . ((a . sF2),(a . sF2)))) is set
(B,F1,A,a,e1) . sF2 is M2( the carrier of A)
the ObjectMap of (B,F1,A,a,e1) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (B,F1,A,a,e1) . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,a,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (B,F1,A,a,e1) . (sF2,sF2))) is set
<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^> is set
(B,F1,A,a,F2,k,e1) ! sF2 is M2(<^((B,F1,A,a,e1) . sF2),((B,F1,A,F2,e1) . sF2)^>)
<^((B,F1,A,a,e1) . sF2),((B,F1,A,F2,e1) . sF2)^> is set
<^(a . sF2),(F2 . sF2)^> is set
<^(F2 . sF2),(e . sF2)^> is set
(B,F1,A,a,e,(a `*` k),e1) ! sF2 is M2(<^((B,F1,A,a,e1) . sF2),((B,F1,A,e,e1) . sF2)^>)
<^((B,F1,A,a,e1) . sF2),((B,F1,A,e,e1) . sF2)^> is set
(a `*` k) ! sF2 is M2(<^(a . sF2),(e . sF2)^>)
<^(a . sF2),(e . sF2)^> is set
e1 . ((a `*` k) ! sF2) is M2(<^(e1 . (a . sF2)),(e1 . (e . sF2))^>)
<^(e1 . (a . sF2)),(e1 . (e . sF2))^> is set
k ! sF2 is M2(<^(a . sF2),(F2 . sF2)^>)
a ! sF2 is M2(<^(F2 . sF2),(e . sF2)^>)
(a ! sF2) * (k ! sF2) is M2(<^(a . sF2),(e . sF2)^>)
e1 . ((a ! sF2) * (k ! sF2)) is M2(<^(e1 . (a . sF2)),(e1 . (e . sF2))^>)
e1 . (k ! sF2) is M2(<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^>)
e1 . (a ! sF2) is M2(<^(e1 . (F2 . sF2)),(e1 . (e . sF2))^>)
<^(e1 . (F2 . sF2)),(e1 . (e . sF2))^> is set
(e1 . (a ! sF2)) * (e1 . (k ! sF2)) is M2(<^(e1 . (a . sF2)),(e1 . (e . sF2))^>)
G1t is M2(<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^>)
(e1 . (a ! sF2)) * G1t is M2(<^(e1 . (a . sF2)),(e1 . (e . sF2))^>)
(B,F1,A,F2,e,a,e1) ! sF2 is M2(<^((B,F1,A,F2,e1) . sF2),((B,F1,A,e,e1) . sF2)^>)
<^((B,F1,A,F2,e1) . sF2),((B,F1,A,e,e1) . sF2)^> is set
((B,F1,A,F2,e,a,e1) ! sF2) * ((B,F1,A,a,F2,k,e1) ! sF2) is M2(<^((B,F1,A,a,e1) . sF2),((B,F1,A,e,e1) . sF2)^>)
((B,F1,A,F2,e,a,e1) `*` (B,F1,A,a,F2,k,e1)) ! sF2 is M2(<^((B,F1,A,a,e1) . sF2),((B,F1,A,e,e1) . sF2)^>)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,F2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
k is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of F2,e
(A,B,F1,F2,e,a,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e)
a is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of e,e1
a `*` k is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of F2,e1
(A,B,F1,F2,e1,a,(a `*` k)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e1)
(A,B,F1,e,e1,a,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,a,e1)
(A,B,F1,e,e1,a,a) `*` (A,B,F1,F2,e,a,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e1)
sF2 is M2( the carrier of A)
a . sF2 is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (sF2,sF2) is M2([: the carrier of B, the carrier of B:])
[sF2,sF2] is set
the ObjectMap of a . [sF2,sF2] is set
K40(( the ObjectMap of a . (sF2,sF2))) is set
F2 . (a . sF2) is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . sF2),(a . sF2)) is M2([: the carrier of F1, the carrier of F1:])
[(a . sF2),(a . sF2)] is set
the ObjectMap of F2 . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of F2 . ((a . sF2),(a . sF2)))) is set
(A,B,F1,a,F2) . sF2 is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,F2) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,F2) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,a,F2) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,a,F2) . (sF2,sF2))) is set
e1 . (a . sF2) is M2( the carrier of F1)
the ObjectMap of e1 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of e1 . ((a . sF2),(a . sF2)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e1 . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of e1 . ((a . sF2),(a . sF2)))) is set
(A,B,F1,a,e1) . sF2 is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e1) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,a,e1) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,a,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,a,e1) . (sF2,sF2))) is set
e . (a . sF2) is M2( the carrier of F1)
the ObjectMap of e is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of e . ((a . sF2),(a . sF2)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of e . ((a . sF2),(a . sF2)))) is set
(A,B,F1,a,e) . sF2 is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,a,e) . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,a,e) . [sF2,sF2] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (sF2,sF2))) is set
<^(e . (a . sF2)),(e1 . (a . sF2))^> is set
(A,B,F1,e,e1,a,a) ! sF2 is M2(<^((A,B,F1,a,e) . sF2),((A,B,F1,a,e1) . sF2)^>)
<^((A,B,F1,a,e) . sF2),((A,B,F1,a,e1) . sF2)^> is set
(A,B,F1,F2,e1,a,(a `*` k)) ! sF2 is M2(<^((A,B,F1,a,F2) . sF2),((A,B,F1,a,e1) . sF2)^>)
<^((A,B,F1,a,F2) . sF2),((A,B,F1,a,e1) . sF2)^> is set
(a `*` k) ! (a . sF2) is M2(<^(F2 . (a . sF2)),(e1 . (a . sF2))^>)
<^(F2 . (a . sF2)),(e1 . (a . sF2))^> is set
k ! (a . sF2) is M2(<^(F2 . (a . sF2)),(e . (a . sF2))^>)
<^(F2 . (a . sF2)),(e . (a . sF2))^> is set
a ! (a . sF2) is M2(<^(e . (a . sF2)),(e1 . (a . sF2))^>)
(a ! (a . sF2)) * (k ! (a . sF2)) is M2(<^(F2 . (a . sF2)),(e1 . (a . sF2))^>)
G1t is M2(<^(e . (a . sF2)),(e1 . (a . sF2))^>)
G1t * (k ! (a . sF2)) is M2(<^(F2 . (a . sF2)),(e1 . (a . sF2))^>)
(A,B,F1,F2,e,a,k) ! sF2 is M2(<^((A,B,F1,a,F2) . sF2),((A,B,F1,a,e) . sF2)^>)
<^((A,B,F1,a,F2) . sF2),((A,B,F1,a,e) . sF2)^> is set
((A,B,F1,e,e1,a,a) ! sF2) * ((A,B,F1,F2,e,a,k) ! sF2) is M2(<^((A,B,F1,a,F2) . sF2),((A,B,F1,a,e1) . sF2)^>)
((A,B,F1,e,e1,a,a) `*` (A,B,F1,F2,e,a,k)) ! sF2 is M2(<^((A,B,F1,a,F2) . sF2),((A,B,F1,a,e1) . sF2)^>)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
the carrier of F1 is non empty set
a is non empty transitive with_units reflexive AltCatStr
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,a
(B,F1,a,e,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,a
k is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,a
(B,F1,a,e,k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,a
a is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of e1,k
(B,F1,a,e1,k,e,a) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,a,e,e1),(B,F1,a,e,k)
the carrier of B is non empty set
(A,B,a,(B,F1,a,e,e1),(B,F1,a,e,k),F2,(B,F1,a,e1,k,e,a)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,F2,(B,F1,a,e,e1)),(A,B,a,F2,(B,F1,a,e,k))
(A,B,a,F2,(B,F1,a,e,e1)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,B,a,F2,(B,F1,a,e,k)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,F1,a,e1,k,(A,B,F1,F2,e),a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,F2,e),e1),(A,F1,a,(A,B,F1,F2,e),k)
(A,F1,a,(A,B,F1,F2,e),e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,F1,a,(A,B,F1,F2,e),k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
G1t is M2( the carrier of A)
(A,B,a,(B,F1,a,e,e1),(B,F1,a,e,k),F2,(B,F1,a,e1,k,e,a)) ! G1t is M2(<^((A,B,a,F2,(B,F1,a,e,e1)) . G1t),((A,B,a,F2,(B,F1,a,e,k)) . G1t)^>)
(A,B,a,F2,(B,F1,a,e,e1)) . G1t is M2( 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 ObjectMap of (A,B,a,F2,(B,F1,a,e,e1)) 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]) M2( 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 ObjectMap of (A,B,a,F2,(B,F1,a,e,e1)) . (G1t,G1t) is M2([: the carrier of a, the carrier of a:])
[G1t,G1t] is set
the ObjectMap of (A,B,a,F2,(B,F1,a,e,e1)) . [G1t,G1t] is set
K40(( the ObjectMap of (A,B,a,F2,(B,F1,a,e,e1)) . (G1t,G1t))) is set
(A,B,a,F2,(B,F1,a,e,k)) . G1t is M2( the carrier of a)
the ObjectMap of (A,B,a,F2,(B,F1,a,e,k)) 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]:])
the ObjectMap of (A,B,a,F2,(B,F1,a,e,k)) . (G1t,G1t) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of (A,B,a,F2,(B,F1,a,e,k)) . [G1t,G1t] is set
K40(( the ObjectMap of (A,B,a,F2,(B,F1,a,e,k)) . (G1t,G1t))) is set
<^((A,B,a,F2,(B,F1,a,e,e1)) . G1t),((A,B,a,F2,(B,F1,a,e,k)) . G1t)^> is set
F2 . G1t is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F2 . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [G1t,G1t] is set
K40(( the ObjectMap of F2 . (G1t,G1t))) is set
(B,F1,a,e1,k,e,a) ! (F2 . G1t) is M2(<^((B,F1,a,e,e1) . (F2 . G1t)),((B,F1,a,e,k) . (F2 . G1t))^>)
(B,F1,a,e,e1) . (F2 . G1t) is M2( the carrier of a)
the ObjectMap of (B,F1,a,e,e1) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of a, the carrier of a:]) M2( 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 (B,F1,a,e,e1) . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of a, the carrier of a:])
[(F2 . G1t),(F2 . G1t)] is set
the ObjectMap of (B,F1,a,e,e1) . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of (B,F1,a,e,e1) . ((F2 . G1t),(F2 . G1t)))) is set
(B,F1,a,e,k) . (F2 . G1t) is M2( the carrier of a)
the ObjectMap of (B,F1,a,e,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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of a, the carrier of a:]:])
the ObjectMap of (B,F1,a,e,k) . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of (B,F1,a,e,k) . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of (B,F1,a,e,k) . ((F2 . G1t),(F2 . G1t)))) is set
<^((B,F1,a,e,e1) . (F2 . G1t)),((B,F1,a,e,k) . (F2 . G1t))^> is set
e . (F2 . G1t) is M2( the carrier of F1)
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of e is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of e . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of e . ((F2 . G1t),(F2 . G1t)))) is set
a ! (e . (F2 . G1t)) is M2(<^(e1 . (e . (F2 . G1t))),(k . (e . (F2 . G1t)))^>)
e1 . (e . (F2 . G1t)) is M2( the carrier of a)
the ObjectMap of e1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:] is non empty set
the ObjectMap of e1 . ((e . (F2 . G1t)),(e . (F2 . G1t))) is M2([: the carrier of a, the carrier of a:])
[(e . (F2 . G1t)),(e . (F2 . G1t))] is set
the ObjectMap of e1 . [(e . (F2 . G1t)),(e . (F2 . G1t))] is set
K40(( the ObjectMap of e1 . ((e . (F2 . G1t)),(e . (F2 . G1t))))) is set
k . (e . (F2 . G1t)) is M2( the carrier of a)
the ObjectMap of k is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:])
the ObjectMap of k . ((e . (F2 . G1t)),(e . (F2 . G1t))) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of k . [(e . (F2 . G1t)),(e . (F2 . G1t))] is set
K40(( the ObjectMap of k . ((e . (F2 . G1t)),(e . (F2 . G1t))))) is set
<^(e1 . (e . (F2 . G1t))),(k . (e . (F2 . G1t)))^> is set
(A,B,F1,F2,e) . G1t is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,F2,e) . (G1t,G1t) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e) . [G1t,G1t] is set
K40(( the ObjectMap of (A,B,F1,F2,e) . (G1t,G1t))) is set
a ! ((A,B,F1,F2,e) . G1t) is M2(<^(e1 . ((A,B,F1,F2,e) . G1t)),(k . ((A,B,F1,F2,e) . G1t))^>)
e1 . ((A,B,F1,F2,e) . G1t) is M2( the carrier of a)
the ObjectMap of e1 . (((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e) . G1t)) is M2([: the carrier of a, the carrier of a:])
[((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e) . G1t)] is set
the ObjectMap of e1 . [((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e) . G1t)] is set
K40(( the ObjectMap of e1 . (((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e) . G1t)))) is set
k . ((A,B,F1,F2,e) . G1t) is M2( the carrier of a)
the ObjectMap of k . (((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e) . G1t)) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of k . [((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e) . G1t)] is set
K40(( the ObjectMap of k . (((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e) . G1t)))) is set
<^(e1 . ((A,B,F1,F2,e) . G1t)),(k . ((A,B,F1,F2,e) . G1t))^> is set
(A,F1,a,e1,k,(A,B,F1,F2,e),a) ! G1t is M2(<^((A,F1,a,(A,B,F1,F2,e),e1) . G1t),((A,F1,a,(A,B,F1,F2,e),k) . G1t)^>)
(A,F1,a,(A,B,F1,F2,e),e1) . G1t is M2( the carrier of a)
the ObjectMap of (A,F1,a,(A,B,F1,F2,e),e1) 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]:])
the ObjectMap of (A,F1,a,(A,B,F1,F2,e),e1) . (G1t,G1t) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of (A,F1,a,(A,B,F1,F2,e),e1) . [G1t,G1t] is set
K40(( the ObjectMap of (A,F1,a,(A,B,F1,F2,e),e1) . (G1t,G1t))) is set
(A,F1,a,(A,B,F1,F2,e),k) . G1t is M2( the carrier of a)
the ObjectMap of (A,F1,a,(A,B,F1,F2,e),k) 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]:])
the ObjectMap of (A,F1,a,(A,B,F1,F2,e),k) . (G1t,G1t) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of (A,F1,a,(A,B,F1,F2,e),k) . [G1t,G1t] is set
K40(( the ObjectMap of (A,F1,a,(A,B,F1,F2,e),k) . (G1t,G1t))) is set
<^((A,F1,a,(A,B,F1,F2,e),e1) . G1t),((A,F1,a,(A,B,F1,F2,e),k) . G1t)^> is set
sF2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,F2,(B,F1,a,e,e1)),(A,B,a,F2,(B,F1,a,e,k))
sF2 ! G1t is M2(<^((A,B,a,F2,(B,F1,a,e,e1)) . G1t),((A,B,a,F2,(B,F1,a,e,k)) . G1t)^>)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
the carrier of F1 is non empty set
a is non empty transitive with_units reflexive AltCatStr
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,a
(A,F1,a,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,a
(A,F1,a,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
k is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of a,B
(F1,a,B,e,k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,B
(F1,a,B,e1,k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,B
a is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of e,e1
(F1,a,B,e,e1,a,k) is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of (F1,a,B,e,k),(F1,a,B,e1,k)
(A,F1,B,(F1,a,B,e,k),(F1,a,B,e1,k),F2,(F1,a,B,e,e1,a,k)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,B,F2,(F1,a,B,e,k)),(A,F1,B,F2,(F1,a,B,e1,k))
(A,F1,B,F2,(F1,a,B,e,k)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,B
(A,F1,B,F2,(F1,a,B,e1,k)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,B
(A,F1,a,e,e1,F2,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,F2,e),(A,F1,a,F2,e1)
(A,a,B,(A,F1,a,F2,e),(A,F1,a,F2,e1),(A,F1,a,e,e1,F2,a),k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,a,B,(A,F1,a,F2,e),k),(A,a,B,(A,F1,a,F2,e1),k)
(A,a,B,(A,F1,a,F2,e),k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,B
(A,a,B,(A,F1,a,F2,e1),k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,B
G1t is M2( the carrier of A)
(A,F1,a,F2,e) . G1t is M2( 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 ObjectMap of (A,F1,a,F2,e) 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]) M2( 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 ObjectMap of (A,F1,a,F2,e) . (G1t,G1t) is M2([: the carrier of a, the carrier of a:])
[G1t,G1t] is set
the ObjectMap of (A,F1,a,F2,e) . [G1t,G1t] is set
K40(( the ObjectMap of (A,F1,a,F2,e) . (G1t,G1t))) is set
F2 . G1t is M2( the carrier of F1)
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of F2 is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . (G1t,G1t) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [G1t,G1t] is set
K40(( the ObjectMap of F2 . (G1t,G1t))) is set
e . (F2 . G1t) is M2( the carrier of a)
the ObjectMap of e is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:] is non empty set
the ObjectMap of e . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of a, the carrier of a:])
[(F2 . G1t),(F2 . G1t)] is set
the ObjectMap of e . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of e . ((F2 . G1t),(F2 . G1t)))) is set
(A,F1,a,F2,e1) . G1t is M2( the carrier of a)
the ObjectMap of (A,F1,a,F2,e1) 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]:])
the ObjectMap of (A,F1,a,F2,e1) . (G1t,G1t) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of (A,F1,a,F2,e1) . [G1t,G1t] is set
K40(( the ObjectMap of (A,F1,a,F2,e1) . (G1t,G1t))) is set
e1 . (F2 . G1t) is M2( the carrier of a)
the ObjectMap of e1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:])
the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of e1 . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)))) is set
(A,F1,B,(F1,a,B,e,k),(F1,a,B,e1,k),F2,(F1,a,B,e,e1,a,k)) ! G1t is M2(<^((A,F1,B,F2,(F1,a,B,e,k)) . G1t),((A,F1,B,F2,(F1,a,B,e1,k)) . G1t)^>)
(A,F1,B,F2,(F1,a,B,e,k)) . G1t is M2( 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 ObjectMap of (A,F1,B,F2,(F1,a,B,e,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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of (A,F1,B,F2,(F1,a,B,e,k)) . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (A,F1,B,F2,(F1,a,B,e,k)) . [G1t,G1t] is set
K40(( the ObjectMap of (A,F1,B,F2,(F1,a,B,e,k)) . (G1t,G1t))) is set
(A,F1,B,F2,(F1,a,B,e1,k)) . G1t is M2( the carrier of B)
the ObjectMap of (A,F1,B,F2,(F1,a,B,e1,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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (A,F1,B,F2,(F1,a,B,e1,k)) . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (A,F1,B,F2,(F1,a,B,e1,k)) . [G1t,G1t] is set
K40(( the ObjectMap of (A,F1,B,F2,(F1,a,B,e1,k)) . (G1t,G1t))) is set
<^((A,F1,B,F2,(F1,a,B,e,k)) . G1t),((A,F1,B,F2,(F1,a,B,e1,k)) . G1t)^> is set
(F1,a,B,e,e1,a,k) ! (F2 . G1t) is M2(<^((F1,a,B,e,k) . (F2 . G1t)),((F1,a,B,e1,k) . (F2 . G1t))^>)
(F1,a,B,e,k) . (F2 . G1t) is M2( the carrier of B)
the ObjectMap of (F1,a,B,e,k) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is non empty set
the ObjectMap of (F1,a,B,e,k) . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (F1,a,B,e,k) . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of (F1,a,B,e,k) . ((F2 . G1t),(F2 . G1t)))) is set
(F1,a,B,e1,k) . (F2 . G1t) is M2( the carrier of B)
the ObjectMap of (F1,a,B,e1,k) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (F1,a,B,e1,k) . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (F1,a,B,e1,k) . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of (F1,a,B,e1,k) . ((F2 . G1t),(F2 . G1t)))) is set
<^((F1,a,B,e,k) . (F2 . G1t)),((F1,a,B,e1,k) . (F2 . G1t))^> is set
a ! (F2 . G1t) is M2(<^(e . (F2 . G1t)),(e1 . (F2 . G1t))^>)
<^(e . (F2 . G1t)),(e1 . (F2 . G1t))^> is set
k . (a ! (F2 . G1t)) is M2(<^(k . (e . (F2 . G1t))),(k . (e1 . (F2 . G1t)))^>)
k . (e . (F2 . G1t)) is M2( the carrier of B)
the ObjectMap of 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:]) V18([: the carrier of a, the carrier of a:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of k . ((e . (F2 . G1t)),(e . (F2 . G1t))) is M2([: the carrier of B, the carrier of B:])
[(e . (F2 . G1t)),(e . (F2 . G1t))] is set
the ObjectMap of k . [(e . (F2 . G1t)),(e . (F2 . G1t))] is set
K40(( the ObjectMap of k . ((e . (F2 . G1t)),(e . (F2 . G1t))))) is set
k . (e1 . (F2 . G1t)) is M2( the carrier of B)
the ObjectMap of k . ((e1 . (F2 . G1t)),(e1 . (F2 . G1t))) is M2([: the carrier of B, the carrier of B:])
[(e1 . (F2 . G1t)),(e1 . (F2 . G1t))] is set
the ObjectMap of k . [(e1 . (F2 . G1t)),(e1 . (F2 . G1t))] is set
K40(( the ObjectMap of k . ((e1 . (F2 . G1t)),(e1 . (F2 . G1t))))) is set
<^(k . (e . (F2 . G1t))),(k . (e1 . (F2 . G1t)))^> is set
(A,F1,a,e,e1,F2,a) ! G1t is M2(<^((A,F1,a,F2,e) . G1t),((A,F1,a,F2,e1) . G1t)^>)
<^((A,F1,a,F2,e) . G1t),((A,F1,a,F2,e1) . G1t)^> is set
k . ((A,F1,a,e,e1,F2,a) ! G1t) is M2(<^(k . ((A,F1,a,F2,e) . G1t)),(k . ((A,F1,a,F2,e1) . G1t))^>)
k . ((A,F1,a,F2,e) . G1t) is M2( the carrier of B)
the ObjectMap of k . (((A,F1,a,F2,e) . G1t),((A,F1,a,F2,e) . G1t)) is M2([: the carrier of B, the carrier of B:])
[((A,F1,a,F2,e) . G1t),((A,F1,a,F2,e) . G1t)] is set
the ObjectMap of k . [((A,F1,a,F2,e) . G1t),((A,F1,a,F2,e) . G1t)] is set
K40(( the ObjectMap of k . (((A,F1,a,F2,e) . G1t),((A,F1,a,F2,e) . G1t)))) is set
k . ((A,F1,a,F2,e1) . G1t) is M2( the carrier of B)
the ObjectMap of k . (((A,F1,a,F2,e1) . G1t),((A,F1,a,F2,e1) . G1t)) is M2([: the carrier of B, the carrier of B:])
[((A,F1,a,F2,e1) . G1t),((A,F1,a,F2,e1) . G1t)] is set
the ObjectMap of k . [((A,F1,a,F2,e1) . G1t),((A,F1,a,F2,e1) . G1t)] is set
K40(( the ObjectMap of k . (((A,F1,a,F2,e1) . G1t),((A,F1,a,F2,e1) . G1t)))) is set
<^(k . ((A,F1,a,F2,e) . G1t)),(k . ((A,F1,a,F2,e1) . G1t))^> is set
(A,a,B,(A,F1,a,F2,e),(A,F1,a,F2,e1),(A,F1,a,e,e1,F2,a),k) ! G1t is M2(<^((A,a,B,(A,F1,a,F2,e),k) . G1t),((A,a,B,(A,F1,a,F2,e1),k) . G1t)^>)
(A,a,B,(A,F1,a,F2,e),k) . G1t is M2( the carrier of B)
the ObjectMap of (A,a,B,(A,F1,a,F2,e),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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (A,a,B,(A,F1,a,F2,e),k) . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (A,a,B,(A,F1,a,F2,e),k) . [G1t,G1t] is set
K40(( the ObjectMap of (A,a,B,(A,F1,a,F2,e),k) . (G1t,G1t))) is set
(A,a,B,(A,F1,a,F2,e1),k) . G1t is M2( the carrier of B)
the ObjectMap of (A,a,B,(A,F1,a,F2,e1),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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (A,a,B,(A,F1,a,F2,e1),k) . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (A,a,B,(A,F1,a,F2,e1),k) . [G1t,G1t] is set
K40(( the ObjectMap of (A,a,B,(A,F1,a,F2,e1),k) . (G1t,G1t))) is set
<^((A,a,B,(A,F1,a,F2,e),k) . G1t),((A,a,B,(A,F1,a,F2,e1),k) . G1t)^> is set
sF2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,B,F2,(F1,a,B,e,k)),(A,F1,B,F2,(F1,a,B,e1,k))
sF2 ! G1t is M2(<^((A,F1,B,F2,(F1,a,B,e,k)) . G1t),((A,F1,B,F2,(F1,a,B,e1,k)) . G1t)^>)
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
the carrier of F1 is non empty set
a is non empty transitive with_units reflexive AltCatStr
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,a
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,a
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of a,A
(F1,a,A,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,A
(F1,a,A,e,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,A
k is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
(a,A,B,e1,k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,B
a is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of F2,e
(F1,a,B,F2,e,a,(a,A,B,e1,k)) is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of (F1,a,B,F2,(a,A,B,e1,k)),(F1,a,B,e,(a,A,B,e1,k))
(F1,a,B,F2,(a,A,B,e1,k)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,B
(F1,a,B,e,(a,A,B,e1,k)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,B
(F1,a,A,F2,e,a,e1) is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of (F1,a,A,F2,e1),(F1,a,A,e,e1)
(F1,A,B,(F1,a,A,F2,e1),(F1,a,A,e,e1),(F1,a,A,F2,e,a,e1),k) is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of (F1,A,B,(F1,a,A,F2,e1),k),(F1,A,B,(F1,a,A,e,e1),k)
(F1,A,B,(F1,a,A,F2,e1),k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,B
(F1,A,B,(F1,a,A,e,e1),k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F1,B
G1t is M2( the carrier of F1)
(F1,a,A,F2,e1) . G1t is M2( 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 ObjectMap of (F1,a,A,F2,e1) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
[:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is non empty set
the ObjectMap of (F1,a,A,F2,e1) . (G1t,G1t) is M2([: the carrier of A, the carrier of A:])
[G1t,G1t] is set
the ObjectMap of (F1,a,A,F2,e1) . [G1t,G1t] is set
K40(( the ObjectMap of (F1,a,A,F2,e1) . (G1t,G1t))) is set
F2 . G1t is M2( 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 ObjectMap of F2 is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:] is non empty set
the ObjectMap of F2 . (G1t,G1t) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of F2 . [G1t,G1t] is set
K40(( the ObjectMap of F2 . (G1t,G1t))) is set
e1 . (F2 . G1t) is M2( the carrier of A)
the ObjectMap of e1 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:]) V18([: the carrier of a, the carrier of a:],[: the carrier of A, the carrier of A:]) M2( 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 e1 . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of A, the carrier of A:])
[(F2 . G1t),(F2 . G1t)] is set
the ObjectMap of e1 . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)))) is set
(F1,a,A,e,e1) . G1t is M2( the carrier of A)
the ObjectMap of (F1,a,A,e,e1) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (F1,a,A,e,e1) . (G1t,G1t) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (F1,a,A,e,e1) . [G1t,G1t] is set
K40(( the ObjectMap of (F1,a,A,e,e1) . (G1t,G1t))) is set
e . G1t is M2( the carrier of a)
the ObjectMap of e is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of a, the carrier of a:]:])
the ObjectMap of e . (G1t,G1t) is M2([: the carrier of a, the carrier of a:])
the ObjectMap of e . [G1t,G1t] is set
K40(( the ObjectMap of e . (G1t,G1t))) is set
e1 . (e . G1t) is M2( the carrier of A)
the ObjectMap of e1 . ((e . G1t),(e . G1t)) is M2([: the carrier of A, the carrier of A:])
[(e . G1t),(e . G1t)] is set
the ObjectMap of e1 . [(e . G1t),(e . G1t)] is set
K40(( the ObjectMap of e1 . ((e . G1t),(e . G1t)))) is set
<^(F2 . G1t),(e . G1t)^> is set
(F1,a,B,F2,e,a,(a,A,B,e1,k)) ! G1t is M2(<^((F1,a,B,F2,(a,A,B,e1,k)) . G1t),((F1,a,B,e,(a,A,B,e1,k)) . G1t)^>)
(F1,a,B,F2,(a,A,B,e1,k)) . G1t is M2( 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 ObjectMap of (F1,a,B,F2,(a,A,B,e1,k)) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:] is non empty set
the ObjectMap of (F1,a,B,F2,(a,A,B,e1,k)) . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (F1,a,B,F2,(a,A,B,e1,k)) . [G1t,G1t] is set
K40(( the ObjectMap of (F1,a,B,F2,(a,A,B,e1,k)) . (G1t,G1t))) is set
(F1,a,B,e,(a,A,B,e1,k)) . G1t is M2( the carrier of B)
the ObjectMap of (F1,a,B,e,(a,A,B,e1,k)) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (F1,a,B,e,(a,A,B,e1,k)) . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (F1,a,B,e,(a,A,B,e1,k)) . [G1t,G1t] is set
K40(( the ObjectMap of (F1,a,B,e,(a,A,B,e1,k)) . (G1t,G1t))) is set
<^((F1,a,B,F2,(a,A,B,e1,k)) . G1t),((F1,a,B,e,(a,A,B,e1,k)) . G1t)^> is set
a ! G1t is M2(<^(F2 . G1t),(e . G1t)^>)
(a,A,B,e1,k) . (a ! G1t) is M2(<^((a,A,B,e1,k) . (F2 . G1t)),((a,A,B,e1,k) . (e . G1t))^>)
(a,A,B,e1,k) . (F2 . G1t) is M2( the carrier of B)
the ObjectMap of (a,A,B,e1,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:]) V18([: the carrier of a, the carrier of a:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of (a,A,B,e1,k) . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (a,A,B,e1,k) . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of (a,A,B,e1,k) . ((F2 . G1t),(F2 . G1t)))) is set
(a,A,B,e1,k) . (e . G1t) is M2( the carrier of B)
the ObjectMap of (a,A,B,e1,k) . ((e . G1t),(e . G1t)) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (a,A,B,e1,k) . [(e . G1t),(e . G1t)] is set
K40(( the ObjectMap of (a,A,B,e1,k) . ((e . G1t),(e . G1t)))) is set
<^((a,A,B,e1,k) . (F2 . G1t)),((a,A,B,e1,k) . (e . G1t))^> is set
e1 . (a ! G1t) is M2(<^(e1 . (F2 . G1t)),(e1 . (e . G1t))^>)
<^(e1 . (F2 . G1t)),(e1 . (e . G1t))^> is set
k . (e1 . (a ! G1t)) is M2(<^(k . (e1 . (F2 . G1t))),(k . (e1 . (e . G1t)))^>)
k . (e1 . (F2 . G1t)) is M2( the carrier of B)
the ObjectMap of 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of k . ((e1 . (F2 . G1t)),(e1 . (F2 . G1t))) is M2([: the carrier of B, the carrier of B:])
[(e1 . (F2 . G1t)),(e1 . (F2 . G1t))] is set
the ObjectMap of k . [(e1 . (F2 . G1t)),(e1 . (F2 . G1t))] is set
K40(( the ObjectMap of k . ((e1 . (F2 . G1t)),(e1 . (F2 . G1t))))) is set
k . (e1 . (e . G1t)) is M2( the carrier of B)
the ObjectMap of k . ((e1 . (e . G1t)),(e1 . (e . G1t))) is M2([: the carrier of B, the carrier of B:])
[(e1 . (e . G1t)),(e1 . (e . G1t))] is set
the ObjectMap of k . [(e1 . (e . G1t)),(e1 . (e . G1t))] is set
K40(( the ObjectMap of k . ((e1 . (e . G1t)),(e1 . (e . G1t))))) is set
<^(k . (e1 . (F2 . G1t))),(k . (e1 . (e . G1t)))^> is set
(F1,a,A,F2,e,a,e1) ! G1t is M2(<^((F1,a,A,F2,e1) . G1t),((F1,a,A,e,e1) . G1t)^>)
<^((F1,a,A,F2,e1) . G1t),((F1,a,A,e,e1) . G1t)^> is set
k . ((F1,a,A,F2,e,a,e1) ! G1t) is M2(<^(k . ((F1,a,A,F2,e1) . G1t)),(k . ((F1,a,A,e,e1) . G1t))^>)
k . ((F1,a,A,F2,e1) . G1t) is M2( the carrier of B)
the ObjectMap of k . (((F1,a,A,F2,e1) . G1t),((F1,a,A,F2,e1) . G1t)) is M2([: the carrier of B, the carrier of B:])
[((F1,a,A,F2,e1) . G1t),((F1,a,A,F2,e1) . G1t)] is set
the ObjectMap of k . [((F1,a,A,F2,e1) . G1t),((F1,a,A,F2,e1) . G1t)] is set
K40(( the ObjectMap of k . (((F1,a,A,F2,e1) . G1t),((F1,a,A,F2,e1) . G1t)))) is set
k . ((F1,a,A,e,e1) . G1t) is M2( the carrier of B)
the ObjectMap of k . (((F1,a,A,e,e1) . G1t),((F1,a,A,e,e1) . G1t)) is M2([: the carrier of B, the carrier of B:])
[((F1,a,A,e,e1) . G1t),((F1,a,A,e,e1) . G1t)] is set
the ObjectMap of k . [((F1,a,A,e,e1) . G1t),((F1,a,A,e,e1) . G1t)] is set
K40(( the ObjectMap of k . (((F1,a,A,e,e1) . G1t),((F1,a,A,e,e1) . G1t)))) is set
<^(k . ((F1,a,A,F2,e1) . G1t)),(k . ((F1,a,A,e,e1) . G1t))^> is set
(F1,A,B,(F1,a,A,F2,e1),(F1,a,A,e,e1),(F1,a,A,F2,e,a,e1),k) ! G1t is M2(<^((F1,A,B,(F1,a,A,F2,e1),k) . G1t),((F1,A,B,(F1,a,A,e,e1),k) . G1t)^>)
(F1,A,B,(F1,a,A,F2,e1),k) . G1t is M2( the carrier of B)
the ObjectMap of (F1,A,B,(F1,a,A,F2,e1),k) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (F1,A,B,(F1,a,A,F2,e1),k) . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (F1,A,B,(F1,a,A,F2,e1),k) . [G1t,G1t] is set
K40(( the ObjectMap of (F1,A,B,(F1,a,A,F2,e1),k) . (G1t,G1t))) is set
(F1,A,B,(F1,a,A,e,e1),k) . G1t is M2( the carrier of B)
the ObjectMap of (F1,A,B,(F1,a,A,e,e1),k) is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of B, the carrier of B:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of (F1,A,B,(F1,a,A,e,e1),k) . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of (F1,A,B,(F1,a,A,e,e1),k) . [G1t,G1t] is set
K40(( the ObjectMap of (F1,A,B,(F1,a,A,e,e1),k) . (G1t,G1t))) is set
<^((F1,A,B,(F1,a,A,F2,e1),k) . G1t),((F1,A,B,(F1,a,A,e,e1),k) . G1t)^> is set
sF2 is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of (F1,a,B,F2,(a,A,B,e1,k)),(F1,a,B,e,(a,A,B,e1,k))
sF2 ! G1t is M2(<^((F1,a,B,F2,(a,A,B,e1,k)) . G1t),((F1,a,B,e,(a,A,B,e1,k)) . G1t)^>)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
idt F2 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of F2,F2
the carrier of B is non empty set
(A,B,F1,F2,F2,a,(idt F2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,F2)
(A,B,F1,a,F2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
idt (A,B,F1,a,F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of (A,B,F1,a,F2),(A,B,F1,a,F2)
e is M2( the carrier of A)
(A,B,F1,F2,F2,a,(idt F2)) ! e is M2(<^((A,B,F1,a,F2) . e),((A,B,F1,a,F2) . e)^>)
(A,B,F1,a,F2) . e is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,a,F2) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,F2) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
[e,e] is set
the ObjectMap of (A,B,F1,a,F2) . [e,e] is set
K40(( the ObjectMap of (A,B,F1,a,F2) . (e,e))) is set
<^((A,B,F1,a,F2) . e),((A,B,F1,a,F2) . e)^> is non empty set
a . e is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
(idt F2) ! (a . e) is M2(<^(F2 . (a . e)),(F2 . (a . e))^>)
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
<^(F2 . (a . e)),(F2 . (a . e))^> is non empty set
idm (F2 . (a . e)) is retraction coretraction mono epi M2(<^(F2 . (a . e)),(F2 . (a . e))^>)
idm ((A,B,F1,a,F2) . e) is retraction coretraction mono epi M2(<^((A,B,F1,a,F2) . e),((A,B,F1,a,F2) . e)^>)
(idt (A,B,F1,a,F2)) ! e is M2(<^((A,B,F1,a,F2) . e),((A,B,F1,a,F2) . e)^>)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
idt a is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,a
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,a,(idt a),F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,F2)
(A,B,F1,a,F2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
idt (A,B,F1,a,F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of (A,B,F1,a,F2),(A,B,F1,a,F2)
e is M2( the carrier of A)
(A,B,F1,a,a,(idt a),F2) ! e is M2(<^((A,B,F1,a,F2) . e),((A,B,F1,a,F2) . e)^>)
(A,B,F1,a,F2) . e is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,a,F2) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,F2) . (e,e) is M2([: the carrier of F1, the carrier of F1:])
[e,e] is set
the ObjectMap of (A,B,F1,a,F2) . [e,e] is set
K40(( the ObjectMap of (A,B,F1,a,F2) . (e,e))) is set
<^((A,B,F1,a,F2) . e),((A,B,F1,a,F2) . e)^> is non empty set
a . e is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
(idt a) ! e is M2(<^(a . e),(a . e)^>)
<^(a . e),(a . e)^> is non empty set
F2 . ((idt a) ! e) is M2(<^(F2 . (a . e)),(F2 . (a . e))^>)
F2 . (a . e) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . e),(a . e)) is M2([: the carrier of F1, the carrier of F1:])
[(a . e),(a . e)] is set
the ObjectMap of F2 . [(a . e),(a . e)] is set
K40(( the ObjectMap of F2 . ((a . e),(a . e)))) is set
<^(F2 . (a . e)),(F2 . (a . e))^> is non empty set
idm (a . e) is retraction coretraction mono epi M2(<^(a . e),(a . e)^>)
F2 . (idm (a . e)) is M2(<^(F2 . (a . e)),(F2 . (a . e))^>)
idm (F2 . (a . e)) is retraction coretraction mono epi M2(<^(F2 . (a . e)),(F2 . (a . e))^>)
idm ((A,B,F1,a,F2) . e) is retraction coretraction mono epi M2(<^((A,B,F1,a,F2) . e),((A,B,F1,a,F2) . e)^>)
(idt (A,B,F1,a,F2)) ! e is M2(<^((A,B,F1,a,F2) . e),((A,B,F1,a,F2) . e)^>)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
id B is reflexive feasible strict Covariant id-preserving comp-preserving covariant V165(B,B) Functor of B,B
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F1,a
(A,B,B,F1,a,F2,(id B)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,B,F1,(id B)),(A,B,B,a,(id B))
(A,B,B,F1,(id B)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,B
(A,B,B,a,(id B)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,B
e is set
e1 is M2( the carrier of A)
F1 . e1 is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (e1,e1) is M2([: the carrier of B, the carrier of B:])
[e1,e1] is set
the ObjectMap of F1 . [e1,e1] is set
K40(( the ObjectMap of F1 . (e1,e1))) is set
a . e1 is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
<^(F1 . e1),(a . e1)^> is set
(A,B,B,F1,a,F2,(id B)) . e is set
F2 ! e1 is M2(<^(F1 . e1),(a . e1)^>)
(id B) . (F2 ! e1) is M2(<^((id B) . (F1 . e1)),((id B) . (a . e1))^>)
(id B) . (F1 . e1) is M2( the carrier of B)
the ObjectMap of (id B) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of (id B) . ((F1 . e1),(F1 . e1)) is M2([: the carrier of B, the carrier of B:])
[(F1 . e1),(F1 . e1)] is set
the ObjectMap of (id B) . [(F1 . e1),(F1 . e1)] is set
K40(( the ObjectMap of (id B) . ((F1 . e1),(F1 . e1)))) is set
(id B) . (a . e1) is M2( the carrier of B)
the ObjectMap of (id B) . ((a . e1),(a . e1)) is M2([: the carrier of B, the carrier of B:])
[(a . e1),(a . e1)] is set
the ObjectMap of (id B) . [(a . e1),(a . e1)] is set
K40(( the ObjectMap of (id B) . ((a . e1),(a . e1)))) is set
<^((id B) . (F1 . e1)),((id B) . (a . e1))^> is set
F2 . e 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
id B is reflexive feasible strict Covariant id-preserving comp-preserving covariant V165(B,B) Functor of B,B
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
F2 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of F1,a
(B,B,A,F1,a,(id B),F2) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,B,A,(id B),F1),(B,B,A,(id B),a)
(B,B,A,(id B),F1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,B,A,(id B),a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
e is set
(B,B,A,F1,a,(id B),F2) . e is set
e1 is M2( the carrier of B)
(id B) . e1 is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap of (id B) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of (id B) . (e1,e1) is M2([: the carrier of B, the carrier of B:])
[e1,e1] is set
the ObjectMap of (id B) . [e1,e1] is set
K40(( the ObjectMap of (id B) . (e1,e1))) is set
F2 ! ((id B) . e1) is M2(<^(F1 . ((id B) . e1)),(a . ((id B) . e1))^>)
F1 . ((id B) . e1) is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 F1 . (((id B) . e1),((id B) . e1)) is M2([: the carrier of A, the carrier of A:])
[((id B) . e1),((id B) . e1)] is set
the ObjectMap of F1 . [((id B) . e1),((id B) . e1)] is set
K40(( the ObjectMap of F1 . (((id B) . e1),((id B) . e1)))) is set
a . ((id B) . e1) is M2( the carrier of A)
the ObjectMap 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 non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of a . (((id B) . e1),((id B) . e1)) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [((id B) . e1),((id B) . e1)] is set
K40(( the ObjectMap of a . (((id B) . e1),((id B) . e1)))) is set
<^(F1 . ((id B) . e1)),(a . ((id B) . e1))^> is set
F2 ! e1 is M2(<^(F1 . e1),(a . e1)^>)
F1 . e1 is M2( the carrier of A)
the ObjectMap of F1 . (e1,e1) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of F1 . [e1,e1] is set
K40(( the ObjectMap of F1 . (e1,e1))) is set
a . e1 is M2( the carrier of A)
the ObjectMap of a . (e1,e1) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
<^(F1 . e1),(a . e1)^> is set
F2 . e is set
A is non empty transitive with_units reflexive AltCatStr
B is non empty transitive with_units reflexive AltCatStr
F1 is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
the carrier of B is non empty set
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
k is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of a,F2
(A,B,F1,a,F2,k,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e)
a is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of e,e1
(A,B,F1,e,e1,F2,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,e),(A,B,F1,F2,e1)
(A,B,F1,e,e1,F2,a) `*` (A,B,F1,a,F2,k,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e1)
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
F1 is non empty transitive with_units reflexive AltCatStr
the carrier of F1 is non empty set
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,A
(B,F1,A,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,A
(B,F1,A,a,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,F1,A,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
k is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of a,F2
(B,F1,A,a,F2,k,e1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e1),(B,F1,A,F2,e1)
a is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) natural_transformation of e,e1
(B,F1,A,a,F2,e,e1,k,a) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e1)
(B,F1,A,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,F1,A,a,F2,k,e) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e)
(B,F1,A,e,e1,F2,a) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,F2,e),(B,F1,A,F2,e1)
(B,F1,A,e,e1,F2,a) `*` (B,F1,A,a,F2,k,e) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e1)
(B,F1,A,e,e1,a,a) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,a,e1)
(B,F1,A,a,F2,k,e1) `*` (B,F1,A,e,e1,a,a) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e1)
sF2 is M2( the carrier of B)
a . sF2 is M2( the carrier of F1)
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of a is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of a . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
[sF2,sF2] is set
the ObjectMap of a . [sF2,sF2] is set
K40(( the ObjectMap of a . (sF2,sF2))) is set
e . (a . sF2) is M2( 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 ObjectMap of e is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is non empty set
the ObjectMap of e . ((a . sF2),(a . sF2)) is M2([: the carrier of A, the carrier of A:])
[(a . sF2),(a . sF2)] is set
the ObjectMap of e . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of e . ((a . sF2),(a . sF2)))) is set
(B,F1,A,a,e) . sF2 is M2( the carrier of A)
the ObjectMap of (B,F1,A,a,e) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 (B,F1,A,a,e) . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,a,e) . [sF2,sF2] is set
K40(( the ObjectMap of (B,F1,A,a,e) . (sF2,sF2))) is set
F2 . sF2 is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of F2 . (sF2,sF2) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [sF2,sF2] is set
K40(( the ObjectMap of F2 . (sF2,sF2))) is set
e1 . (F2 . sF2) is M2( the carrier of A)
the ObjectMap of e1 is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of e1 . ((F2 . sF2),(F2 . sF2)) is M2([: the carrier of A, the carrier of A:])
[(F2 . sF2),(F2 . sF2)] is set
the ObjectMap of e1 . [(F2 . sF2),(F2 . sF2)] is set
K40(( the ObjectMap of e1 . ((F2 . sF2),(F2 . sF2)))) is set
(B,F1,A,F2,e1) . sF2 is M2( the carrier of A)
the ObjectMap of (B,F1,A,F2,e1) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (B,F1,A,F2,e1) . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,F2,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (B,F1,A,F2,e1) . (sF2,sF2))) is set
(B,F1,A,F2,e) . sF2 is M2( the carrier of A)
the ObjectMap of (B,F1,A,F2,e) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (B,F1,A,F2,e) . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,F2,e) . [sF2,sF2] is set
K40(( the ObjectMap of (B,F1,A,F2,e) . (sF2,sF2))) is set
<^((B,F1,A,F2,e) . sF2),((B,F1,A,F2,e1) . sF2)^> is set
a ! (F2 . sF2) is M2(<^(e . (F2 . sF2)),(e1 . (F2 . sF2))^>)
e . (F2 . sF2) is M2( the carrier of A)
the ObjectMap of e . ((F2 . sF2),(F2 . sF2)) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of e . [(F2 . sF2),(F2 . sF2)] is set
K40(( the ObjectMap of e . ((F2 . sF2),(F2 . sF2)))) is set
<^(e . (F2 . sF2)),(e1 . (F2 . sF2))^> is set
e1 . (a . sF2) is M2( the carrier of A)
the ObjectMap of e1 . ((a . sF2),(a . sF2)) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of e1 . [(a . sF2),(a . sF2)] is set
K40(( the ObjectMap of e1 . ((a . sF2),(a . sF2)))) is set
<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^> is set
(B,F1,A,a,F2,k,e1) ! sF2 is M2(<^((B,F1,A,a,e1) . sF2),((B,F1,A,F2,e1) . sF2)^>)
(B,F1,A,a,e1) . sF2 is M2( the carrier of A)
the ObjectMap of (B,F1,A,a,e1) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (B,F1,A,a,e1) . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,a,e1) . [sF2,sF2] is set
K40(( the ObjectMap of (B,F1,A,a,e1) . (sF2,sF2))) is set
<^((B,F1,A,a,e1) . sF2),((B,F1,A,F2,e1) . sF2)^> is set
<^(a . sF2),(F2 . sF2)^> is set
((B,F1,A,e,e1,F2,a) `*` (B,F1,A,a,F2,k,e)) ! sF2 is M2(<^((B,F1,A,a,e) . sF2),((B,F1,A,F2,e1) . sF2)^>)
<^((B,F1,A,a,e) . sF2),((B,F1,A,F2,e1) . sF2)^> is set
(B,F1,A,a,F2,k,e) ! sF2 is M2(<^((B,F1,A,a,e) . sF2),((B,F1,A,F2,e) . sF2)^>)
<^((B,F1,A,a,e) . sF2),((B,F1,A,F2,e) . sF2)^> is set
(B,F1,A,e,e1,F2,a) ! sF2 is M2(<^((B,F1,A,F2,e) . sF2),((B,F1,A,F2,e1) . sF2)^>)
((B,F1,A,e,e1,F2,a) ! sF2) * ((B,F1,A,a,F2,k,e) ! sF2) is M2(<^((B,F1,A,a,e) . sF2),((B,F1,A,F2,e1) . sF2)^>)
G1t is M2(<^((B,F1,A,F2,e) . sF2),((B,F1,A,F2,e1) . sF2)^>)
G1t * ((B,F1,A,a,F2,k,e) ! sF2) is M2(<^((B,F1,A,a,e) . sF2),((B,F1,A,F2,e1) . sF2)^>)
k ! sF2 is M2(<^(a . sF2),(F2 . sF2)^>)
e . (k ! sF2) is M2(<^(e . (a . sF2)),(e . (F2 . sF2))^>)
<^(e . (a . sF2)),(e . (F2 . sF2))^> is set
(a ! (F2 . sF2)) * (e . (k ! sF2)) is M2(<^(e . (a . sF2)),(e1 . (F2 . sF2))^>)
<^(e . (a . sF2)),(e1 . (F2 . sF2))^> is set
a ! (a . sF2) is M2(<^(e . (a . sF2)),(e1 . (a . sF2))^>)
<^(e . (a . sF2)),(e1 . (a . sF2))^> is set
e1 . (k ! sF2) is M2(<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^>)
(e1 . (k ! sF2)) * (a ! (a . sF2)) is M2(<^(e . (a . sF2)),(e1 . (F2 . sF2))^>)
fa is M2(<^(e1 . (a . sF2)),(e1 . (F2 . sF2))^>)
fa * (a ! (a . sF2)) is M2(<^(e . (a . sF2)),(e1 . (F2 . sF2))^>)
(B,F1,A,e,e1,a,a) ! sF2 is M2(<^((B,F1,A,a,e) . sF2),((B,F1,A,a,e1) . sF2)^>)
<^((B,F1,A,a,e) . sF2),((B,F1,A,a,e1) . sF2)^> is set
((B,F1,A,a,F2,k,e1) ! sF2) * ((B,F1,A,e,e1,a,a) ! sF2) is M2(<^((B,F1,A,a,e) . sF2),((B,F1,A,F2,e1) . sF2)^>)
((B,F1,A,a,F2,k,e1) `*` (B,F1,A,e,e1,a,a)) ! sF2 is M2(<^((B,F1,A,a,e) . sF2),((B,F1,A,F2,e1) . sF2)^>)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
id B is reflexive feasible strict Covariant id-preserving comp-preserving covariant V165(B,B) Functor of B,B
idt (id B) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of id B, id B
the carrier of B is non empty set
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F1,a
(A,B,B,F1,a,(id B),(id B),F2,(idt (id B))) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,B,F1,(id B)),(A,B,B,a,(id B))
(A,B,B,F1,(id B)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,B
(A,B,B,a,(id B)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,B
(A,B,B,F1,a,F2,(id B)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,B,F1,(id B)),(A,B,B,a,(id B))
(A,B,B,(id B),(id B),a,(idt (id B))) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,B,a,(id B)),(A,B,B,a,(id B))
(A,B,B,(id B),(id B),a,(idt (id B))) `*` (A,B,B,F1,a,F2,(id B)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,B,F1,(id B)),(A,B,B,a,(id B))
idt (A,B,B,a,(id B)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of (A,B,B,a,(id B)),(A,B,B,a,(id B))
(idt (A,B,B,a,(id B))) `*` (A,B,B,F1,a,F2,(id B)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,B,F1,(id B)),(A,B,B,a,(id B))
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
id B is reflexive feasible strict Covariant id-preserving comp-preserving covariant V165(B,B) Functor of B,B
idt (id B) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of id B, id B
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
F2 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of F1,a
(B,B,A,(id B),(id B),F1,a,(idt (id B)),F2) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,B,A,(id B),F1),(B,B,A,(id B),a)
(B,B,A,(id B),F1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,B,A,(id B),a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,B,A,(id B),(id B),(idt (id B)),F1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,B,A,(id B),F1),(B,B,A,(id B),F1)
(B,B,A,F1,a,(id B),F2) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,B,A,(id B),F1),(B,B,A,(id B),a)
(B,B,A,F1,a,(id B),F2) `*` (B,B,A,(id B),(id B),(idt (id B)),F1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,B,A,(id B),F1),(B,B,A,(id B),a)
idt (B,B,A,(id B),F1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of (B,B,A,(id B),F1),(B,B,A,(id B),F1)
(B,B,A,F1,a,(id B),F2) `*` (idt (B,B,A,(id B),F1)) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,B,A,(id B),F1),(B,B,A,(id B),a)
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
F1 is non empty transitive with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,A
idt e is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) natural_transformation of e,e
the carrier of F1 is non empty set
e1 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of a,F2
(B,F1,A,a,F2,e1,e) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e)
(B,F1,A,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,F1,A,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,F1,A,a,F2,e,e,e1,(idt e)) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e)
(B,F1,A,e,e,F2,(idt e)) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,F2,e),(B,F1,A,F2,e)
(B,F1,A,e,e,F2,(idt e)) `*` (B,F1,A,a,F2,e1,e) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e)
idt (B,F1,A,F2,e) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of (B,F1,A,F2,e),(B,F1,A,F2,e)
(idt (B,F1,A,F2,e)) `*` (B,F1,A,a,F2,e1,e) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e)
A is non empty transitive with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
idt a is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,a
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e1 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of F2,e
(A,B,F1,F2,e,a,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e)
(A,B,F1,a,F2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,a,a,F2,e,(idt a),e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e)
(A,B,F1,a,a,(idt a),F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,F2)
(A,B,F1,F2,e,a,e1) `*` (A,B,F1,a,a,(idt a),F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e)
idt (A,B,F1,a,F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of (A,B,F1,a,F2),(A,B,F1,a,F2)
(A,B,F1,F2,e,a,e1) `*` (idt (A,B,F1,a,F2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e)
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive associative with_units reflexive AltCatStr
the carrier of F1 is non empty set
a is non empty transitive associative with_units reflexive AltCatStr
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
k is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,e,k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,a
sF2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,a
(B,F1,a,e1,a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,a
(B,F1,a,k,sF2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,a
G1t is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F2,e
fa is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of e1,k
(A,B,F1,F2,e,e1,k,G1t,fa) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,e1),(A,B,F1,e,k)
(A,B,F1,e,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,e,G1t,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,e1),(A,B,F1,e,e1)
(A,B,F1,e1,k,e,fa) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,e,e1),(A,B,F1,e,k)
(A,B,F1,e1,k,e,fa) `*` (A,B,F1,F2,e,G1t,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,e1),(A,B,F1,e,k)
t1 is Relation-like the carrier of F1 -defined Function-like non empty V14( the carrier of F1) transformation of a,sF2
(B,F1,a,e1,k,a,sF2,fa,t1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,a,e1,a),(B,F1,a,k,sF2)
(B,F1,a,k,a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,a
(B,F1,a,e1,k,fa,a) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,a,e1,a),(B,F1,a,k,a)
(B,F1,a,a,sF2,k,t1) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,a,k,a),(B,F1,a,k,sF2)
(B,F1,a,a,sF2,k,t1) `*` (B,F1,a,e1,k,fa,a) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,a,e1,a),(B,F1,a,k,sF2)
(A,B,a,F2,e,(B,F1,a,e1,a),(B,F1,a,k,sF2),G1t,(B,F1,a,e1,k,a,sF2,fa,t1)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,F2,(B,F1,a,e1,a)),(A,B,a,e,(B,F1,a,k,sF2))
(A,B,a,F2,(B,F1,a,e1,a)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,B,a,e,(B,F1,a,k,sF2)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,B,a,e,(B,F1,a,e1,a)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,B,a,F2,e,G1t,(B,F1,a,e1,a)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,F2,(B,F1,a,e1,a)),(A,B,a,e,(B,F1,a,e1,a))
(A,B,a,(B,F1,a,e1,a),(B,F1,a,k,sF2),e,(B,F1,a,e1,k,a,sF2,fa,t1)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,e,(B,F1,a,e1,a)),(A,B,a,e,(B,F1,a,k,sF2))
(A,B,a,(B,F1,a,e1,a),(B,F1,a,k,sF2),e,(B,F1,a,e1,k,a,sF2,fa,t1)) `*` (A,B,a,F2,e,G1t,(B,F1,a,e1,a)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,F2,(B,F1,a,e1,a)),(A,B,a,e,(B,F1,a,k,sF2))
(A,F1,a,(A,B,F1,F2,e1),(A,B,F1,e,k),a,sF2,(A,B,F1,F2,e,e1,k,G1t,fa),t1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,F2,e1),a),(A,F1,a,(A,B,F1,e,k),sF2)
(A,F1,a,(A,B,F1,F2,e1),a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,F1,a,(A,B,F1,e,k),sF2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,F1,a,(A,B,F1,e,k),a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,F1,a,(A,B,F1,F2,e1),(A,B,F1,e,k),(A,B,F1,F2,e,e1,k,G1t,fa),a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,F2,e1),a),(A,F1,a,(A,B,F1,e,k),a)
(A,F1,a,a,sF2,(A,B,F1,e,k),t1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,e,k),a),(A,F1,a,(A,B,F1,e,k),sF2)
(A,F1,a,a,sF2,(A,B,F1,e,k),t1) `*` (A,F1,a,(A,B,F1,F2,e1),(A,B,F1,e,k),(A,B,F1,F2,e,e1,k,G1t,fa),a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,F2,e1),a),(A,F1,a,(A,B,F1,e,k),sF2)
(A,B,a,(B,F1,a,e1,a),(B,F1,a,k,a),e,(B,F1,a,e1,k,fa,a)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,e,(B,F1,a,e1,a)),(A,B,a,e,(B,F1,a,k,a))
(A,B,a,e,(B,F1,a,k,a)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,F1,a,(A,B,F1,e,e1),(A,B,F1,e,k),(A,B,F1,e1,k,e,fa),a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,e,e1),a),(A,F1,a,(A,B,F1,e,k),a)
(A,F1,a,(A,B,F1,e,e1),a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(A,F1,a,(A,B,F1,F2,e1),(A,B,F1,e,e1),(A,B,F1,F2,e,G1t,e1),a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,F2,e1),a),(A,F1,a,(A,B,F1,e,e1),a)
(A,B,a,(B,F1,a,k,a),(B,F1,a,k,sF2),e,(B,F1,a,a,sF2,k,t1)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,e,(B,F1,a,k,a)),(A,B,a,e,(B,F1,a,k,sF2))
(A,B,a,(B,F1,a,k,a),(B,F1,a,k,sF2),e,(B,F1,a,a,sF2,k,t1)) `*` (A,B,a,(B,F1,a,e1,a),(B,F1,a,k,a),e,(B,F1,a,e1,k,fa,a)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,e,(B,F1,a,e1,a)),(A,B,a,e,(B,F1,a,k,sF2))
((A,B,a,(B,F1,a,k,a),(B,F1,a,k,sF2),e,(B,F1,a,a,sF2,k,t1)) `*` (A,B,a,(B,F1,a,e1,a),(B,F1,a,k,a),e,(B,F1,a,e1,k,fa,a))) `*` (A,B,a,F2,e,G1t,(B,F1,a,e1,a)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,a,F2,(B,F1,a,e1,a)),(A,B,a,e,(B,F1,a,k,sF2))
(A,F1,a,(A,B,F1,e,e1),(A,B,F1,e,k),(A,B,F1,e1,k,e,fa),a) `*` (A,F1,a,(A,B,F1,F2,e1),(A,B,F1,e,e1),(A,B,F1,F2,e,G1t,e1),a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,F2,e1),a),(A,F1,a,(A,B,F1,e,k),a)
(A,F1,a,a,sF2,(A,B,F1,e,k),t1) `*` ((A,F1,a,(A,B,F1,e,e1),(A,B,F1,e,k),(A,B,F1,e1,k,e,fa),a) `*` (A,F1,a,(A,B,F1,F2,e1),(A,B,F1,e,e1),(A,B,F1,F2,e,G1t,e1),a)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,F1,a,(A,B,F1,F2,e1),a),(A,F1,a,(A,B,F1,e,k),sF2)
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
F1 is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
the carrier of A is non empty set
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,F2
k is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of e,e1
(A,B,F1,a,F2,e,e1,a,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e1)
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,a,F2,a,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e)
(A,B,F1,e,e1,F2,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,e),(A,B,F1,F2,e1)
(A,B,F1,e,e1,F2,k) `*` (A,B,F1,a,F2,a,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e1)
G1t is M2( the carrier of A)
fa is M2( the carrier of A)
<^G1t,fa^> is set
(A,B,F1,a,e) . G1t is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,a,e) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,e) . (G1t,G1t) is M2([: the carrier of F1, the carrier of F1:])
[G1t,G1t] is set
the ObjectMap of (A,B,F1,a,e) . [G1t,G1t] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (G1t,G1t))) is set
(A,B,F1,a,e) . fa is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e) . (fa,fa) is M2([: the carrier of F1, the carrier of F1:])
[fa,fa] is set
the ObjectMap of (A,B,F1,a,e) . [fa,fa] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (fa,fa))) is set
<^((A,B,F1,a,e) . G1t),((A,B,F1,a,e) . fa)^> is set
(A,B,F1,F2,e1) . G1t is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e1) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,F2,e1) . (G1t,G1t) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e1) . [G1t,G1t] is set
K40(( the ObjectMap of (A,B,F1,F2,e1) . (G1t,G1t))) is set
F2 . G1t is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F2 . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [G1t,G1t] is set
K40(( the ObjectMap of F2 . (G1t,G1t))) is set
e1 . (F2 . G1t) is M2( the carrier of F1)
the ObjectMap of e1 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of F1, the carrier of F1:])
[(F2 . G1t),(F2 . G1t)] is set
the ObjectMap of e1 . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of e1 . ((F2 . G1t),(F2 . G1t)))) is set
(A,B,F1,F2,e) . G1t is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,F2,e) . (G1t,G1t) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e) . [G1t,G1t] is set
K40(( the ObjectMap of (A,B,F1,F2,e) . (G1t,G1t))) is set
<^((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e1) . G1t)^> is set
k ! (F2 . G1t) is M2(<^(e . (F2 . G1t)),(e1 . (F2 . G1t))^>)
e . (F2 . G1t) is M2( the carrier of F1)
the ObjectMap of e is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of e . ((F2 . G1t),(F2 . G1t)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e . [(F2 . G1t),(F2 . G1t)] is set
K40(( the ObjectMap of e . ((F2 . G1t),(F2 . G1t)))) is set
<^(e . (F2 . G1t)),(e1 . (F2 . G1t))^> is set
(A,B,F1,F2,e1) . fa is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e1) . (fa,fa) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e1) . [fa,fa] is set
K40(( the ObjectMap of (A,B,F1,F2,e1) . (fa,fa))) is set
F2 . fa is M2( the carrier of B)
the ObjectMap of F2 . (fa,fa) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [fa,fa] is set
K40(( the ObjectMap of F2 . (fa,fa))) is set
e1 . (F2 . fa) is M2( the carrier of F1)
the ObjectMap of e1 . ((F2 . fa),(F2 . fa)) is M2([: the carrier of F1, the carrier of F1:])
[(F2 . fa),(F2 . fa)] is set
the ObjectMap of e1 . [(F2 . fa),(F2 . fa)] is set
K40(( the ObjectMap of e1 . ((F2 . fa),(F2 . fa)))) is set
(A,B,F1,F2,e) . fa is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e) . (fa,fa) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e) . [fa,fa] is set
K40(( the ObjectMap of (A,B,F1,F2,e) . (fa,fa))) is set
<^((A,B,F1,F2,e) . fa),((A,B,F1,F2,e1) . fa)^> is set
k ! (F2 . fa) is M2(<^(e . (F2 . fa)),(e1 . (F2 . fa))^>)
e . (F2 . fa) is M2( the carrier of F1)
the ObjectMap of e . ((F2 . fa),(F2 . fa)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e . [(F2 . fa),(F2 . fa)] is set
K40(( the ObjectMap of e . ((F2 . fa),(F2 . fa)))) is set
<^(e . (F2 . fa)),(e1 . (F2 . fa))^> is set
a . G1t is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (G1t,G1t) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [G1t,G1t] is set
K40(( the ObjectMap of a . (G1t,G1t))) is set
e . (a . G1t) is M2( the carrier of F1)
the ObjectMap of e . ((a . G1t),(a . G1t)) is M2([: the carrier of F1, the carrier of F1:])
[(a . G1t),(a . G1t)] is set
the ObjectMap of e . [(a . G1t),(a . G1t)] is set
K40(( the ObjectMap of e . ((a . G1t),(a . G1t)))) is set
<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e) . fa)^> is set
a . fa is M2( the carrier of B)
the ObjectMap of a . (fa,fa) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [fa,fa] is set
K40(( the ObjectMap of a . (fa,fa))) is set
f is M2(<^G1t,fa^>)
a . f is M2(<^(a . G1t),(a . fa)^>)
<^(a . G1t),(a . fa)^> is set
a ! fa is M2(<^(a . fa),(F2 . fa)^>)
<^(a . fa),(F2 . fa)^> is set
(a ! fa) * (a . f) is M2(<^(a . G1t),(F2 . fa)^>)
<^(a . G1t),(F2 . fa)^> is set
e . ((a ! fa) * (a . f)) is M2(<^(e . (a . G1t)),(e . (F2 . fa))^>)
<^(e . (a . G1t)),(e . (F2 . fa))^> is set
<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e) . G1t)^> is set
a ! G1t is M2(<^(a . G1t),(F2 . G1t)^>)
<^(a . G1t),(F2 . G1t)^> is set
e . (a ! G1t) is M2(<^(e . (a . G1t)),(e . (F2 . G1t))^>)
<^(e . (a . G1t)),(e . (F2 . G1t))^> is set
e1 . (a . G1t) is M2( the carrier of F1)
the ObjectMap of e1 . ((a . G1t),(a . G1t)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e1 . [(a . G1t),(a . G1t)] is set
K40(( the ObjectMap of e1 . ((a . G1t),(a . G1t)))) is set
<^(e . (a . G1t)),(e1 . (a . G1t))^> is set
e . (a . fa) is M2( the carrier of F1)
the ObjectMap of e . ((a . fa),(a . fa)) is M2([: the carrier of F1, the carrier of F1:])
[(a . fa),(a . fa)] is set
the ObjectMap of e . [(a . fa),(a . fa)] is set
K40(( the ObjectMap of e . ((a . fa),(a . fa)))) is set
<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e) . fa)^> is set
e . (a ! fa) is M2(<^(e . (a . fa)),(e . (F2 . fa))^>)
<^(e . (a . fa)),(e . (F2 . fa))^> is set
e . (a . f) is M2(<^(e . (a . G1t)),(e . (a . fa))^>)
<^(e . (a . G1t)),(e . (a . fa))^> is set
(A,B,F1,e,e1,F2,k) . G1t is set
(e . (a ! fa)) * (e . (a . f)) is M2(<^(e . (a . G1t)),(e . (F2 . fa))^>)
G1F1f is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,a,e) . fa)^>)
G1tb is M2(<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e) . fa)^>)
G1tb * G1F1f is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e) . fa)^>)
<^((A,B,F1,F2,e1) . G1t),((A,B,F1,F2,e1) . fa)^> is set
F2 . f is M2(<^(F2 . G1t),(F2 . fa)^>)
<^(F2 . G1t),(F2 . fa)^> is set
e1 . (F2 . f) is M2(<^(e1 . (F2 . G1t)),(e1 . (F2 . fa))^>)
<^(e1 . (F2 . G1t)),(e1 . (F2 . fa))^> is set
(A,B,F1,e,e1,F2,k) . fa is set
<^(e1 . (a . G1t)),(e1 . (F2 . G1t))^> is set
(A,B,F1,a,e) . f is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,a,e) . fa)^>)
(A,B,F1,a,F2,e,e1,a,k) ! fa is M2(<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e1) . fa)^>)
<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e1) . fa)^> is set
((A,B,F1,a,F2,e,e1,a,k) ! fa) * ((A,B,F1,a,e) . f) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^> is set
(A,B,F1,a,F2,a,e) ! fa is M2(<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e) . fa)^>)
(A,B,F1,e,e1,F2,k) ! fa is M2(<^((A,B,F1,F2,e) . fa),((A,B,F1,F2,e1) . fa)^>)
((A,B,F1,e,e1,F2,k) ! fa) * ((A,B,F1,a,F2,a,e) ! fa) is M2(<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e1) . fa)^>)
(((A,B,F1,e,e1,F2,k) ! fa) * ((A,B,F1,a,F2,a,e) ! fa)) * ((A,B,F1,a,e) . f) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
sF2b is M2(<^((A,B,F1,F2,e) . fa),((A,B,F1,F2,e1) . fa)^>)
sF2b * ((A,B,F1,a,F2,a,e) ! fa) is M2(<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e1) . fa)^>)
(sF2b * ((A,B,F1,a,F2,a,e) ! fa)) * ((A,B,F1,a,e) . f) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
sF2b * G1tb is M2(<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e1) . fa)^>)
(sF2b * G1tb) * ((A,B,F1,a,e) . f) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
(sF2b * G1tb) * G1F1f is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
G1tbF1f is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e) . fa)^>)
sF2b * G1tbF1f is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
(k ! (F2 . fa)) * (e . ((a ! fa) * (a . f))) is M2(<^(e . (a . G1t)),(e1 . (F2 . fa))^>)
<^(e . (a . G1t)),(e1 . (F2 . fa))^> is set
k ! (a . G1t) is M2(<^(e . (a . G1t)),(e1 . (a . G1t))^>)
e1 . ((a ! fa) * (a . f)) is M2(<^(e1 . (a . G1t)),(e1 . (F2 . fa))^>)
<^(e1 . (a . G1t)),(e1 . (F2 . fa))^> is set
(e1 . ((a ! fa) * (a . f))) * (k ! (a . G1t)) is M2(<^(e . (a . G1t)),(e1 . (F2 . fa))^>)
(F2 . f) * (a ! G1t) is M2(<^(a . G1t),(F2 . fa)^>)
e1 . ((F2 . f) * (a ! G1t)) is M2(<^(e1 . (a . G1t)),(e1 . (F2 . fa))^>)
(e1 . ((F2 . f) * (a ! G1t))) * (k ! (a . G1t)) is M2(<^(e . (a . G1t)),(e1 . (F2 . fa))^>)
e1 . (a ! G1t) is M2(<^(e1 . (a . G1t)),(e1 . (F2 . G1t))^>)
(e1 . (F2 . f)) * (e1 . (a ! G1t)) is M2(<^(e1 . (a . G1t)),(e1 . (F2 . fa))^>)
((e1 . (F2 . f)) * (e1 . (a ! G1t))) * (k ! (a . G1t)) is M2(<^(e . (a . G1t)),(e1 . (F2 . fa))^>)
(e1 . (a ! G1t)) * (k ! (a . G1t)) is M2(<^(e . (a . G1t)),(e1 . (F2 . G1t))^>)
<^(e . (a . G1t)),(e1 . (F2 . G1t))^> is set
(e1 . (F2 . f)) * ((e1 . (a ! G1t)) * (k ! (a . G1t))) is M2(<^(e . (a . G1t)),(e1 . (F2 . fa))^>)
(k ! (F2 . G1t)) * (e . (a ! G1t)) is M2(<^(e . (a . G1t)),(e1 . (F2 . G1t))^>)
(e1 . (F2 . f)) * ((k ! (F2 . G1t)) * (e . (a ! G1t))) is M2(<^(e . (a . G1t)),(e1 . (F2 . fa))^>)
G1ta is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e) . G1t)^>)
t1 is M2(<^((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e1) . G1t)^>)
t1 * G1ta is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . G1t)^>)
<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . G1t)^> is set
G2F2f is M2(<^((A,B,F1,F2,e1) . G1t),((A,B,F1,F2,e1) . fa)^>)
G2F2f * (t1 * G1ta) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
(A,B,F1,F2,e1) . f is M2(<^((A,B,F1,F2,e1) . G1t),((A,B,F1,F2,e1) . fa)^>)
((A,B,F1,F2,e1) . f) * (t1 * G1ta) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
(A,B,F1,e,e1,F2,k) ! G1t is M2(<^((A,B,F1,F2,e) . G1t),((A,B,F1,F2,e1) . G1t)^>)
((A,B,F1,e,e1,F2,k) ! G1t) * G1ta is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . G1t)^>)
((A,B,F1,F2,e1) . f) * (((A,B,F1,e,e1,F2,k) ! G1t) * G1ta) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
(A,B,F1,a,F2,a,e) ! G1t is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e) . G1t)^>)
((A,B,F1,e,e1,F2,k) ! G1t) * ((A,B,F1,a,F2,a,e) ! G1t) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . G1t)^>)
((A,B,F1,F2,e1) . f) * (((A,B,F1,e,e1,F2,k) ! G1t) * ((A,B,F1,a,F2,a,e) ! G1t)) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
(A,B,F1,a,F2,e,e1,a,k) ! G1t is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . G1t)^>)
((A,B,F1,F2,e1) . f) * ((A,B,F1,a,F2,e,e1,a,k) ! G1t) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
G1t is M2( the carrier of A)
fa is M2( the carrier of A)
<^G1t,fa^> is set
(A,B,F1,a,e) . G1t is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e) . (G1t,G1t) is M2([: the carrier of F1, the carrier of F1:])
[G1t,G1t] is set
the ObjectMap of (A,B,F1,a,e) . [G1t,G1t] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (G1t,G1t))) is set
(A,B,F1,a,e) . fa is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e) . (fa,fa) is M2([: the carrier of F1, the carrier of F1:])
[fa,fa] is set
the ObjectMap of (A,B,F1,a,e) . [fa,fa] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (fa,fa))) is set
(A,B,F1,F2,e1) . fa is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e1) . (fa,fa) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e1) . [fa,fa] is set
K40(( the ObjectMap of (A,B,F1,F2,e1) . (fa,fa))) is set
t1 is M2(<^G1t,fa^>)
(A,B,F1,a,e) . t1 is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,a,e) . fa)^>)
<^((A,B,F1,a,e) . G1t),((A,B,F1,a,e) . fa)^> is set
(A,B,F1,a,F2,e,e1,a,k) ! fa is M2(<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e1) . fa)^>)
<^((A,B,F1,a,e) . fa),((A,B,F1,F2,e1) . fa)^> is set
((A,B,F1,a,F2,e,e1,a,k) ! fa) * ((A,B,F1,a,e) . t1) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^> is set
(A,B,F1,F2,e1) . G1t is M2( the carrier of F1)
the ObjectMap of (A,B,F1,F2,e1) . (G1t,G1t) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,F2,e1) . [G1t,G1t] is set
K40(( the ObjectMap of (A,B,F1,F2,e1) . (G1t,G1t))) is set
(A,B,F1,a,F2,e,e1,a,k) ! G1t is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . G1t)^>)
<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . G1t)^> is set
(A,B,F1,F2,e1) . t1 is M2(<^((A,B,F1,F2,e1) . G1t),((A,B,F1,F2,e1) . fa)^>)
<^((A,B,F1,F2,e1) . G1t),((A,B,F1,F2,e1) . fa)^> is set
((A,B,F1,F2,e1) . t1) * ((A,B,F1,a,F2,e,e1,a,k) ! G1t) is M2(<^((A,B,F1,a,e) . G1t),((A,B,F1,F2,e1) . fa)^>)
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive associative with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,A
(B,F1,A,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,F1,A,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
e1 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of a,F2
(B,F1,A,a,F2,e1,e) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e)
k is M2( the carrier of B)
a is M2( the carrier of B)
<^k,a^> is set
(B,F1,A,a,e) . k is M2( 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 ObjectMap of (B,F1,A,a,e) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 ObjectMap of (B,F1,A,a,e) . (k,k) is M2([: the carrier of A, the carrier of A:])
[k,k] is set
the ObjectMap of (B,F1,A,a,e) . [k,k] is set
K40(( the ObjectMap of (B,F1,A,a,e) . (k,k))) is set
(B,F1,A,a,e) . a is M2( the carrier of A)
the ObjectMap of (B,F1,A,a,e) . (a,a) is M2([: the carrier of A, the carrier of A:])
[a,a] is set
the ObjectMap of (B,F1,A,a,e) . [a,a] is set
K40(( the ObjectMap of (B,F1,A,a,e) . (a,a))) is set
(B,F1,A,F2,e) . a is M2( the carrier of A)
the ObjectMap of (B,F1,A,F2,e) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (B,F1,A,F2,e) . (a,a) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,F2,e) . [a,a] is set
K40(( the ObjectMap of (B,F1,A,F2,e) . (a,a))) is set
(B,F1,A,a,F2,e1,e) ! a is M2(<^((B,F1,A,a,e) . a),((B,F1,A,F2,e) . a)^>)
<^((B,F1,A,a,e) . a),((B,F1,A,F2,e) . a)^> is set
(B,F1,A,F2,e) . k is M2( the carrier of A)
the ObjectMap of (B,F1,A,F2,e) . (k,k) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,F2,e) . [k,k] is set
K40(( the ObjectMap of (B,F1,A,F2,e) . (k,k))) is set
(B,F1,A,a,F2,e1,e) ! k is M2(<^((B,F1,A,a,e) . k),((B,F1,A,F2,e) . k)^>)
<^((B,F1,A,a,e) . k),((B,F1,A,F2,e) . k)^> is set
a . a is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of a is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of a . (a,a) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of a . [a,a] is set
K40(( the ObjectMap of a . (a,a))) is set
e . (a . a) is M2( the carrier of A)
the ObjectMap of e is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is non empty set
the ObjectMap of e . ((a . a),(a . a)) is M2([: the carrier of A, the carrier of A:])
[(a . a),(a . a)] is set
the ObjectMap of e . [(a . a),(a . a)] is set
K40(( the ObjectMap of e . ((a . a),(a . a)))) is set
a . k is M2( the carrier of F1)
the ObjectMap of a . (k,k) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
<^(a . k),(a . a)^> is set
F2 . a is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of F2 . (a,a) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [a,a] is set
K40(( the ObjectMap of F2 . (a,a))) is set
<^(a . a),(F2 . a)^> is set
F2 . k is M2( the carrier of F1)
the ObjectMap of F2 . (k,k) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [k,k] is set
K40(( the ObjectMap of F2 . (k,k))) is set
<^(a . k),(F2 . k)^> is set
e . (a . k) is M2( the carrier of A)
the ObjectMap of e . ((a . k),(a . k)) is M2([: the carrier of A, the carrier of A:])
[(a . k),(a . k)] is set
the ObjectMap of e . [(a . k),(a . k)] is set
K40(( the ObjectMap of e . ((a . k),(a . k)))) is set
<^(e . (a . k)),((B,F1,A,F2,e) . k)^> is set
e1 ! k is M2(<^(a . k),(F2 . k)^>)
e . (e1 ! k) is M2(<^(e . (a . k)),(e . (F2 . k))^>)
e . (F2 . k) is M2( the carrier of A)
the ObjectMap of e . ((F2 . k),(F2 . k)) is M2([: the carrier of A, the carrier of A:])
[(F2 . k),(F2 . k)] is set
the ObjectMap of e . [(F2 . k),(F2 . k)] is set
K40(( the ObjectMap of e . ((F2 . k),(F2 . k)))) is set
<^(e . (a . k)),(e . (F2 . k))^> is set
e . (F2 . a) is M2( the carrier of A)
the ObjectMap of e . ((F2 . a),(F2 . a)) is M2([: the carrier of A, the carrier of A:])
[(F2 . a),(F2 . a)] is set
the ObjectMap of e . [(F2 . a),(F2 . a)] is set
K40(( the ObjectMap of e . ((F2 . a),(F2 . a)))) is set
<^((B,F1,A,a,e) . a),(e . (F2 . a))^> is set
e1 ! a is M2(<^(a . a),(F2 . a)^>)
e . (e1 ! a) is M2(<^(e . (a . a)),(e . (F2 . a))^>)
<^(e . (a . a)),(e . (F2 . a))^> is set
fa is M2(<^k,a^>)
(B,F1,A,a,e) . fa is M2(<^((B,F1,A,a,e) . k),((B,F1,A,a,e) . a)^>)
<^((B,F1,A,a,e) . k),((B,F1,A,a,e) . a)^> is set
((B,F1,A,a,F2,e1,e) ! a) * ((B,F1,A,a,e) . fa) is M2(<^((B,F1,A,a,e) . k),((B,F1,A,F2,e) . a)^>)
<^((B,F1,A,a,e) . k),((B,F1,A,F2,e) . a)^> is set
(B,F1,A,F2,e) . fa is M2(<^((B,F1,A,F2,e) . k),((B,F1,A,F2,e) . a)^>)
<^((B,F1,A,F2,e) . k),((B,F1,A,F2,e) . a)^> is set
((B,F1,A,F2,e) . fa) * ((B,F1,A,a,F2,e1,e) ! k) is M2(<^((B,F1,A,a,e) . k),((B,F1,A,F2,e) . a)^>)
<^(F2 . k),(F2 . a)^> is set
a . fa is M2(<^(a . k),(a . a)^>)
e . (a . fa) is M2(<^(e . (a . k)),(e . (a . a))^>)
<^(e . (a . k)),(e . (a . a))^> is set
G1t is M2(<^((B,F1,A,a,e) . a),(e . (F2 . a))^>)
G1t * ((B,F1,A,a,e) . fa) is M2(<^((B,F1,A,a,e) . k),(e . (F2 . a))^>)
<^((B,F1,A,a,e) . k),(e . (F2 . a))^> is set
t1 is M2(<^((B,F1,A,a,e) . k),((B,F1,A,a,e) . a)^>)
G1t * t1 is M2(<^((B,F1,A,a,e) . k),(e . (F2 . a))^>)
(e1 ! a) * (a . fa) is M2(<^(a . k),(F2 . a)^>)
<^(a . k),(F2 . a)^> is set
e . ((e1 ! a) * (a . fa)) is M2(<^(e . (a . k)),(e . (F2 . a))^>)
<^(e . (a . k)),(e . (F2 . a))^> is set
F2 . fa is M2(<^(F2 . k),(F2 . a)^>)
(F2 . fa) * (e1 ! k) is M2(<^(a . k),(F2 . a)^>)
e . ((F2 . fa) * (e1 ! k)) is M2(<^(e . (a . k)),(e . (F2 . a))^>)
e . (F2 . fa) is M2(<^(e . (F2 . k)),(e . (F2 . a))^>)
<^(e . (F2 . k)),(e . (F2 . a))^> is set
(e . (F2 . fa)) * (e . (e1 ! k)) is M2(<^(e . (a . k)),(e . (F2 . a))^>)
sF2 is M2(<^(e . (a . k)),((B,F1,A,F2,e) . k)^>)
((B,F1,A,F2,e) . fa) * sF2 is M2(<^(e . (a . k)),((B,F1,A,F2,e) . a)^>)
<^(e . (a . k)),((B,F1,A,F2,e) . a)^> is set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive associative with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,F2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e1 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of F2,e
(A,B,F1,F2,e,a,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e)
k is M2( the carrier of A)
a is M2( the carrier of A)
<^k,a^> is set
(A,B,F1,a,F2) . k is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,a,F2) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,F2) . (k,k) is M2([: the carrier of F1, the carrier of F1:])
[k,k] is set
the ObjectMap of (A,B,F1,a,F2) . [k,k] is set
K40(( the ObjectMap of (A,B,F1,a,F2) . (k,k))) is set
(A,B,F1,a,F2) . a is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,F2) . (a,a) is M2([: the carrier of F1, the carrier of F1:])
[a,a] is set
the ObjectMap of (A,B,F1,a,F2) . [a,a] is set
K40(( the ObjectMap of (A,B,F1,a,F2) . (a,a))) is set
(A,B,F1,a,e) . a is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,a,e) . (a,a) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,a,e) . [a,a] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (a,a))) is set
(A,B,F1,F2,e,a,e1) ! a is M2(<^((A,B,F1,a,F2) . a),((A,B,F1,a,e) . a)^>)
<^((A,B,F1,a,F2) . a),((A,B,F1,a,e) . a)^> is set
(A,B,F1,a,e) . k is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e) . (k,k) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,a,e) . [k,k] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (k,k))) is set
(A,B,F1,F2,e,a,e1) ! k is M2(<^((A,B,F1,a,F2) . k),((A,B,F1,a,e) . k)^>)
<^((A,B,F1,a,F2) . k),((A,B,F1,a,e) . k)^> is set
a . k is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
a . a is M2( the carrier of B)
the ObjectMap of a . (a,a) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [a,a] is set
K40(( the ObjectMap of a . (a,a))) is set
<^(a . k),(a . a)^> is set
F2 . (a . k) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . k),(a . k)) is M2([: the carrier of F1, the carrier of F1:])
[(a . k),(a . k)] is set
the ObjectMap of F2 . [(a . k),(a . k)] is set
K40(( the ObjectMap of F2 . ((a . k),(a . k)))) is set
<^(F2 . (a . k)),((A,B,F1,a,e) . k)^> is set
e1 ! (a . k) is M2(<^(F2 . (a . k)),(e . (a . k))^>)
e . (a . k) is M2( the carrier of F1)
the ObjectMap of e is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of e . ((a . k),(a . k)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e . [(a . k),(a . k)] is set
K40(( the ObjectMap of e . ((a . k),(a . k)))) is set
<^(F2 . (a . k)),(e . (a . k))^> is set
G1t is M2(<^k,a^>)
(A,B,F1,a,F2) . G1t is M2(<^((A,B,F1,a,F2) . k),((A,B,F1,a,F2) . a)^>)
<^((A,B,F1,a,F2) . k),((A,B,F1,a,F2) . a)^> is set
((A,B,F1,F2,e,a,e1) ! a) * ((A,B,F1,a,F2) . G1t) is M2(<^((A,B,F1,a,F2) . k),((A,B,F1,a,e) . a)^>)
<^((A,B,F1,a,F2) . k),((A,B,F1,a,e) . a)^> is set
(A,B,F1,a,e) . G1t is M2(<^((A,B,F1,a,e) . k),((A,B,F1,a,e) . a)^>)
<^((A,B,F1,a,e) . k),((A,B,F1,a,e) . a)^> is set
((A,B,F1,a,e) . G1t) * ((A,B,F1,F2,e,a,e1) ! k) is M2(<^((A,B,F1,a,F2) . k),((A,B,F1,a,e) . a)^>)
e . (a . a) is M2( the carrier of F1)
the ObjectMap of e . ((a . a),(a . a)) is M2([: the carrier of F1, the carrier of F1:])
[(a . a),(a . a)] is set
the ObjectMap of e . [(a . a),(a . a)] is set
K40(( the ObjectMap of e . ((a . a),(a . a)))) is set
e1 ! (a . a) is M2(<^(F2 . (a . a)),(e . (a . a))^>)
F2 . (a . a) is M2( the carrier of F1)
the ObjectMap of F2 . ((a . a),(a . a)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [(a . a),(a . a)] is set
K40(( the ObjectMap of F2 . ((a . a),(a . a)))) is set
<^(F2 . (a . a)),(e . (a . a))^> is set
a . G1t is M2(<^(a . k),(a . a)^>)
F2 . (a . G1t) is M2(<^(F2 . (a . k)),(F2 . (a . a))^>)
<^(F2 . (a . k)),(F2 . (a . a))^> is set
fa is M2(<^((A,B,F1,a,F2) . a),((A,B,F1,a,e) . a)^>)
fa * ((A,B,F1,a,F2) . G1t) is M2(<^((A,B,F1,a,F2) . k),((A,B,F1,a,e) . a)^>)
t1 is M2(<^((A,B,F1,a,F2) . k),((A,B,F1,a,F2) . a)^>)
fa * t1 is M2(<^((A,B,F1,a,F2) . k),((A,B,F1,a,e) . a)^>)
e . (a . G1t) is M2(<^(e . (a . k)),(e . (a . a))^>)
<^(e . (a . k)),(e . (a . a))^> is set
(e . (a . G1t)) * (e1 ! (a . k)) is M2(<^(F2 . (a . k)),(e . (a . a))^>)
<^(F2 . (a . k)),(e . (a . a))^> is set
sF2 is M2(<^(F2 . (a . k)),((A,B,F1,a,e) . k)^>)
((A,B,F1,a,e) . G1t) * sF2 is M2(<^(F2 . (a . k)),((A,B,F1,a,e) . a)^>)
<^(F2 . (a . k)),((A,B,F1,a,e) . a)^> is set
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
F1 is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
the carrier of B is non empty set
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
k is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,F2
a is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of e,e1
(A,B,F1,a,F2,e,e1,k,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e1)
(A,B,F1,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,a,F2,k,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e)
(A,B,F1,e,e1,F2,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,e),(A,B,F1,F2,e1)
(A,B,F1,e,e1,F2,a) `*` (A,B,F1,a,F2,k,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e1)
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive associative with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
k is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,F2,k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,e,a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
sF2 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of e1,k
G1t is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of k,a
G1t `*` sF2 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of e1,a
fa is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of a,F2
(A,B,F1,a,F2,e1,k,fa,sF2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,k)
(A,B,F1,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,a,F2,fa,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,e1)
(A,B,F1,e1,k,F2,sF2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,e1),(A,B,F1,F2,k)
(A,B,F1,e1,k,F2,sF2) `*` (A,B,F1,a,F2,fa,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,k)
t1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F2,e
t1 `*` fa is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of a,e
(A,B,F1,a,e,e1,a,(t1 `*` fa),(G1t `*` sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,e,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,a,e,(t1 `*` fa),e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,e1)
(A,B,F1,e1,a,e,(G1t `*` sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,e,e1),(A,B,F1,e,a)
(A,B,F1,e1,a,e,(G1t `*` sF2)) `*` (A,B,F1,a,e,(t1 `*` fa),e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,F2,e,k,a,t1,G1t) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,k),(A,B,F1,e,a)
(A,B,F1,e,k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,e,t1,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,k),(A,B,F1,e,k)
(A,B,F1,k,a,e,G1t) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,e,k),(A,B,F1,e,a)
(A,B,F1,k,a,e,G1t) `*` (A,B,F1,F2,e,t1,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,k),(A,B,F1,e,a)
(A,B,F1,F2,e,k,a,t1,G1t) `*` (A,B,F1,a,F2,e1,k,fa,sF2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,a,k) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,e1,k,a,sF2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,a,k)
(A,B,F1,a,F2,fa,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,k),(A,B,F1,F2,k)
(A,B,F1,a,F2,fa,k) `*` (A,B,F1,e1,k,a,sF2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,k)
(A,B,F1,a,a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,F2,a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,k,a,F2,G1t) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,k),(A,B,F1,F2,a)
(A,B,F1,F2,e,t1,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,a),(A,B,F1,e,a)
(A,B,F1,F2,e,t1,a) `*` (A,B,F1,k,a,F2,G1t) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,k),(A,B,F1,e,a)
(A,B,F1,e1,a,a,(G1t `*` sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,a,a)
(A,B,F1,a,e,(t1 `*` fa),a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,a),(A,B,F1,e,a)
(A,B,F1,a,e,(t1 `*` fa),a) `*` (A,B,F1,e1,a,a,(G1t `*` sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,a,F2,fa,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,a),(A,B,F1,F2,a)
(A,B,F1,F2,e,t1,a) `*` (A,B,F1,a,F2,fa,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,a),(A,B,F1,e,a)
((A,B,F1,F2,e,t1,a) `*` (A,B,F1,a,F2,fa,a)) `*` (A,B,F1,e1,a,a,(G1t `*` sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
G1t `*` sF2 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of e1,a
(A,B,F1,e1,a,a,(G1t `*` sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,a,a)
((A,B,F1,F2,e,t1,a) `*` (A,B,F1,a,F2,fa,a)) `*` (A,B,F1,e1,a,a,(G1t `*` sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,k,a,a,G1t) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,k),(A,B,F1,a,a)
(A,B,F1,k,a,a,G1t) `*` (A,B,F1,e1,k,a,sF2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,a,a)
((A,B,F1,F2,e,t1,a) `*` (A,B,F1,a,F2,fa,a)) `*` ((A,B,F1,k,a,a,G1t) `*` (A,B,F1,e1,k,a,sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,a,F2,fa,a) `*` ((A,B,F1,k,a,a,G1t) `*` (A,B,F1,e1,k,a,sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,a)
(A,B,F1,F2,e,t1,a) `*` ((A,B,F1,a,F2,fa,a) `*` ((A,B,F1,k,a,a,G1t) `*` (A,B,F1,e1,k,a,sF2))) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,a,F2,fa,a) `*` (A,B,F1,k,a,a,G1t) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,k),(A,B,F1,F2,a)
((A,B,F1,a,F2,fa,a) `*` (A,B,F1,k,a,a,G1t)) `*` (A,B,F1,e1,k,a,sF2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,a)
(A,B,F1,F2,e,t1,a) `*` (((A,B,F1,a,F2,fa,a) `*` (A,B,F1,k,a,a,G1t)) `*` (A,B,F1,e1,k,a,sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,a,F2,k,a,fa,G1t) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,k),(A,B,F1,F2,a)
(A,B,F1,k,a,F2,G1t) `*` (A,B,F1,a,F2,fa,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,k),(A,B,F1,F2,a)
(A,B,F1,a,F2,k,a,fa,G1t) `*` (A,B,F1,e1,k,a,sF2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,a)
(A,B,F1,F2,e,t1,a) `*` ((A,B,F1,a,F2,k,a,fa,G1t) `*` (A,B,F1,e1,k,a,sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
(A,B,F1,k,a,F2,G1t) `*` ((A,B,F1,a,F2,fa,k) `*` (A,B,F1,e1,k,a,sF2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,F2,a)
(A,B,F1,F2,e,t1,a) `*` ((A,B,F1,k,a,F2,G1t) `*` ((A,B,F1,a,F2,fa,k) `*` (A,B,F1,e1,k,a,sF2))) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e1),(A,B,F1,e,a)
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
F2 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of F1,a
e1 is set
k is M2( the carrier of B)
F1 . k is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 ObjectMap of F1 . (k,k) is M2([: the carrier of A, the carrier of A:])
[k,k] is set
the ObjectMap of F1 . [k,k] is set
K40(( the ObjectMap of F1 . (k,k))) is set
a . k is M2( the carrier of A)
the ObjectMap 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 non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of a . (k,k) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
F2 ! k is M2(<^(F1 . k),(a . k)^>)
<^(F1 . k),(a . k)^> is set
(F2 ! k) " is M2(<^(a . k),(F1 . k)^>)
<^(a . k),(F1 . k)^> is set
e1 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) set
k is M2( the carrier of B)
e1 . k is set
a . k is M2( 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 ObjectMap 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 non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 ObjectMap of a . (k,k) is M2([: the carrier of A, the carrier of A:])
[k,k] is set
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
F1 . k is M2( the carrier of A)
the ObjectMap of F1 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of F1 . (k,k) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of F1 . [k,k] is set
K40(( the ObjectMap of F1 . (k,k))) is set
<^(a . k),(F1 . k)^> is set
a is M2( the carrier of B)
F1 . a is M2( the carrier of A)
the ObjectMap of F1 . (a,a) is M2([: the carrier of A, the carrier of A:])
[a,a] is set
the ObjectMap of F1 . [a,a] is set
K40(( the ObjectMap of F1 . (a,a))) is set
a . a is M2( the carrier of A)
the ObjectMap of a . (a,a) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [a,a] is set
K40(( the ObjectMap of a . (a,a))) is set
F2 ! a is M2(<^(F1 . a),(a . a)^>)
<^(F1 . a),(a . a)^> is set
(F2 ! a) " is M2(<^(a . a),(F1 . a)^>)
<^(a . a),(F1 . a)^> is set
a is M2( the carrier of B)
sF2 is M2( the carrier of B)
<^a,sF2^> is set
F1 . a is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 ObjectMap of F1 . (a,a) is M2([: the carrier of A, the carrier of A:])
[a,a] is set
the ObjectMap of F1 . [a,a] is set
K40(( the ObjectMap of F1 . (a,a))) is set
F1 . sF2 is M2( the carrier of A)
the ObjectMap of F1 . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
[sF2,sF2] is set
the ObjectMap of F1 . [sF2,sF2] is set
K40(( the ObjectMap of F1 . (sF2,sF2))) is set
<^(F1 . a),(F1 . sF2)^> is set
k is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of a,F1
k . sF2 is set
a . sF2 is M2( the carrier of A)
the ObjectMap 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 non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of a . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [sF2,sF2] is set
K40(( the ObjectMap of a . (sF2,sF2))) is set
F2 ! sF2 is M2(<^(F1 . sF2),(a . sF2)^>)
<^(F1 . sF2),(a . sF2)^> is set
a . a is M2( the carrier of A)
the ObjectMap of a . (a,a) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [a,a] is set
K40(( the ObjectMap of a . (a,a))) is set
<^(a . a),(F1 . a)^> is set
<^(F1 . a),(a . a)^> is set
k . a is set
t1 is M2( the carrier of B)
F1 . t1 is M2( the carrier of A)
the ObjectMap of F1 . (t1,t1) is M2([: the carrier of A, the carrier of A:])
[t1,t1] is set
the ObjectMap of F1 . [t1,t1] is set
K40(( the ObjectMap of F1 . (t1,t1))) is set
a . t1 is M2( the carrier of A)
the ObjectMap of a . (t1,t1) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [t1,t1] is set
K40(( the ObjectMap of a . (t1,t1))) is set
F2 ! t1 is M2(<^(F1 . t1),(a . t1)^>)
<^(F1 . t1),(a . t1)^> is set
(F2 ! t1) " is M2(<^(a . t1),(F1 . t1)^>)
<^(a . t1),(F1 . t1)^> is set
F2 ! a is M2(<^(F1 . a),(a . a)^>)
<^(a . sF2),(F1 . sF2)^> is set
<^(a . a),(a . sF2)^> is set
<^(a . a),(F1 . sF2)^> is set
G1t is M2(<^a,sF2^>)
a . G1t is M2(<^(a . a),(a . sF2)^>)
k ! sF2 is M2(<^(a . sF2),(F1 . sF2)^>)
(k ! sF2) * (a . G1t) is M2(<^(a . a),(F1 . sF2)^>)
idm (a . a) is retraction coretraction iso mono epi M2(<^(a . a),(a . a)^>)
<^(a . a),(a . a)^> is non empty set
((k ! sF2) * (a . G1t)) * (idm (a . a)) is M2(<^(a . a),(F1 . sF2)^>)
fa is M2(<^(a . a),(F1 . a)^>)
(F2 ! a) * fa is M2(<^(a . a),(a . a)^>)
((k ! sF2) * (a . G1t)) * ((F2 ! a) * fa) is M2(<^(a . a),(F1 . sF2)^>)
k ! a is M2(<^(a . a),(F1 . a)^>)
(F2 ! a) * (k ! a) is M2(<^(a . a),(a . a)^>)
((k ! sF2) * (a . G1t)) * ((F2 ! a) * (k ! a)) is M2(<^(a . a),(F1 . sF2)^>)
((k ! sF2) * (a . G1t)) * (F2 ! a) is M2(<^(F1 . a),(F1 . sF2)^>)
(((k ! sF2) * (a . G1t)) * (F2 ! a)) * (k ! a) is M2(<^(a . a),(F1 . sF2)^>)
(a . G1t) * (F2 ! a) is M2(<^(F1 . a),(a . sF2)^>)
<^(F1 . a),(a . sF2)^> is set
(k ! sF2) * ((a . G1t) * (F2 ! a)) is M2(<^(F1 . a),(F1 . sF2)^>)
((k ! sF2) * ((a . G1t) * (F2 ! a))) * (k ! a) is M2(<^(a . a),(F1 . sF2)^>)
F1 . G1t is M2(<^(F1 . a),(F1 . sF2)^>)
(F2 ! sF2) * (F1 . G1t) is M2(<^(F1 . a),(a . sF2)^>)
(k ! sF2) * ((F2 ! sF2) * (F1 . G1t)) is M2(<^(F1 . a),(F1 . sF2)^>)
((k ! sF2) * ((F2 ! sF2) * (F1 . G1t))) * (k ! a) is M2(<^(a . a),(F1 . sF2)^>)
(k ! sF2) * (F2 ! sF2) is M2(<^(F1 . sF2),(F1 . sF2)^>)
<^(F1 . sF2),(F1 . sF2)^> is non empty set
((k ! sF2) * (F2 ! sF2)) * (F1 . G1t) is M2(<^(F1 . a),(F1 . sF2)^>)
(((k ! sF2) * (F2 ! sF2)) * (F1 . G1t)) * (k ! a) is M2(<^(a . a),(F1 . sF2)^>)
(F2 ! sF2) " is M2(<^(a . sF2),(F1 . sF2)^>)
((F2 ! sF2) ") * (F2 ! sF2) is M2(<^(F1 . sF2),(F1 . sF2)^>)
(((F2 ! sF2) ") * (F2 ! sF2)) * (F1 . G1t) is M2(<^(F1 . a),(F1 . sF2)^>)
((((F2 ! sF2) ") * (F2 ! sF2)) * (F1 . G1t)) * (k ! a) is M2(<^(a . a),(F1 . sF2)^>)
idm (F1 . sF2) is retraction coretraction iso mono epi M2(<^(F1 . sF2),(F1 . sF2)^>)
(idm (F1 . sF2)) * (F1 . G1t) is M2(<^(F1 . a),(F1 . sF2)^>)
((idm (F1 . sF2)) * (F1 . G1t)) * (k ! a) is M2(<^(a . a),(F1 . sF2)^>)
(F1 . G1t) * (k ! a) is M2(<^(a . a),(F1 . sF2)^>)
t1 is M2( the carrier of B)
F1 . t1 is M2( the carrier of A)
the ObjectMap of F1 . (t1,t1) is M2([: the carrier of A, the carrier of A:])
[t1,t1] is set
the ObjectMap of F1 . [t1,t1] is set
K40(( the ObjectMap of F1 . (t1,t1))) is set
a . t1 is M2( the carrier of A)
the ObjectMap of a . (t1,t1) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [t1,t1] is set
K40(( the ObjectMap of a . (t1,t1))) is set
F2 ! t1 is M2(<^(F1 . t1),(a . t1)^>)
<^(F1 . t1),(a . t1)^> is set
(F2 ! t1) " is M2(<^(a . t1),(F1 . t1)^>)
<^(a . t1),(F1 . t1)^> is set
t1 is M2( the carrier of B)
F1 . t1 is M2( the carrier of A)
the ObjectMap of F1 . (t1,t1) is M2([: the carrier of A, the carrier of A:])
[t1,t1] is set
the ObjectMap of F1 . [t1,t1] is set
K40(( the ObjectMap of F1 . (t1,t1))) is set
a . t1 is M2( the carrier of A)
the ObjectMap of a . (t1,t1) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [t1,t1] is set
K40(( the ObjectMap of a . (t1,t1))) is set
F2 ! t1 is M2(<^(F1 . t1),(a . t1)^>)
<^(F1 . t1),(a . t1)^> is set
(F2 ! t1) " is M2(<^(a . t1),(F1 . t1)^>)
<^(a . t1),(F1 . t1)^> is set
a is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of a,F1
sF2 is M2( the carrier of B)
a . sF2 is set
F1 . sF2 is M2( the carrier of A)
the ObjectMap of F1 . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
[sF2,sF2] is set
the ObjectMap of F1 . [sF2,sF2] is set
K40(( the ObjectMap of F1 . (sF2,sF2))) is set
a . sF2 is M2( the carrier of A)
the ObjectMap of a . (sF2,sF2) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [sF2,sF2] is set
K40(( the ObjectMap of a . (sF2,sF2))) is set
F2 ! sF2 is M2(<^(F1 . sF2),(a . sF2)^>)
<^(F1 . sF2),(a . sF2)^> is set
(F2 ! sF2) " is M2(<^(a . sF2),(F1 . sF2)^>)
<^(a . sF2),(F1 . sF2)^> is set
a ! sF2 is M2(<^(a . sF2),(F1 . sF2)^>)
G1t is M2( the carrier of B)
F1 . G1t is M2( the carrier of A)
the ObjectMap of F1 . (G1t,G1t) is M2([: the carrier of A, the carrier of A:])
[G1t,G1t] is set
the ObjectMap of F1 . [G1t,G1t] is set
K40(( the ObjectMap of F1 . (G1t,G1t))) is set
a . G1t is M2( the carrier of A)
the ObjectMap of a . (G1t,G1t) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of a . [G1t,G1t] is set
K40(( the ObjectMap of a . (G1t,G1t))) is set
F2 ! G1t is M2(<^(F1 . G1t),(a . G1t)^>)
<^(F1 . G1t),(a . G1t)^> is set
(F2 ! G1t) " is M2(<^(a . G1t),(F1 . G1t)^>)
<^(a . G1t),(F1 . G1t)^> is set
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
idt F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F2,F2
e is M2( the carrier of A)
F2 . e is M2( 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 ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F2 . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of F2 . [e,e] is set
K40(( the ObjectMap of F2 . (e,e))) is set
(idt F2) ! e is M2(<^(F2 . e),(F2 . e)^>)
<^(F2 . e),(F2 . e)^> is non empty set
idm (F2 . e) is retraction coretraction iso mono epi M2(<^(F2 . e),(F2 . e)^>)
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F2,e
k is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of e,F2
a is M2( the carrier of A)
e . a is M2( 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 ObjectMap of e 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of e . (a,a) is M2([: the carrier of B, the carrier of B:])
[a,a] is set
the ObjectMap of e . [a,a] is set
K40(( the ObjectMap of e . (a,a))) is set
F2 . a is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (a,a) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [a,a] is set
K40(( the ObjectMap of F2 . (a,a))) is set
k ! a is M2(<^(e . a),(F2 . a)^>)
<^(e . a),(F2 . a)^> is set
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
the carrier of A is non empty set
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
the carrier of A is non empty set
e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F1,a
e1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,F2
e1 `*` e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F1,F2
k is M2( the carrier of A)
F1 . k is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (k,k) is M2([: the carrier of B, the carrier of B:])
[k,k] is set
the ObjectMap of F1 . [k,k] is set
K40(( the ObjectMap of F1 . (k,k))) is set
F2 . k is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [k,k] is set
K40(( the ObjectMap of F2 . (k,k))) is set
(e1 `*` e) ! k is M2(<^(F1 . k),(F2 . k)^>)
<^(F1 . k),(F2 . k)^> is set
a . k is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
e1 ! k is M2(<^(a . k),(F2 . k)^>)
<^(a . k),(F2 . k)^> is set
<^(F2 . k),(F1 . k)^> is set
e ! k is M2(<^(F1 . k),(a . k)^>)
<^(F1 . k),(a . k)^> is set
e1 `*` e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F1,F2
(e1 `*` e) ! k is M2(<^(F1 . k),(F2 . k)^>)
(e1 ! k) * (e ! k) is M2(<^(F1 . k),(F2 . k)^>)
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,a)
e1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F2)
e1 `*` e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F1,F2
k is M2( the carrier of A)
F1 . k is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (k,k) is M2([: the carrier of B, the carrier of B:])
[k,k] is set
the ObjectMap of F1 . [k,k] is set
K40(( the ObjectMap of F1 . (k,k))) is set
F2 . k is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [k,k] is set
K40(( the ObjectMap of F2 . (k,k))) is set
(e1 `*` e) ! k is M2(<^(F1 . k),(F2 . k)^>)
<^(F1 . k),(F2 . k)^> is set
a . k is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
<^(F1 . k),(a . k)^> is set
<^(F2 . k),(F1 . k)^> is set
<^(a . k),(F2 . k)^> is set
e1 `*` e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F1,F2
(e1 `*` e) ! k is M2(<^(F1 . k),(F2 . k)^>)
e ! k is M2(<^(F1 . k),(a . k)^>)
e1 ! k is M2(<^(a . k),(F2 . k)^>)
(e1 ! k) * (e ! k) is M2(<^(F1 . k),(F2 . k)^>)
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive associative with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F1,A
(B,F1,A,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
(B,F1,A,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B,A
e1 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) (B,F1,a,F2)
(B,F1,A,a,F2,e1,e) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) transformation of (B,F1,A,a,e),(B,F1,A,F2,e)
a is M2( the carrier of B)
(B,F1,A,a,e) . a is M2( 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 ObjectMap of (B,F1,A,a,e) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 ObjectMap of (B,F1,A,a,e) . (a,a) is M2([: the carrier of A, the carrier of A:])
[a,a] is set
the ObjectMap of (B,F1,A,a,e) . [a,a] is set
K40(( the ObjectMap of (B,F1,A,a,e) . (a,a))) is set
a . a is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of a is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of a . (a,a) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of a . [a,a] is set
K40(( the ObjectMap of a . (a,a))) is set
e . (a . a) is M2( the carrier of A)
the ObjectMap of e is Relation-like [: the carrier of F1, the carrier of F1:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of F1, the carrier of F1:]) V18([: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:])
[:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of F1, the carrier of F1:],[: the carrier of A, the carrier of A:]:] is non empty set
the ObjectMap of e . ((a . a),(a . a)) is M2([: the carrier of A, the carrier of A:])
[(a . a),(a . a)] is set
the ObjectMap of e . [(a . a),(a . a)] is set
K40(( the ObjectMap of e . ((a . a),(a . a)))) is set
(B,F1,A,F2,e) . a is M2( the carrier of A)
the ObjectMap of (B,F1,A,F2,e) 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of (B,F1,A,F2,e) . (a,a) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,F2,e) . [a,a] is set
K40(( the ObjectMap of (B,F1,A,F2,e) . (a,a))) is set
F2 . a is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of F2 . (a,a) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of F2 . [a,a] is set
K40(( the ObjectMap of F2 . (a,a))) is set
e . (F2 . a) is M2( the carrier of A)
the ObjectMap of e . ((F2 . a),(F2 . a)) is M2([: the carrier of A, the carrier of A:])
[(F2 . a),(F2 . a)] is set
the ObjectMap of e . [(F2 . a),(F2 . a)] is set
K40(( the ObjectMap of e . ((F2 . a),(F2 . a)))) is set
<^(F2 . a),(a . a)^> is set
k is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) natural_transformation of (B,F1,A,a,e),(B,F1,A,F2,e)
k ! a is M2(<^((B,F1,A,a,e) . a),((B,F1,A,F2,e) . a)^>)
<^((B,F1,A,a,e) . a),((B,F1,A,F2,e) . a)^> is set
e1 ! a is M2(<^(a . a),(F2 . a)^>)
<^(a . a),(F2 . a)^> is set
e . (e1 ! a) is M2(<^(e . (a . a)),(e . (F2 . a))^>)
<^(e . (a . a)),(e . (F2 . a))^> is set
a is M2( the carrier of B)
(B,F1,A,a,e) . a is M2( the carrier of A)
the ObjectMap of (B,F1,A,a,e) . (a,a) is M2([: the carrier of A, the carrier of A:])
[a,a] is set
the ObjectMap of (B,F1,A,a,e) . [a,a] is set
K40(( the ObjectMap of (B,F1,A,a,e) . (a,a))) is set
(B,F1,A,F2,e) . a is M2( the carrier of A)
the ObjectMap of (B,F1,A,F2,e) . (a,a) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of (B,F1,A,F2,e) . [a,a] is set
K40(( the ObjectMap of (B,F1,A,F2,e) . (a,a))) is set
k ! a is M2(<^((B,F1,A,a,e) . a),((B,F1,A,F2,e) . a)^>)
<^((B,F1,A,a,e) . a),((B,F1,A,F2,e) . a)^> is set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive associative with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,F2) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e1 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) (B,F1,F2,e)
(A,B,F1,F2,e,a,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,F2),(A,B,F1,a,e)
k is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of (A,B,F1,a,F2),(A,B,F1,a,e)
a is M2( the carrier of A)
k ! a is M2(<^((A,B,F1,a,F2) . a),((A,B,F1,a,e) . a)^>)
(A,B,F1,a,F2) . a is M2( the carrier of F1)
the carrier of F1 is non empty set
[: the carrier of F1, the carrier of F1:] is Relation-like non empty set
the ObjectMap of (A,B,F1,a,F2) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
[: 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 F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of (A,B,F1,a,F2) . (a,a) is M2([: the carrier of F1, the carrier of F1:])
[a,a] is set
the ObjectMap of (A,B,F1,a,F2) . [a,a] is set
K40(( the ObjectMap of (A,B,F1,a,F2) . (a,a))) is set
(A,B,F1,a,e) . a is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) V18([: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of (A,B,F1,a,e) . (a,a) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,a,e) . [a,a] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (a,a))) is set
<^((A,B,F1,a,F2) . a),((A,B,F1,a,e) . a)^> is set
a . a is M2( the carrier of B)
[: the carrier of B, the carrier of B:] is Relation-like non empty set
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (a,a) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [a,a] is set
K40(( the ObjectMap of a . (a,a))) is set
e1 ! (a . a) is M2(<^(F2 . (a . a)),(e . (a . a))^>)
F2 . (a . a) is M2( the carrier of F1)
the ObjectMap of F2 is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
[:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:] is non empty set
the ObjectMap of F2 . ((a . a),(a . a)) is M2([: the carrier of F1, the carrier of F1:])
[(a . a),(a . a)] is set
the ObjectMap of F2 . [(a . a),(a . a)] is set
K40(( the ObjectMap of F2 . ((a . a),(a . a)))) is set
e . (a . a) is M2( the carrier of F1)
the ObjectMap of e is Relation-like [: the carrier of B, the carrier of B:] -defined [: the carrier of F1, the carrier of F1:] -valued Function-like non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of F1, the carrier of F1:]:])
the ObjectMap of e . ((a . a),(a . a)) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of e . [(a . a),(a . a)] is set
K40(( the ObjectMap of e . ((a . a),(a . a)))) is set
<^(F2 . (a . a)),(e . (a . a))^> is set
a is M2( the carrier of A)
(A,B,F1,a,F2) . a is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,F2) . (a,a) is M2([: the carrier of F1, the carrier of F1:])
[a,a] is set
the ObjectMap of (A,B,F1,a,F2) . [a,a] is set
K40(( the ObjectMap of (A,B,F1,a,F2) . (a,a))) is set
(A,B,F1,a,e) . a is M2( the carrier of F1)
the ObjectMap of (A,B,F1,a,e) . (a,a) is M2([: the carrier of F1, the carrier of F1:])
the ObjectMap of (A,B,F1,a,e) . [a,a] is set
K40(( the ObjectMap of (A,B,F1,a,e) . (a,a))) is set
k ! a is M2(<^((A,B,F1,a,F2) . a),((A,B,F1,a,e) . a)^>)
<^((A,B,F1,a,F2) . a),((A,B,F1,a,e) . a)^> is set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is non empty transitive associative with_units reflexive AltCatStr
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,a,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
e1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,F1
(A,B,F1,F2,e1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
k is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F2)
a is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) (B,F1,e,e1)
(A,B,F1,a,F2,e,e1,k,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e1)
(A,B,F1,F2,e) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,F1
(A,B,F1,a,F2,k,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e)
(A,B,F1,e,e1,F2,a) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,F2,e),(A,B,F1,F2,e1)
(A,B,F1,e,e1,F2,a) `*` (A,B,F1,a,F2,k,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of (A,B,F1,a,e),(A,B,F1,F2,e1)
G1t is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of (A,B,F1,a,e),(A,B,F1,F2,e)
sF2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of (A,B,F1,F2,e),(A,B,F1,F2,e1)
sF2 `*` G1t is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of (A,B,F1,a,e),(A,B,F1,F2,e1)
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,a)
e is M2( the carrier of A)
F1 . e is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of F1 . [e,e] is set
K40(( the ObjectMap of F1 . (e,e))) is set
a . e is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
F2 ! e is M2(<^(F1 . e),(a . e)^>)
<^(F1 . e),(a . e)^> is set
e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,F1
e1 is M2( the carrier of A)
a . e1 is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (e1,e1) is M2([: the carrier of B, the carrier of B:])
[e1,e1] is set
the ObjectMap of a . [e1,e1] is set
K40(( the ObjectMap of a . (e1,e1))) is set
F1 . e1 is M2( the carrier of B)
the ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F1 . (e1,e1) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F1 . [e1,e1] is set
K40(( the ObjectMap of F1 . (e1,e1))) is set
e ! e1 is M2(<^(a . e1),(F1 . e1)^>)
<^(a . e1),(F1 . e1)^> is set
e1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F1)
k is M2( the carrier of A)
e1 . k is set
F1 . k is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (k,k) is M2([: the carrier of B, the carrier of B:])
[k,k] is set
the ObjectMap of F1 . [k,k] is set
K40(( the ObjectMap of F1 . (k,k))) is set
a . k is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
F2 ! k is M2(<^(F1 . k),(a . k)^>)
<^(F1 . k),(a . k)^> is set
(F2 ! k) " is M2(<^(a . k),(F1 . k)^>)
<^(a . k),(F1 . k)^> is set
e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F1)
e1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F1)
k is M2( the carrier of A)
e ! k is M2(<^(a . k),(F1 . k)^>)
a . k is M2( 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 ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of a . (k,k) is M2([: the carrier of B, the carrier of B:])
[k,k] is set
the ObjectMap of a . [k,k] is set
K40(( the ObjectMap of a . (k,k))) is set
F1 . k is M2( the carrier of B)
the ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F1 . (k,k) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F1 . [k,k] is set
K40(( the ObjectMap of F1 . (k,k))) is set
<^(a . k),(F1 . k)^> is set
e . k is set
F2 ! k is M2(<^(F1 . k),(a . k)^>)
<^(F1 . k),(a . k)^> is set
(F2 ! k) " is M2(<^(a . k),(F1 . k)^>)
e1 . k is set
e1 ! k is M2(<^(a . k),(F1 . k)^>)
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
the carrier of B is non empty set
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B,A
F2 is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) (B,A,F1,a)
(B,A,F1,a,F2) is Relation-like the carrier of B -defined Function-like non empty V14( the carrier of B) (B,A,a,F1)
e is M2( the carrier of B)
(B,A,F1,a,F2) ! e is M2(<^(a . e),(F1 . e)^>)
a . e is M2( 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 ObjectMap 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 non empty V14([: the carrier of B, the carrier of B:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( 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 ObjectMap of a . (e,e) is M2([: the carrier of A, the carrier of A:])
[e,e] is set
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
F1 . e is M2( the carrier of A)
the ObjectMap of F1 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:]) V18([: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]) M2( bool [:[: the carrier of B, the carrier of B:],[: the carrier of A, the carrier of A:]:])
the ObjectMap of F1 . (e,e) is M2([: the carrier of A, the carrier of A:])
the ObjectMap of F1 . [e,e] is set
K40(( the ObjectMap of F1 . (e,e))) is set
<^(a . e),(F1 . e)^> is set
F2 ! e is M2(<^(F1 . e),(a . e)^>)
<^(F1 . e),(a . e)^> is set
(F2 ! e) " is M2(<^(a . e),(F1 . e)^>)
(B,A,F1,a,F2) . e is set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
idt a is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,a
F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,a)
(A,B,F1,a,F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F1)
F2 `*` (A,B,F1,a,F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,a
e is M2( the carrier of A)
F1 . e is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of F1 . [e,e] is set
K40(( the ObjectMap of F1 . (e,e))) is set
a . e is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
F2 ! e is M2(<^(F1 . e),(a . e)^>)
<^(F1 . e),(a . e)^> is set
(F2 `*` (A,B,F1,a,F2)) ! e is M2(<^(a . e),(a . e)^>)
<^(a . e),(a . e)^> is non empty set
F2 `*` (A,B,F1,a,F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of a,a
(F2 `*` (A,B,F1,a,F2)) ! e is M2(<^(a . e),(a . e)^>)
(A,B,F1,a,F2) ! e is M2(<^(a . e),(F1 . e)^>)
<^(a . e),(F1 . e)^> is set
(F2 ! e) * ((A,B,F1,a,F2) ! e) is M2(<^(a . e),(a . e)^>)
(F2 ! e) " is M2(<^(a . e),(F1 . e)^>)
(F2 ! e) * ((F2 ! e) ") is M2(<^(a . e),(a . e)^>)
idm (a . e) is retraction coretraction iso mono epi M2(<^(a . e),(a . e)^>)
(idt a) ! e is M2(<^(a . e),(a . e)^>)
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
idt F1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F1,F1
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,a)
(A,B,F1,a,F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F1)
(A,B,F1,a,F2) `*` F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F1,F1
e is M2( the carrier of A)
F1 . e is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of F1 . [e,e] is set
K40(( the ObjectMap of F1 . (e,e))) is set
a . e is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
F2 ! e is M2(<^(F1 . e),(a . e)^>)
<^(F1 . e),(a . e)^> is set
((A,B,F1,a,F2) `*` F2) ! e is M2(<^(F1 . e),(F1 . e)^>)
<^(F1 . e),(F1 . e)^> is non empty set
(A,B,F1,a,F2) `*` F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F1,F1
((A,B,F1,a,F2) `*` F2) ! e is M2(<^(F1 . e),(F1 . e)^>)
(A,B,F1,a,F2) ! e is M2(<^(a . e),(F1 . e)^>)
<^(a . e),(F1 . e)^> is set
((A,B,F1,a,F2) ! e) * (F2 ! e) is M2(<^(F1 . e),(F1 . e)^>)
(F2 ! e) " is M2(<^(a . e),(F1 . e)^>)
((F2 ! e) ") * (F2 ! e) is M2(<^(F1 . e),(F1 . e)^>)
idm (F1 . e) is retraction coretraction iso mono epi M2(<^(F1 . e),(F1 . e)^>)
(idt F1) ! e is M2(<^(F1 . e),(F1 . e)^>)
A is non empty transitive associative with_units reflexive AltCatStr
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
idt F1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F1,F1
the carrier of A is non empty set
the Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F1)
(A,B,F1,F1, the Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F1)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F1)
the Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F1) `*` (A,B,F1,F1, the Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F1)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F1,F1
idt F1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F1,F1
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,a)
(A,B,F1,a,F2) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F1)
(A,B,a,F1,(A,B,F1,a,F2)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,a)
e is M2( the carrier of A)
F1 . e is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (e,e) is M2([: the carrier of B, the carrier of B:])
[e,e] is set
the ObjectMap of F1 . [e,e] is set
K40(( the ObjectMap of F1 . (e,e))) is set
a . e is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (e,e) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [e,e] is set
K40(( the ObjectMap of a . (e,e))) is set
<^(F1 . e),(a . e)^> is set
<^(a . e),(F1 . e)^> is set
F2 ! e is M2(<^(F1 . e),(a . e)^>)
(A,B,a,F1,(A,B,F1,a,F2)) ! e is M2(<^(F1 . e),(a . e)^>)
(A,B,F1,a,F2) ! e is M2(<^(a . e),(F1 . e)^>)
((A,B,F1,a,F2) ! e) " is M2(<^(F1 . e),(a . e)^>)
(F2 ! e) " is M2(<^(a . e),(F1 . e)^>)
((F2 ! e) ") " is M2(<^(F1 . e),(a . e)^>)
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
F2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F2)
(A,B,F1,F2,e) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F2,F1)
e1 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F2,a)
e1 `*` e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of F1,a
(A,B,F2,a,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F2)
(A,B,F1,F2,e) `*` (A,B,F2,a,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of a,F1
k is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,a)
(A,B,F1,a,k) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,a,F1)
a is M2( the carrier of A)
F1 . a is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (a,a) is M2([: the carrier of B, the carrier of B:])
[a,a] is set
the ObjectMap of F1 . [a,a] is set
K40(( the ObjectMap of F1 . (a,a))) is set
F2 . a is M2( the carrier of B)
the ObjectMap of F2 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of F2 . (a,a) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of F2 . [a,a] is set
K40(( the ObjectMap of F2 . (a,a))) is set
<^(F1 . a),(F2 . a)^> is set
a . a is M2( the carrier of B)
the ObjectMap 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( bool [:[: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]:])
the ObjectMap of a . (a,a) is M2([: the carrier of B, the carrier of B:])
the ObjectMap of a . [a,a] is set
K40(( the ObjectMap of a . (a,a))) is set
<^(F2 . a),(a . a)^> is set
<^(a . a),(F1 . a)^> is set
e ! a is M2(<^(F1 . a),(F2 . a)^>)
e1 ! a is M2(<^(F2 . a),(a . a)^>)
(A,B,F1,a,k) ! a is M2(<^(a . a),(F1 . a)^>)
(e1 `*` e) ! a is M2(<^(F1 . a),(a . a)^>)
<^(F1 . a),(a . a)^> is set
((e1 `*` e) ! a) " is M2(<^(a . a),(F1 . a)^>)
e1 `*` e is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of F1,a
(e1 `*` e) ! a is M2(<^(F1 . a),(a . a)^>)
((e1 `*` e) ! a) " is M2(<^(a . a),(F1 . a)^>)
(e1 ! a) * (e ! a) is M2(<^(F1 . a),(a . a)^>)
((e1 ! a) * (e ! a)) " is M2(<^(a . a),(F1 . a)^>)
(e1 ! a) " is M2(<^(a . a),(F2 . a)^>)
<^(a . a),(F2 . a)^> is set
(e ! a) " is M2(<^(F2 . a),(F1 . a)^>)
<^(F2 . a),(F1 . a)^> is set
((e ! a) ") * ((e1 ! a) ") is M2(<^(a . a),(F1 . a)^>)
(A,B,F2,a,e1) ! a is M2(<^(a . a),(F2 . a)^>)
((e ! a) ") * ((A,B,F2,a,e1) ! a) is M2(<^(a . a),(F1 . a)^>)
(A,B,F1,F2,e) ! a is M2(<^(F2 . a),(F1 . a)^>)
((A,B,F1,F2,e) ! a) * ((A,B,F2,a,e1) ! a) is M2(<^(a . a),(F1 . a)^>)
(A,B,F1,F2,e) `*` (A,B,F2,a,e1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of a,F1
((A,B,F1,F2,e) `*` (A,B,F2,a,e1)) ! a is M2(<^(a . a),(F1 . a)^>)
((A,B,F1,F2,e) `*` (A,B,F2,a,e1)) ! a is M2(<^(a . a),(F1 . a)^>)
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
B is non empty transitive associative with_units reflexive AltCatStr
F1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,B
(A,B,F1) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F1)
(A,B,F1,F1,(A,B,F1)) is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) (A,B,F1,F1)
a is M2( the carrier of A)
(A,B,F1,F1,(A,B,F1)) ! a is M2(<^(F1 . a),(F1 . a)^>)
F1 . a is M2( 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 ObjectMap of F1 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:]) V18([: the carrier of A, the carrier of A:],[: the carrier of B, the carrier of B:]) M2( 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 ObjectMap of F1 . (a,a) is M2([: the carrier of B, the carrier of B:])
[a,a] is set
the ObjectMap of F1 . [a,a] is set
K40(( the ObjectMap of F1 . (a,a))) is set
<^(F1 . a),(F1 . a)^> is non empty set
(A,B,F1) ! a is M2(<^(F1 . a),(F1 . a)^>)
((A,B,F1) ! a) " is M2(<^(F1 . a),(F1 . a)^>)
idm (F1 . a) is retraction coretraction iso mono epi M2(<^(F1 . a),(F1 . a)^>)
(idm (F1 . a)) " is M2(<^(F1 . a),(F1 . a)^>)