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)^>)