:: YELLOW20 semantic presentation

K154() is M2( bool K150())
K150() is set
bool K150() is non empty set
K116() is set
bool K116() is non empty set
bool K154() is non empty set
{} is set
the Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty Function-yielding V37() set
1 is non empty set
{{},1} is set
proj1 {} is set
proj2 {} is set
A1 is non empty transitive with_units reflexive AltCatStr
A2 is non empty transitive with_units reflexive AltCatStr
the carrier of A1 is non empty set
the carrier of A2 is non empty set
F is reflexive feasible FunctorStr over A1,A2
F " is strict FunctorStr over A2,A1
B2 is M2( the carrier of A1)
F . B2 is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
G is M2( the carrier of A2)
(F ") . G is M2( the carrier of A1)
the ObjectMap of (F ") is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (F ") . (G,G) is M2([: the carrier of A1, the carrier of A1:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (F ") . [G,G] is set
( the ObjectMap of (F ") . (G,G)) `1 is set
(F ") * F is strict FunctorStr over A1,A1
id A1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A1,A1
((F ") * F) . B2 is M2( the carrier of A1)
the ObjectMap of ((F ") * F) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of ((F ") * F) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of ((F ") * F) . [B2,B2] is set
( the ObjectMap of ((F ") * F) . (B2,B2)) `1 is set
B1 is reflexive feasible FunctorStr over A2,A1
F * B1 is feasible strict FunctorStr over A2,A2
id A2 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
(F * B1) . G is M2( the carrier of A2)
the ObjectMap of (F * B1) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (F * B1) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (F * B1) . [G,G] is set
( the ObjectMap of (F * B1) . (G,G)) `1 is set
A1 is non empty transitive with_units reflexive AltCatStr
A2 is non empty transitive with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is reflexive feasible Covariant FunctorStr over A1,A2
F " is strict FunctorStr over A2,A1
B1 is reflexive feasible Covariant FunctorStr over A2,A1
B2 is M2( the carrier of A1)
G is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A1 . [B2,G] is set
F . B2 is M2( the carrier of A2)
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
F . G is M2( the carrier of A2)
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
<^(F . B2),(F . G)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((F . B2),(F . G)) is set
[(F . B2),(F . G)] is V15() set
{(F . B2),(F . G)} is set
{(F . B2)} is set
{{(F . B2),(F . G)},{(F . B2)}} is set
the Arrows of A2 . [(F . B2),(F . G)] is set
B1 . (F . B2) is M2( the carrier of A1)
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of B1 . ((F . B2),(F . B2)) is M2([: the carrier of A1, the carrier of A1:])
[(F . B2),(F . B2)] is V15() set
{(F . B2),(F . B2)} is set
{{(F . B2),(F . B2)},{(F . B2)}} is set
the ObjectMap of B1 . [(F . B2),(F . B2)] is set
( the ObjectMap of B1 . ((F . B2),(F . B2))) `1 is set
B1 . (F . G) is M2( the carrier of A1)
the ObjectMap of B1 . ((F . G),(F . G)) is M2([: the carrier of A1, the carrier of A1:])
[(F . G),(F . G)] is V15() set
{(F . G),(F . G)} is set
{(F . G)} is set
{{(F . G),(F . G)},{(F . G)}} is set
the ObjectMap of B1 . [(F . G),(F . G)] is set
( the ObjectMap of B1 . ((F . G),(F . G))) `1 is set
b is M2(<^B2,G^>)
F . b is M2(<^(F . B2),(F . G)^>)
c is M2(<^(F . B2),(F . G)^>)
B1 . c is M2(<^(B1 . (F . B2)),(B1 . (F . G))^>)
<^(B1 . (F . B2)),(B1 . (F . G))^> is set
the Arrows of A1 . ((B1 . (F . B2)),(B1 . (F . G))) is set
[(B1 . (F . B2)),(B1 . (F . G))] is V15() set
{(B1 . (F . B2)),(B1 . (F . G))} is set
{(B1 . (F . B2))} is set
{{(B1 . (F . B2)),(B1 . (F . G))},{(B1 . (F . B2))}} is set
the Arrows of A1 . [(B1 . (F . B2)),(B1 . (F . G))] is set
(F ") * F is strict FunctorStr over A1,A1
id A1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A1,A1
B1 * F is reflexive feasible strict Covariant FunctorStr over A1,A1
(B1 * F) . b is M2(<^((B1 * F) . B2),((B1 * F) . G)^>)
(B1 * F) . B2 is M2( the carrier of A1)
the ObjectMap of (B1 * F) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (B1 * F) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (B1 * F) . [B2,B2] is set
( the ObjectMap of (B1 * F) . (B2,B2)) `1 is set
(B1 * F) . G is M2( the carrier of A1)
the ObjectMap of (B1 * F) . (G,G) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (B1 * F) . [G,G] is set
( the ObjectMap of (B1 * F) . (G,G)) `1 is set
<^((B1 * F) . B2),((B1 * F) . G)^> is set
the Arrows of A1 . (((B1 * F) . B2),((B1 * F) . G)) is set
[((B1 * F) . B2),((B1 * F) . G)] is V15() set
{((B1 * F) . B2),((B1 * F) . G)} is set
{((B1 * F) . B2)} is set
{{((B1 * F) . B2),((B1 * F) . G)},{((B1 * F) . B2)}} is set
the Arrows of A1 . [((B1 * F) . B2),((B1 * F) . G)] is set
F * B1 is reflexive feasible strict Covariant FunctorStr over A2,A2
id A2 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
(F * B1) . c is M2(<^((F * B1) . (F . B2)),((F * B1) . (F . G))^>)
(F * B1) . (F . B2) is M2( the carrier of A2)
the ObjectMap of (F * B1) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (F * B1) . ((F . B2),(F . B2)) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (F * B1) . [(F . B2),(F . B2)] is set
( the ObjectMap of (F * B1) . ((F . B2),(F . B2))) `1 is set
(F * B1) . (F . G) is M2( the carrier of A2)
the ObjectMap of (F * B1) . ((F . G),(F . G)) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (F * B1) . [(F . G),(F . G)] is set
( the ObjectMap of (F * B1) . ((F . G),(F . G))) `1 is set
<^((F * B1) . (F . B2)),((F * B1) . (F . G))^> is set
the Arrows of A2 . (((F * B1) . (F . B2)),((F * B1) . (F . G))) is set
[((F * B1) . (F . B2)),((F * B1) . (F . G))] is V15() set
{((F * B1) . (F . B2)),((F * B1) . (F . G))} is set
{((F * B1) . (F . B2))} is set
{{((F * B1) . (F . B2)),((F * B1) . (F . G))},{((F * B1) . (F . B2))}} is set
the Arrows of A2 . [((F * B1) . (F . B2)),((F * B1) . (F . G))] is set
A1 is non empty transitive with_units reflexive AltCatStr
A2 is non empty transitive with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is reflexive feasible Contravariant FunctorStr over A1,A2
F " is strict FunctorStr over A2,A1
B1 is reflexive feasible Contravariant FunctorStr over A2,A1
B2 is M2( the carrier of A1)
G is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A1 . [B2,G] is set
F . G is M2( the carrier of A2)
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
<^(F . G),(F . B2)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((F . G),(F . B2)) is set
[(F . G),(F . B2)] is V15() set
{(F . G),(F . B2)} is set
{(F . G)} is set
{{(F . G),(F . B2)},{(F . G)}} is set
the Arrows of A2 . [(F . G),(F . B2)] is set
B1 . (F . B2) is M2( the carrier of A1)
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of B1 . ((F . B2),(F . B2)) is M2([: the carrier of A1, the carrier of A1:])
[(F . B2),(F . B2)] is V15() set
{(F . B2),(F . B2)} is set
{(F . B2)} is set
{{(F . B2),(F . B2)},{(F . B2)}} is set
the ObjectMap of B1 . [(F . B2),(F . B2)] is set
( the ObjectMap of B1 . ((F . B2),(F . B2))) `1 is set
B1 . (F . G) is M2( the carrier of A1)
the ObjectMap of B1 . ((F . G),(F . G)) is M2([: the carrier of A1, the carrier of A1:])
[(F . G),(F . G)] is V15() set
{(F . G),(F . G)} is set
{{(F . G),(F . G)},{(F . G)}} is set
the ObjectMap of B1 . [(F . G),(F . G)] is set
( the ObjectMap of B1 . ((F . G),(F . G))) `1 is set
b is M2(<^B2,G^>)
F . b is M2(<^(F . G),(F . B2)^>)
c is M2(<^(F . G),(F . B2)^>)
B1 . c is M2(<^(B1 . (F . B2)),(B1 . (F . G))^>)
<^(B1 . (F . B2)),(B1 . (F . G))^> is set
the Arrows of A1 . ((B1 . (F . B2)),(B1 . (F . G))) is set
[(B1 . (F . B2)),(B1 . (F . G))] is V15() set
{(B1 . (F . B2)),(B1 . (F . G))} is set
{(B1 . (F . B2))} is set
{{(B1 . (F . B2)),(B1 . (F . G))},{(B1 . (F . B2))}} is set
the Arrows of A1 . [(B1 . (F . B2)),(B1 . (F . G))] is set
(F ") * F is strict FunctorStr over A1,A1
id A1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A1,A1
B1 * F is reflexive feasible strict Covariant FunctorStr over A1,A1
(B1 * F) . b is M2(<^((B1 * F) . B2),((B1 * F) . G)^>)
(B1 * F) . B2 is M2( the carrier of A1)
the ObjectMap of (B1 * F) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (B1 * F) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (B1 * F) . [B2,B2] is set
( the ObjectMap of (B1 * F) . (B2,B2)) `1 is set
(B1 * F) . G is M2( the carrier of A1)
the ObjectMap of (B1 * F) . (G,G) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (B1 * F) . [G,G] is set
( the ObjectMap of (B1 * F) . (G,G)) `1 is set
<^((B1 * F) . B2),((B1 * F) . G)^> is set
the Arrows of A1 . (((B1 * F) . B2),((B1 * F) . G)) is set
[((B1 * F) . B2),((B1 * F) . G)] is V15() set
{((B1 * F) . B2),((B1 * F) . G)} is set
{((B1 * F) . B2)} is set
{{((B1 * F) . B2),((B1 * F) . G)},{((B1 * F) . B2)}} is set
the Arrows of A1 . [((B1 * F) . B2),((B1 * F) . G)] is set
F * B1 is reflexive feasible strict Covariant FunctorStr over A2,A2
id A2 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
(F * B1) . c is M2(<^((F * B1) . (F . G)),((F * B1) . (F . B2))^>)
(F * B1) . (F . G) is M2( the carrier of A2)
the ObjectMap of (F * B1) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (F * B1) . ((F . G),(F . G)) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (F * B1) . [(F . G),(F . G)] is set
( the ObjectMap of (F * B1) . ((F . G),(F . G))) `1 is set
(F * B1) . (F . B2) is M2( the carrier of A2)
the ObjectMap of (F * B1) . ((F . B2),(F . B2)) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (F * B1) . [(F . B2),(F . B2)] is set
( the ObjectMap of (F * B1) . ((F . B2),(F . B2))) `1 is set
<^((F * B1) . (F . G)),((F * B1) . (F . B2))^> is set
the Arrows of A2 . (((F * B1) . (F . G)),((F * B1) . (F . B2))) is set
[((F * B1) . (F . G)),((F * B1) . (F . B2))] is V15() set
{((F * B1) . (F . G)),((F * B1) . (F . B2))} is set
{((F * B1) . (F . G))} is set
{{((F * B1) . (F . G)),((F * B1) . (F . B2))},{((F * B1) . (F . G))}} is set
the Arrows of A2 . [((F * B1) . (F . G)),((F * B1) . (F . B2))] is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
id A2 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
F is feasible id-preserving Functor of A1,A2
F " is strict FunctorStr over A2,A1
(F ") * F is strict FunctorStr over A1,A1
id A1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A1,A1
B2 is feasible id-preserving Functor of A2,A1
F * B2 is feasible strict FunctorStr over A2,A2
the ObjectMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the MorphMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B2, the Arrows of A2, the Arrows of A1
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
FunctorStr(# the ObjectMap of B2, the MorphMap of B2 #) is strict FunctorStr over A2,A1
(id A1) * B2 is feasible strict FunctorStr over A2,A1
B1 is feasible FunctorStr over A2,A1
B1 * (id A2) is feasible strict FunctorStr over A2,A1
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
id A1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A1,A1
F is feasible id-preserving Functor of A1,A2
F " is strict FunctorStr over A2,A1
B1 is feasible FunctorStr over A2,A1
F * B1 is feasible strict FunctorStr over A2,A2
id A2 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
B2 is feasible id-preserving Functor of A2,A1
B2 * F is feasible strict FunctorStr over A1,A1
the ObjectMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the MorphMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B2, the Arrows of A2, the Arrows of A1
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
FunctorStr(# the ObjectMap of B2, the MorphMap of B2 #) is strict FunctorStr over A2,A1
(id A1) * B1 is feasible strict FunctorStr over A2,A1
B2 * (id A2) is feasible strict id-preserving FunctorStr over A2,A1
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A2 is non empty set
F is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
F " is strict FunctorStr over A2,A1
B1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A2,A1
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the MorphMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A2, the Arrows of A1
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
FunctorStr(# the ObjectMap of B1, the MorphMap of B1 #) is strict FunctorStr over A2,A1
B2 is M2( the carrier of A2)
G is M2( the carrier of A2)
<^B2,G^> is set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
F * B1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A2,A2
b is M2(<^B2,G^>)
(F * B1) . b is M2(<^((F * B1) . B2),((F * B1) . G)^>)
(F * B1) . B2 is M2( the carrier of A2)
the ObjectMap of (F * B1) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (F * B1) . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (F * B1) . [B2,B2] is set
( the ObjectMap of (F * B1) . (B2,B2)) `1 is set
(F * B1) . G is M2( the carrier of A2)
the ObjectMap of (F * B1) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (F * B1) . [G,G] is set
( the ObjectMap of (F * B1) . (G,G)) `1 is set
<^((F * B1) . B2),((F * B1) . G)^> is set
the Arrows of A2 . (((F * B1) . B2),((F * B1) . G)) is set
[((F * B1) . B2),((F * B1) . G)] is V15() set
{((F * B1) . B2),((F * B1) . G)} is set
{((F * B1) . B2)} is set
{{((F * B1) . B2),((F * B1) . G)},{((F * B1) . B2)}} is set
the Arrows of A2 . [((F * B1) . B2),((F * B1) . G)] is set
B1 . B2 is M2( the carrier of A1)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
B1 . G is M2( the carrier of A1)
the ObjectMap of B1 . (G,G) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [G,G] is set
( the ObjectMap of B1 . (G,G)) `1 is set
B1 . b is M2(<^(B1 . B2),(B1 . G)^>)
<^(B1 . B2),(B1 . G)^> is set
the Arrows of A1 . ((B1 . B2),(B1 . G)) is set
[(B1 . B2),(B1 . G)] is V15() set
{(B1 . B2),(B1 . G)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . G)},{(B1 . B2)}} is set
the Arrows of A1 . [(B1 . B2),(B1 . G)] is set
F . (B1 . b) is M2(<^(F . (B1 . B2)),(F . (B1 . G))^>)
F . (B1 . B2) is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . ((B1 . B2),(B1 . B2)) is M2([: the carrier of A2, the carrier of A2:])
[(B1 . B2),(B1 . B2)] is V15() set
{(B1 . B2),(B1 . B2)} is set
{{(B1 . B2),(B1 . B2)},{(B1 . B2)}} is set
the ObjectMap of F . [(B1 . B2),(B1 . B2)] is set
( the ObjectMap of F . ((B1 . B2),(B1 . B2))) `1 is set
F . (B1 . G) is M2( the carrier of A2)
the ObjectMap of F . ((B1 . G),(B1 . G)) is M2([: the carrier of A2, the carrier of A2:])
[(B1 . G),(B1 . G)] is V15() set
{(B1 . G),(B1 . G)} is set
{(B1 . G)} is set
{{(B1 . G),(B1 . G)},{(B1 . G)}} is set
the ObjectMap of F . [(B1 . G),(B1 . G)] is set
( the ObjectMap of F . ((B1 . G),(B1 . G))) `1 is set
<^(F . (B1 . B2)),(F . (B1 . G))^> is set
the Arrows of A2 . ((F . (B1 . B2)),(F . (B1 . G))) is set
[(F . (B1 . B2)),(F . (B1 . G))] is V15() set
{(F . (B1 . B2)),(F . (B1 . G))} is set
{(F . (B1 . B2))} is set
{{(F . (B1 . B2)),(F . (B1 . G))},{(F . (B1 . B2))}} is set
the Arrows of A2 . [(F . (B1 . B2)),(F . (B1 . G))] is set
id A2 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
(id A2) . b is M2(<^((id A2) . B2),((id A2) . G)^>)
(id A2) . B2 is M2( the carrier of A2)
the ObjectMap of (id A2) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:])
the ObjectMap of (id A2) . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (id A2) . [B2,B2] is set
( the ObjectMap of (id A2) . (B2,B2)) `1 is set
(id A2) . G is M2( the carrier of A2)
the ObjectMap of (id A2) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (id A2) . [G,G] is set
( the ObjectMap of (id A2) . (G,G)) `1 is set
<^((id A2) . B2),((id A2) . G)^> is set
the Arrows of A2 . (((id A2) . B2),((id A2) . G)) is set
[((id A2) . B2),((id A2) . G)] is V15() set
{((id A2) . B2),((id A2) . G)} is set
{((id A2) . B2)} is set
{{((id A2) . B2),((id A2) . G)},{((id A2) . B2)}} is set
the Arrows of A2 . [((id A2) . B2),((id A2) . G)] is set
B2 is M2( the carrier of A2)
(F * B1) . B2 is M2( the carrier of A2)
the ObjectMap of (F * B1) . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (F * B1) . [B2,B2] is set
( the ObjectMap of (F * B1) . (B2,B2)) `1 is set
B1 . B2 is M2( the carrier of A1)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
F . (B1 . B2) is M2( the carrier of A2)
the ObjectMap of F . ((B1 . B2),(B1 . B2)) is M2([: the carrier of A2, the carrier of A2:])
[(B1 . B2),(B1 . B2)] is V15() set
{(B1 . B2),(B1 . B2)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . B2)},{(B1 . B2)}} is set
the ObjectMap of F . [(B1 . B2),(B1 . B2)] is set
( the ObjectMap of F . ((B1 . B2),(B1 . B2))) `1 is set
(id A2) . B2 is M2( the carrier of A2)
the ObjectMap of (id A2) . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (id A2) . [B2,B2] is set
( the ObjectMap of (id A2) . (B2,B2)) `1 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A2 is non empty set
F is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
F " is strict FunctorStr over A2,A1
B1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A2,A1
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the MorphMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A2, the Arrows of A1
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
FunctorStr(# the ObjectMap of B1, the MorphMap of B1 #) is strict FunctorStr over A2,A1
B2 is M2( the carrier of A2)
G is M2( the carrier of A2)
<^B2,G^> is set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
F * B1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A2,A2
b is M2(<^B2,G^>)
(F * B1) . b is M2(<^((F * B1) . B2),((F * B1) . G)^>)
(F * B1) . B2 is M2( the carrier of A2)
the ObjectMap of (F * B1) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (F * B1) . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (F * B1) . [B2,B2] is set
( the ObjectMap of (F * B1) . (B2,B2)) `1 is set
(F * B1) . G is M2( the carrier of A2)
the ObjectMap of (F * B1) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (F * B1) . [G,G] is set
( the ObjectMap of (F * B1) . (G,G)) `1 is set
<^((F * B1) . B2),((F * B1) . G)^> is set
the Arrows of A2 . (((F * B1) . B2),((F * B1) . G)) is set
[((F * B1) . B2),((F * B1) . G)] is V15() set
{((F * B1) . B2),((F * B1) . G)} is set
{((F * B1) . B2)} is set
{{((F * B1) . B2),((F * B1) . G)},{((F * B1) . B2)}} is set
the Arrows of A2 . [((F * B1) . B2),((F * B1) . G)] is set
B1 . G is M2( the carrier of A1)
the ObjectMap of B1 . (G,G) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [G,G] is set
( the ObjectMap of B1 . (G,G)) `1 is set
B1 . B2 is M2( the carrier of A1)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
B1 . b is M2(<^(B1 . G),(B1 . B2)^>)
<^(B1 . G),(B1 . B2)^> is set
the Arrows of A1 . ((B1 . G),(B1 . B2)) is set
[(B1 . G),(B1 . B2)] is V15() set
{(B1 . G),(B1 . B2)} is set
{(B1 . G)} is set
{{(B1 . G),(B1 . B2)},{(B1 . G)}} is set
the Arrows of A1 . [(B1 . G),(B1 . B2)] is set
F . (B1 . b) is M2(<^(F . (B1 . B2)),(F . (B1 . G))^>)
F . (B1 . B2) is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . ((B1 . B2),(B1 . B2)) is M2([: the carrier of A2, the carrier of A2:])
[(B1 . B2),(B1 . B2)] is V15() set
{(B1 . B2),(B1 . B2)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . B2)},{(B1 . B2)}} is set
the ObjectMap of F . [(B1 . B2),(B1 . B2)] is set
( the ObjectMap of F . ((B1 . B2),(B1 . B2))) `1 is set
F . (B1 . G) is M2( the carrier of A2)
the ObjectMap of F . ((B1 . G),(B1 . G)) is M2([: the carrier of A2, the carrier of A2:])
[(B1 . G),(B1 . G)] is V15() set
{(B1 . G),(B1 . G)} is set
{{(B1 . G),(B1 . G)},{(B1 . G)}} is set
the ObjectMap of F . [(B1 . G),(B1 . G)] is set
( the ObjectMap of F . ((B1 . G),(B1 . G))) `1 is set
<^(F . (B1 . B2)),(F . (B1 . G))^> is set
the Arrows of A2 . ((F . (B1 . B2)),(F . (B1 . G))) is set
[(F . (B1 . B2)),(F . (B1 . G))] is V15() set
{(F . (B1 . B2)),(F . (B1 . G))} is set
{(F . (B1 . B2))} is set
{{(F . (B1 . B2)),(F . (B1 . G))},{(F . (B1 . B2))}} is set
the Arrows of A2 . [(F . (B1 . B2)),(F . (B1 . G))] is set
id A2 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
(id A2) . b is M2(<^((id A2) . B2),((id A2) . G)^>)
(id A2) . B2 is M2( the carrier of A2)
the ObjectMap of (id A2) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:])
the ObjectMap of (id A2) . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (id A2) . [B2,B2] is set
( the ObjectMap of (id A2) . (B2,B2)) `1 is set
(id A2) . G is M2( the carrier of A2)
the ObjectMap of (id A2) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (id A2) . [G,G] is set
( the ObjectMap of (id A2) . (G,G)) `1 is set
<^((id A2) . B2),((id A2) . G)^> is set
the Arrows of A2 . (((id A2) . B2),((id A2) . G)) is set
[((id A2) . B2),((id A2) . G)] is V15() set
{((id A2) . B2),((id A2) . G)} is set
{((id A2) . B2)} is set
{{((id A2) . B2),((id A2) . G)},{((id A2) . B2)}} is set
the Arrows of A2 . [((id A2) . B2),((id A2) . G)] is set
B2 is M2( the carrier of A2)
(F * B1) . B2 is M2( the carrier of A2)
the ObjectMap of (F * B1) . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (F * B1) . [B2,B2] is set
( the ObjectMap of (F * B1) . (B2,B2)) `1 is set
B1 . B2 is M2( the carrier of A1)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
F . (B1 . B2) is M2( the carrier of A2)
the ObjectMap of F . ((B1 . B2),(B1 . B2)) is M2([: the carrier of A2, the carrier of A2:])
[(B1 . B2),(B1 . B2)] is V15() set
{(B1 . B2),(B1 . B2)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . B2)},{(B1 . B2)}} is set
the ObjectMap of F . [(B1 . B2),(B1 . B2)] is set
( the ObjectMap of F . ((B1 . B2),(B1 . B2))) `1 is set
(id A2) . B2 is M2( the carrier of A2)
the ObjectMap of (id A2) . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (id A2) . [B2,B2] is set
( the ObjectMap of (id A2) . (B2,B2)) `1 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
F " is strict FunctorStr over A2,A1
B1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A2,A1
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the MorphMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A2, the Arrows of A1
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
FunctorStr(# the ObjectMap of B1, the MorphMap of B1 #) is strict FunctorStr over A2,A1
B2 is M2( the carrier of A1)
G is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A1 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A1 . [B2,G] is set
B1 * F is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A1,A1
b is M2(<^B2,G^>)
(B1 * F) . b is M2(<^((B1 * F) . B2),((B1 * F) . G)^>)
(B1 * F) . B2 is M2( the carrier of A1)
the ObjectMap of (B1 * F) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (B1 * F) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (B1 * F) . [B2,B2] is set
( the ObjectMap of (B1 * F) . (B2,B2)) `1 is set
(B1 * F) . G is M2( the carrier of A1)
the ObjectMap of (B1 * F) . (G,G) is M2([: the carrier of A1, the carrier of A1:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (B1 * F) . [G,G] is set
( the ObjectMap of (B1 * F) . (G,G)) `1 is set
<^((B1 * F) . B2),((B1 * F) . G)^> is set
the Arrows of A1 . (((B1 * F) . B2),((B1 * F) . G)) is set
[((B1 * F) . B2),((B1 * F) . G)] is V15() set
{((B1 * F) . B2),((B1 * F) . G)} is set
{((B1 * F) . B2)} is set
{{((B1 * F) . B2),((B1 * F) . G)},{((B1 * F) . B2)}} is set
the Arrows of A1 . [((B1 * F) . B2),((B1 * F) . G)] is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
F . G is M2( the carrier of A2)
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
F . b is M2(<^(F . B2),(F . G)^>)
<^(F . B2),(F . G)^> is set
the Arrows of A2 . ((F . B2),(F . G)) is set
[(F . B2),(F . G)] is V15() set
{(F . B2),(F . G)} is set
{(F . B2)} is set
{{(F . B2),(F . G)},{(F . B2)}} is set
the Arrows of A2 . [(F . B2),(F . G)] is set
B1 . (F . b) is M2(<^(B1 . (F . B2)),(B1 . (F . G))^>)
B1 . (F . B2) is M2( the carrier of A1)
the ObjectMap of B1 . ((F . B2),(F . B2)) is M2([: the carrier of A1, the carrier of A1:])
[(F . B2),(F . B2)] is V15() set
{(F . B2),(F . B2)} is set
{{(F . B2),(F . B2)},{(F . B2)}} is set
the ObjectMap of B1 . [(F . B2),(F . B2)] is set
( the ObjectMap of B1 . ((F . B2),(F . B2))) `1 is set
B1 . (F . G) is M2( the carrier of A1)
the ObjectMap of B1 . ((F . G),(F . G)) is M2([: the carrier of A1, the carrier of A1:])
[(F . G),(F . G)] is V15() set
{(F . G),(F . G)} is set
{(F . G)} is set
{{(F . G),(F . G)},{(F . G)}} is set
the ObjectMap of B1 . [(F . G),(F . G)] is set
( the ObjectMap of B1 . ((F . G),(F . G))) `1 is set
<^(B1 . (F . B2)),(B1 . (F . G))^> is set
the Arrows of A1 . ((B1 . (F . B2)),(B1 . (F . G))) is set
[(B1 . (F . B2)),(B1 . (F . G))] is V15() set
{(B1 . (F . B2)),(B1 . (F . G))} is set
{(B1 . (F . B2))} is set
{{(B1 . (F . B2)),(B1 . (F . G))},{(B1 . (F . B2))}} is set
the Arrows of A1 . [(B1 . (F . B2)),(B1 . (F . G))] is set
id A1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A1,A1
(id A1) . b is M2(<^((id A1) . B2),((id A1) . G)^>)
(id A1) . B2 is M2( the carrier of A1)
the ObjectMap of (id A1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:])
the ObjectMap of (id A1) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (id A1) . [B2,B2] is set
( the ObjectMap of (id A1) . (B2,B2)) `1 is set
(id A1) . G is M2( the carrier of A1)
the ObjectMap of (id A1) . (G,G) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (id A1) . [G,G] is set
( the ObjectMap of (id A1) . (G,G)) `1 is set
<^((id A1) . B2),((id A1) . G)^> is set
the Arrows of A1 . (((id A1) . B2),((id A1) . G)) is set
[((id A1) . B2),((id A1) . G)] is V15() set
{((id A1) . B2),((id A1) . G)} is set
{((id A1) . B2)} is set
{{((id A1) . B2),((id A1) . G)},{((id A1) . B2)}} is set
the Arrows of A1 . [((id A1) . B2),((id A1) . G)] is set
B2 is M2( the carrier of A1)
(B1 * F) . B2 is M2( the carrier of A1)
the ObjectMap of (B1 * F) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (B1 * F) . [B2,B2] is set
( the ObjectMap of (B1 * F) . (B2,B2)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
B1 . (F . B2) is M2( the carrier of A1)
the ObjectMap of B1 . ((F . B2),(F . B2)) is M2([: the carrier of A1, the carrier of A1:])
[(F . B2),(F . B2)] is V15() set
{(F . B2),(F . B2)} is set
{(F . B2)} is set
{{(F . B2),(F . B2)},{(F . B2)}} is set
the ObjectMap of B1 . [(F . B2),(F . B2)] is set
( the ObjectMap of B1 . ((F . B2),(F . B2))) `1 is set
(id A1) . B2 is M2( the carrier of A1)
the ObjectMap of (id A1) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (id A1) . [B2,B2] is set
( the ObjectMap of (id A1) . (B2,B2)) `1 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
F " is strict FunctorStr over A2,A1
B1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A2,A1
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the MorphMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A2, the Arrows of A1
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
FunctorStr(# the ObjectMap of B1, the MorphMap of B1 #) is strict FunctorStr over A2,A1
B2 is M2( the carrier of A1)
G is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A1 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A1 . [B2,G] is set
B1 * F is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A1,A1
b is M2(<^B2,G^>)
(B1 * F) . b is M2(<^((B1 * F) . B2),((B1 * F) . G)^>)
(B1 * F) . B2 is M2( the carrier of A1)
the ObjectMap of (B1 * F) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (B1 * F) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (B1 * F) . [B2,B2] is set
( the ObjectMap of (B1 * F) . (B2,B2)) `1 is set
(B1 * F) . G is M2( the carrier of A1)
the ObjectMap of (B1 * F) . (G,G) is M2([: the carrier of A1, the carrier of A1:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (B1 * F) . [G,G] is set
( the ObjectMap of (B1 * F) . (G,G)) `1 is set
<^((B1 * F) . B2),((B1 * F) . G)^> is set
the Arrows of A1 . (((B1 * F) . B2),((B1 * F) . G)) is set
[((B1 * F) . B2),((B1 * F) . G)] is V15() set
{((B1 * F) . B2),((B1 * F) . G)} is set
{((B1 * F) . B2)} is set
{{((B1 * F) . B2),((B1 * F) . G)},{((B1 * F) . B2)}} is set
the Arrows of A1 . [((B1 * F) . B2),((B1 * F) . G)] is set
F . G is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
F . b is M2(<^(F . G),(F . B2)^>)
<^(F . G),(F . B2)^> is set
the Arrows of A2 . ((F . G),(F . B2)) is set
[(F . G),(F . B2)] is V15() set
{(F . G),(F . B2)} is set
{(F . G)} is set
{{(F . G),(F . B2)},{(F . G)}} is set
the Arrows of A2 . [(F . G),(F . B2)] is set
B1 . (F . b) is M2(<^(B1 . (F . B2)),(B1 . (F . G))^>)
B1 . (F . B2) is M2( the carrier of A1)
the ObjectMap of B1 . ((F . B2),(F . B2)) is M2([: the carrier of A1, the carrier of A1:])
[(F . B2),(F . B2)] is V15() set
{(F . B2),(F . B2)} is set
{(F . B2)} is set
{{(F . B2),(F . B2)},{(F . B2)}} is set
the ObjectMap of B1 . [(F . B2),(F . B2)] is set
( the ObjectMap of B1 . ((F . B2),(F . B2))) `1 is set
B1 . (F . G) is M2( the carrier of A1)
the ObjectMap of B1 . ((F . G),(F . G)) is M2([: the carrier of A1, the carrier of A1:])
[(F . G),(F . G)] is V15() set
{(F . G),(F . G)} is set
{{(F . G),(F . G)},{(F . G)}} is set
the ObjectMap of B1 . [(F . G),(F . G)] is set
( the ObjectMap of B1 . ((F . G),(F . G))) `1 is set
<^(B1 . (F . B2)),(B1 . (F . G))^> is set
the Arrows of A1 . ((B1 . (F . B2)),(B1 . (F . G))) is set
[(B1 . (F . B2)),(B1 . (F . G))] is V15() set
{(B1 . (F . B2)),(B1 . (F . G))} is set
{(B1 . (F . B2))} is set
{{(B1 . (F . B2)),(B1 . (F . G))},{(B1 . (F . B2))}} is set
the Arrows of A1 . [(B1 . (F . B2)),(B1 . (F . G))] is set
id A1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A1,A1
(id A1) . b is M2(<^((id A1) . B2),((id A1) . G)^>)
(id A1) . B2 is M2( the carrier of A1)
the ObjectMap of (id A1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:])
the ObjectMap of (id A1) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (id A1) . [B2,B2] is set
( the ObjectMap of (id A1) . (B2,B2)) `1 is set
(id A1) . G is M2( the carrier of A1)
the ObjectMap of (id A1) . (G,G) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (id A1) . [G,G] is set
( the ObjectMap of (id A1) . (G,G)) `1 is set
<^((id A1) . B2),((id A1) . G)^> is set
the Arrows of A1 . (((id A1) . B2),((id A1) . G)) is set
[((id A1) . B2),((id A1) . G)] is V15() set
{((id A1) . B2),((id A1) . G)} is set
{((id A1) . B2)} is set
{{((id A1) . B2),((id A1) . G)},{((id A1) . B2)}} is set
the Arrows of A1 . [((id A1) . B2),((id A1) . G)] is set
B2 is M2( the carrier of A1)
(B1 * F) . B2 is M2( the carrier of A1)
the ObjectMap of (B1 * F) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (B1 * F) . [B2,B2] is set
( the ObjectMap of (B1 * F) . (B2,B2)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
B1 . (F . B2) is M2( the carrier of A1)
the ObjectMap of B1 . ((F . B2),(F . B2)) is M2([: the carrier of A1, the carrier of A1:])
[(F . B2),(F . B2)] is V15() set
{(F . B2),(F . B2)} is set
{(F . B2)} is set
{{(F . B2),(F . B2)},{(F . B2)}} is set
the ObjectMap of B1 . [(F . B2),(F . B2)] is set
( the ObjectMap of B1 . ((F . B2),(F . B2))) `1 is set
(id A1) . B2 is M2( the carrier of A1)
the ObjectMap of (id A1) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (id A1) . [B2,B2] is set
( the ObjectMap of (id A1) . (B2,B2)) `1 is set
F is AltCatStr
the Comp of F is Relation-like [: the carrier of F, the carrier of F, the carrier of F:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of F, the Arrows of F|},{| the Arrows of F|}
the carrier of F is set
[: the carrier of F, the carrier of F, the carrier of F:] is set
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like total set
[: the carrier of F, the carrier of F:] is Relation-like set
{| the Arrows of F, the Arrows of F|} is Relation-like [: the carrier of F, the carrier of F, the carrier of F:] -defined Function-like total set
{| the Arrows of F|} is Relation-like [: the carrier of F, the carrier of F, the carrier of F:] -defined Function-like total set
B1 is AltCatStr
the Comp of B1 is Relation-like [: the carrier of B1, the carrier of B1, the carrier of B1:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of B1, the Arrows of B1|},{| the Arrows of B1|}
the carrier of B1 is set
[: the carrier of B1, the carrier of B1, the carrier of B1:] is set
the Arrows of B1 is Relation-like [: the carrier of B1, the carrier of B1:] -defined Function-like total set
[: the carrier of B1, the carrier of B1:] is Relation-like set
{| the Arrows of B1, the Arrows of B1|} is Relation-like [: the carrier of B1, the carrier of B1, the carrier of B1:] -defined Function-like total set
{| the Arrows of B1|} is Relation-like [: the carrier of B1, the carrier of B1, the carrier of B1:] -defined Function-like total set
B2 is set
G is set
b is set
[B2,G,b] is V15() V16() set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
[[B2,G],b] is V15() set
{[B2,G],b} is set
{[B2,G]} is Relation-like Function-like set
{{[B2,G],b},{[B2,G]}} is set
the Comp of B1 . [B2,G,b] is Relation-like Function-like set
the Comp of F . [B2,G,b] is Relation-like Function-like set
A1 is AltCatStr
A2 is AltCatStr
the Comp of A1 is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of A1, the Arrows of A1|},{| the Arrows of A1|}
the carrier of A1 is set
[: the carrier of A1, the carrier of A1, the carrier of A1:] is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like total set
[: the carrier of A1, the carrier of A1:] is Relation-like set
{| the Arrows of A1, the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total set
{| the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total set
the Comp of A2 is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of A2, the Arrows of A2|},{| the Arrows of A2|}
the carrier of A2 is set
[: the carrier of A2, the carrier of A2, the carrier of A2:] is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like total set
[: the carrier of A2, the carrier of A2:] is Relation-like set
{| the Arrows of A2, the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total set
{| the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total set
G is set
F is set
B1 is set
B2 is set
[F,B1,B2] is V15() V16() set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
[[F,B1],B2] is V15() set
{[F,B1],B2} is set
{[F,B1]} is Relation-like Function-like set
{{[F,B1],B2},{[F,B1]}} is set
the Comp of A1 . [F,B1,B2] is Relation-like Function-like set
proj1 ( the Comp of A1 . [F,B1,B2]) is set
the Comp of A2 . [F,B1,B2] is Relation-like Function-like set
proj1 ( the Comp of A2 . [F,B1,B2]) is set
(proj1 ( the Comp of A1 . [F,B1,B2])) /\ (proj1 ( the Comp of A2 . [F,B1,B2])) is set
( the Comp of A1 . [F,B1,B2]) . G is set
( the Comp of A2 . [F,B1,B2]) . G is set
G is set
F is set
B1 is set
B2 is set
[F,B1,B2] is V15() V16() set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
[[F,B1],B2] is V15() set
{[F,B1],B2} is set
{[F,B1]} is Relation-like Function-like set
{{[F,B1],B2},{[F,B1]}} is set
the Comp of A1 . [F,B1,B2] is Relation-like Function-like set
proj1 ( the Comp of A1 . [F,B1,B2]) is set
the Comp of A2 . [F,B1,B2] is Relation-like Function-like set
proj1 ( the Comp of A2 . [F,B1,B2]) is set
(proj1 ( the Comp of A1 . [F,B1,B2])) /\ (proj1 ( the Comp of A2 . [F,B1,B2])) is set
( the Comp of A1 . [F,B1,B2]) . G is set
( the Comp of A2 . [F,B1,B2]) . G is set
A1 is non empty transitive AltCatStr
A2 is non empty transitive AltCatStr
the carrier of A1 is non empty set
the carrier of A2 is non empty set
F is M2( the carrier of A1)
B1 is M2( the carrier of A1)
<^F,B1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of A1 . [F,B1] is set
B2 is M2( the carrier of A1)
<^B1,B2^> is set
the Arrows of A1 . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of A1 . [B1,B2] is set
G is M2( the carrier of A2)
b is M2( the carrier of A2)
<^G,b^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of A2 . [G,b] is set
c is M2( the carrier of A2)
<^b,c^> is set
the Arrows of A2 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of A2 . [b,c] is set
c1 is M2(<^G,b^>)
b1 is M2(<^F,B1^>)
f1 is M2(<^b,c^>)
f is M2(<^B1,B2^>)
<^G,c^> is set
the Arrows of A2 . (G,c) is set
[G,c] is V15() set
{G,c} is set
{{G,c},{G}} is set
the Arrows of A2 . [G,c] is set
[:( the Arrows of A2 . (b,c)),( the Arrows of A2 . (G,b)):] is Relation-like set
the Comp of A2 is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of A2, the Arrows of A2|},{| the Arrows of A2|}
[: the carrier of A2, the carrier of A2, the carrier of A2:] is non empty set
{| the Arrows of A2, the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
{| the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Comp of A2 . (G,b,c) is Relation-like [:( the Arrows of A2 . (b,c)),( the Arrows of A2 . (G,b)):] -defined the Arrows of A2 . (G,c) -valued Function-like quasi_total M2( bool [:[:( the Arrows of A2 . (b,c)),( the Arrows of A2 . (G,b)):],( the Arrows of A2 . (G,c)):])
[:[:( the Arrows of A2 . (b,c)),( the Arrows of A2 . (G,b)):],( the Arrows of A2 . (G,c)):] is Relation-like set
bool [:[:( the Arrows of A2 . (b,c)),( the Arrows of A2 . (G,b)):],( the Arrows of A2 . (G,c)):] is non empty set
dom ( the Comp of A2 . (G,b,c)) is Relation-like the Arrows of A2 . (b,c) -defined the Arrows of A2 . (G,b) -valued M2( bool [:( the Arrows of A2 . (b,c)),( the Arrows of A2 . (G,b)):])
bool [:( the Arrows of A2 . (b,c)),( the Arrows of A2 . (G,b)):] is non empty set
[:<^b,c^>,<^G,b^>:] is Relation-like set
[f1,c1] is V15() set
{f1,c1} is set
{f1} is set
{{f1,c1},{f1}} is set
<^F,B2^> is set
the Arrows of A1 . (F,B2) is set
[F,B2] is V15() set
{F,B2} is set
{{F,B2},{F}} is set
the Arrows of A1 . [F,B2] is set
[:( the Arrows of A1 . (B1,B2)),( the Arrows of A1 . (F,B1)):] is Relation-like set
the Comp of A1 is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of A1, the Arrows of A1|},{| the Arrows of A1|}
[: the carrier of A1, the carrier of A1, the carrier of A1:] is non empty set
{| the Arrows of A1, the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
{| the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Comp of A1 . (F,B1,B2) is Relation-like [:( the Arrows of A1 . (B1,B2)),( the Arrows of A1 . (F,B1)):] -defined the Arrows of A1 . (F,B2) -valued Function-like quasi_total M2( bool [:[:( the Arrows of A1 . (B1,B2)),( the Arrows of A1 . (F,B1)):],( the Arrows of A1 . (F,B2)):])
[:[:( the Arrows of A1 . (B1,B2)),( the Arrows of A1 . (F,B1)):],( the Arrows of A1 . (F,B2)):] is Relation-like set
bool [:[:( the Arrows of A1 . (B1,B2)),( the Arrows of A1 . (F,B1)):],( the Arrows of A1 . (F,B2)):] is non empty set
dom ( the Comp of A1 . (F,B1,B2)) is Relation-like the Arrows of A1 . (B1,B2) -defined the Arrows of A1 . (F,B1) -valued M2( bool [:( the Arrows of A1 . (B1,B2)),( the Arrows of A1 . (F,B1)):])
bool [:( the Arrows of A1 . (B1,B2)),( the Arrows of A1 . (F,B1)):] is non empty set
[:<^B1,B2^>,<^F,B1^>:] is Relation-like set
[f,b1] is V15() set
{f,b1} is set
{f} is set
{{f,b1},{f}} is set
[F,B1,B2] is V15() V16() set
[[F,B1],B2] is V15() set
{[F,B1],B2} is set
{[F,B1]} is Relation-like Function-like set
{{[F,B1],B2},{[F,B1]}} is set
the Comp of A1 . [F,B1,B2] is Relation-like Function-like set
[G,b,c] is V15() V16() set
[[G,b],c] is V15() set
{[G,b],c} is set
{[G,b]} is Relation-like Function-like set
{{[G,b],c},{[G,b]}} is set
the Comp of A2 . [G,b,c] is Relation-like Function-like set
f * b1 is M2(<^F,B2^>)
( the Comp of A1 . (F,B1,B2)) . (f,b1) is set
( the Comp of A1 . (F,B1,B2)) . [f,b1] is set
( the Comp of A2 . (G,b,c)) . (f1,c1) is set
( the Comp of A2 . (G,b,c)) . [f1,c1] is set
f1 * c1 is M2(<^G,c^>)
G is set
F is set
B1 is set
B2 is set
[F,B1,B2] is V15() V16() set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
[[F,B1],B2] is V15() set
{[F,B1],B2} is set
{[F,B1]} is Relation-like Function-like set
{{[F,B1],B2},{[F,B1]}} is set
the Comp of A1 . [F,B1,B2] is Relation-like Function-like set
proj1 ( the Comp of A1 . [F,B1,B2]) is set
the Comp of A2 . [F,B1,B2] is Relation-like Function-like set
proj1 ( the Comp of A2 . [F,B1,B2]) is set
(proj1 ( the Comp of A1 . [F,B1,B2])) /\ (proj1 ( the Comp of A2 . [F,B1,B2])) is set
( the Comp of A1 . [F,B1,B2]) . G is set
( the Comp of A2 . [F,B1,B2]) . G is set
dom the Comp of A1 is non empty M2( bool [: the carrier of A1, the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1, the carrier of A1:] is non empty set
dom the Comp of A2 is non empty M2( bool [: the carrier of A2, the carrier of A2, the carrier of A2:])
bool [: the carrier of A2, the carrier of A2, the carrier of A2:] is non empty set
b is M2( the carrier of A1)
c is M2( the carrier of A1)
b1 is M2( the carrier of A1)
the Comp of A1 . (b,c,b1) is Relation-like [:( the Arrows of A1 . (c,b1)),( the Arrows of A1 . (b,c)):] -defined the Arrows of A1 . (b,b1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of A1 . (c,b1)),( the Arrows of A1 . (b,c)):],( the Arrows of A1 . (b,b1)):])
the Arrows of A1 . (c,b1) is set
[c,b1] is V15() set
{c,b1} is set
{c} is set
{{c,b1},{c}} is set
the Arrows of A1 . [c,b1] is set
the Arrows of A1 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of A1 . [b,c] is set
[:( the Arrows of A1 . (c,b1)),( the Arrows of A1 . (b,c)):] is Relation-like set
the Arrows of A1 . (b,b1) is set
[b,b1] is V15() set
{b,b1} is set
{{b,b1},{b}} is set
the Arrows of A1 . [b,b1] is set
[:[:( the Arrows of A1 . (c,b1)),( the Arrows of A1 . (b,c)):],( the Arrows of A1 . (b,b1)):] is Relation-like set
bool [:[:( the Arrows of A1 . (c,b1)),( the Arrows of A1 . (b,c)):],( the Arrows of A1 . (b,b1)):] is non empty set
[b,c,b1] is V15() V16() set
[[b,c],b1] is V15() set
{[b,c],b1} is set
{[b,c]} is Relation-like Function-like set
{{[b,c],b1},{[b,c]}} is set
the Comp of A1 . [b,c,b1] is Relation-like Function-like set
<^c,b1^> is set
<^b,c^> is set
[:<^c,b1^>,<^b,c^>:] is Relation-like set
<^b,b1^> is set
dom ( the Comp of A1 . (b,c,b1)) is Relation-like the Arrows of A1 . (c,b1) -defined the Arrows of A1 . (b,c) -valued M2( bool [:( the Arrows of A1 . (c,b1)),( the Arrows of A1 . (b,c)):])
bool [:( the Arrows of A1 . (c,b1)),( the Arrows of A1 . (b,c)):] is non empty set
c1 is set
a9 is set
[c1,a9] is V15() set
{c1,a9} is set
{c1} is set
{{c1,a9},{c1}} is set
c1 is M2( the carrier of A2)
f is M2( the carrier of A2)
f1 is M2( the carrier of A2)
the Comp of A2 . (c1,f,f1) is Relation-like [:( the Arrows of A2 . (f,f1)),( the Arrows of A2 . (c1,f)):] -defined the Arrows of A2 . (c1,f1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of A2 . (f,f1)),( the Arrows of A2 . (c1,f)):],( the Arrows of A2 . (c1,f1)):])
the Arrows of A2 . (f,f1) is set
[f,f1] is V15() set
{f,f1} is set
{f} is set
{{f,f1},{f}} is set
the Arrows of A2 . [f,f1] is set
the Arrows of A2 . (c1,f) is set
[c1,f] is V15() set
{c1,f} is set
{c1} is set
{{c1,f},{c1}} is set
the Arrows of A2 . [c1,f] is set
[:( the Arrows of A2 . (f,f1)),( the Arrows of A2 . (c1,f)):] is Relation-like set
the Arrows of A2 . (c1,f1) is set
[c1,f1] is V15() set
{c1,f1} is set
{{c1,f1},{c1}} is set
the Arrows of A2 . [c1,f1] is set
[:[:( the Arrows of A2 . (f,f1)),( the Arrows of A2 . (c1,f)):],( the Arrows of A2 . (c1,f1)):] is Relation-like set
bool [:[:( the Arrows of A2 . (f,f1)),( the Arrows of A2 . (c1,f)):],( the Arrows of A2 . (c1,f1)):] is non empty set
[c1,f,f1] is V15() V16() set
[[c1,f],f1] is V15() set
{[c1,f],f1} is set
{[c1,f]} is Relation-like Function-like set
{{[c1,f],f1},{[c1,f]}} is set
the Comp of A2 . [c1,f,f1] is Relation-like Function-like set
<^f,f1^> is set
<^c1,f^> is set
[:<^f,f1^>,<^c1,f^>:] is Relation-like set
<^c1,f1^> is set
dom ( the Comp of A2 . (c1,f,f1)) is Relation-like the Arrows of A2 . (f,f1) -defined the Arrows of A2 . (c1,f) -valued M2( bool [:( the Arrows of A2 . (f,f1)),( the Arrows of A2 . (c1,f)):])
bool [:( the Arrows of A2 . (f,f1)),( the Arrows of A2 . (c1,f)):] is non empty set
b9 is M2(<^b,c^>)
c9 is M2(<^c,b1^>)
( the Comp of A1 . [b,c,b1]) . G is set
( the Comp of A1 . (b,c,b1)) . (c9,b9) is set
[c9,b9] is V15() set
{c9,b9} is set
{c9} is set
{{c9,b9},{c9}} is set
( the Comp of A1 . (b,c,b1)) . [c9,b9] is set
c9 * b9 is M2(<^b,b1^>)
g9 is M2(<^c1,f^>)
f9 is M2(<^f,f1^>)
f9 * g9 is M2(<^c1,f1^>)
( the Comp of A2 . (c1,f,f1)) . (f9,g9) is set
[f9,g9] is V15() set
{f9,g9} is set
{f9} is set
{{f9,g9},{f9}} is set
( the Comp of A2 . (c1,f,f1)) . [f9,g9] is set
A1 is non empty transitive semi-functional V106() with_units reflexive para-functional AltCatStr
A2 is non empty transitive semi-functional V106() with_units reflexive para-functional AltCatStr
the carrier of A1 is non empty set
F is M2( the carrier of A1)
B1 is M2( the carrier of A1)
<^F,B1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of A1 . [F,B1] is set
B2 is M2( the carrier of A1)
<^B1,B2^> is set
the Arrows of A1 . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of A1 . [B1,B2] is set
the carrier of A2 is non empty set
G is M2( the carrier of A2)
b is M2( the carrier of A2)
<^G,b^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of A2 . [G,b] is set
c is M2( the carrier of A2)
<^b,c^> is set
the Arrows of A2 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of A2 . [b,c] is set
c1 is Relation-like Function-like M2(<^G,b^>)
b1 is Relation-like Function-like M2(<^F,B1^>)
A1 -carrier_of F is set
A1 -carrier_of B1 is set
[:(A1 -carrier_of F),(A1 -carrier_of B1):] is Relation-like set
bool [:(A1 -carrier_of F),(A1 -carrier_of B1):] is non empty set
c1 is Relation-like Function-like M2(<^b,c^>)
f1 is Relation-like Function-like M2(<^B1,B2^>)
<^G,c^> is set
the Arrows of A2 . (G,c) is set
[G,c] is V15() set
{G,c} is set
{{G,c},{G}} is set
the Arrows of A2 . [G,c] is set
A1 -carrier_of B2 is set
[:(A1 -carrier_of B1),(A1 -carrier_of B2):] is Relation-like set
bool [:(A1 -carrier_of B1),(A1 -carrier_of B2):] is non empty set
<^F,B2^> is set
the Arrows of A1 . (F,B2) is set
[F,B2] is V15() set
{F,B2} is set
{{F,B2},{F}} is set
the Arrows of A1 . [F,B2] is set
f1 * b1 is Relation-like Function-like M2(<^F,B2^>)
f is Relation-like A1 -carrier_of F -defined A1 -carrier_of B1 -valued Function-like quasi_total M2( bool [:(A1 -carrier_of F),(A1 -carrier_of B1):])
a9 is Relation-like A1 -carrier_of B1 -defined A1 -carrier_of B2 -valued Function-like quasi_total M2( bool [:(A1 -carrier_of B1),(A1 -carrier_of B2):])
a9 * f is Relation-like A1 -carrier_of F -defined A1 -carrier_of B2 -valued Function-like M2( bool [:(A1 -carrier_of F),(A1 -carrier_of B2):])
[:(A1 -carrier_of F),(A1 -carrier_of B2):] is Relation-like set
bool [:(A1 -carrier_of F),(A1 -carrier_of B2):] is non empty set
c1 * c1 is Relation-like Function-like M2(<^G,c^>)
A1 is Relation-like Function-like set
proj1 A1 is set
A2 is Relation-like Function-like set
proj1 A2 is set
(proj1 A1) /\ (proj1 A2) is set
F is Relation-like Function-like set
proj1 F is set
B1 is Relation-like Function-like set
proj1 B1 is set
B2 is set
F . B2 is set
A1 . B2 is set
A2 . B2 is set
(A1 . B2) /\ (A2 . B2) is set
B1 . B2 is set
F is Relation-like Function-like set
proj1 F is set
B1 is Relation-like Function-like set
proj1 B1 is set
B2 is Relation-like Function-like set
proj1 B2 is set
(proj1 B1) /\ (proj1 B2) is set
(proj1 B2) /\ (proj1 B1) is set
G is set
F . G is set
B2 . G is set
B1 . G is set
(B2 . G) /\ (B1 . G) is set
A1 is set
A2 is Relation-like A1 -defined Function-like total set
F is Relation-like A1 -defined Function-like total set
(A2,F) is Relation-like Function-like set
A2 /\ F is Relation-like A1 -defined Function-like total set
dom A2 is M2( bool A1)
bool A1 is non empty set
dom F is M2( bool A1)
proj1 (A2,F) is set
A1 /\ A1 is set
B1 is Relation-like A1 -defined Function-like total set
B2 is set
B1 . B2 is set
A2 . B2 is set
F . B2 is set
(A2 . B2) /\ (F . B2) is set
A1 is set
A2 is set
A1 /\ A2 is set
F is Relation-like A1 -defined Function-like total set
B1 is Relation-like A2 -defined Function-like total set
(F,B1) is Relation-like Function-like set
dom F is M2( bool A1)
bool A1 is non empty set
dom B1 is M2( bool A2)
bool A2 is non empty set
proj1 (F,B1) is set
A1 is set
A2 is set
F is Relation-like A1 -defined Function-like total set
B1 is Relation-like Function-like set
(F,B1) is Relation-like Function-like set
B2 is Relation-like A2 -defined Function-like total set
dom F is M2( bool A1)
bool A1 is non empty set
dom B2 is M2( bool A2)
bool A2 is non empty set
proj1 B1 is set
A1 /\ (proj1 B1) is set
G is set
B2 . G is set
F . G is set
B1 . G is set
(F . G) /\ (B1 . G) is set
A1 is set
A2 is set
A1 /\ A2 is set
F is Relation-like A1 -defined Function-like total set
B1 is Relation-like A1 -defined Function-like total set
B2 is Relation-like A2 -defined Function-like total set
(F,B2) is Relation-like Function-like set
G is Relation-like A2 -defined Function-like total set
(B1,G) is Relation-like Function-like set
b is Relation-like A1 /\ A2 -defined Function-like total set
c is Relation-like A1 /\ A2 -defined Function-like total set
b1 is Relation-like A1 -defined Function-like total Function-yielding V37() ManySortedFunction of F,B1
dom b1 is M2( bool A1)
bool A1 is non empty set
c1 is Relation-like A2 -defined Function-like total Function-yielding V37() ManySortedFunction of B2,G
dom c1 is M2( bool A2)
bool A2 is non empty set
(b1,c1) is Relation-like Function-like set
dom B1 is M2( bool A1)
dom G is M2( bool A2)
dom F is M2( bool A1)
dom B2 is M2( bool A2)
f is Relation-like A1 /\ A2 -defined Function-like total set
f1 is set
f . f1 is set
b . f1 is set
c . f1 is set
[:(b . f1),(c . f1):] is Relation-like set
bool [:(b . f1),(c . f1):] is non empty set
b1 . f1 is Relation-like Function-like set
c1 . f1 is Relation-like Function-like set
(b1 . f1) /\ (c1 . f1) is Relation-like set
B2 . f1 is set
G . f1 is set
[:(B2 . f1),(G . f1):] is Relation-like set
bool [:(B2 . f1),(G . f1):] is non empty set
F . f1 is set
(F . f1) /\ (B2 . f1) is set
B1 . f1 is set
(B1 . f1) /\ (G . f1) is set
[:(F . f1),(B1 . f1):] is Relation-like set
bool [:(F . f1),(B1 . f1):] is non empty set
A1 is set
[:A1,A1:] is Relation-like set
A2 is set
[:A2,A2:] is Relation-like set
A1 /\ A2 is set
[:(A1 /\ A2),(A1 /\ A2):] is Relation-like set
F is Relation-like [:A1,A1:] -defined Function-like total set
{|F|} is Relation-like [:A1,A1,A1:] -defined Function-like total set
[:A1,A1,A1:] is set
B1 is Relation-like [:A2,A2:] -defined Function-like total set
(F,B1) is Relation-like Function-like set
{|B1|} is Relation-like [:A2,A2,A2:] -defined Function-like total set
[:A2,A2,A2:] is set
({|F|},{|B1|}) is Relation-like Function-like set
[:A1,A1:] /\ [:A2,A2:] is Relation-like set
[:[:A1,A1:],A1:] is Relation-like set
[:[:A2,A2:],A2:] is Relation-like set
[:A1,A1,A1:] /\ [:A2,A2,A2:] is set
[:[:(A1 /\ A2),(A1 /\ A2):],(A1 /\ A2):] is Relation-like set
[:(A1 /\ A2),(A1 /\ A2),(A1 /\ A2):] is set
dom F is Relation-like A1 -defined A1 -valued M2( bool [:A1,A1:])
bool [:A1,A1:] is non empty set
dom B1 is Relation-like A2 -defined A2 -valued M2( bool [:A2,A2:])
bool [:A2,A2:] is non empty set
G is set
b is set
c is set
b1 is set
[b,c,b1] is V15() V16() set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
[[b,c],b1] is V15() set
{[b,c],b1} is set
{[b,c]} is Relation-like Function-like set
{{[b,c],b1},{[b,c]}} is set
[b,b1] is V15() set
{b,b1} is set
{{b,b1},{b}} is set
{|B1|} . (b,c,b1) is set
B1 . (b,b1) is set
B1 . [b,b1] is set
{|F|} . (b,c,b1) is set
F . (b,b1) is set
F . [b,b1] is set
B2 is Relation-like [:(A1 /\ A2),(A1 /\ A2):] -defined Function-like total set
{|B2|} is Relation-like [:(A1 /\ A2),(A1 /\ A2),(A1 /\ A2):] -defined Function-like total set
{|B2|} . (b,c,b1) is set
B2 . (b,b1) is set
B2 . [b,b1] is set
{|B2|} . G is set
(F . (b,b1)) /\ (B1 . [b,b1]) is set
{|F|} . G is set
({|F|} . G) /\ (B1 . (b,b1)) is set
{|B1|} . G is set
({|F|} . G) /\ ({|B1|} . G) is set
dom {|B2|} is M2( bool [:(A1 /\ A2),(A1 /\ A2),(A1 /\ A2):])
bool [:(A1 /\ A2),(A1 /\ A2),(A1 /\ A2):] is non empty set
dom {|F|} is M2( bool [:A1,A1,A1:])
bool [:A1,A1,A1:] is non empty set
dom {|B1|} is M2( bool [:A2,A2,A2:])
bool [:A2,A2,A2:] is non empty set
A1 is set
[:A1,A1:] is Relation-like set
A2 is set
[:A2,A2:] is Relation-like set
A1 /\ A2 is set
[:(A1 /\ A2),(A1 /\ A2):] is Relation-like set
F is Relation-like [:A1,A1:] -defined Function-like total set
B1 is Relation-like [:A1,A1:] -defined Function-like total set
{|F,B1|} is Relation-like [:A1,A1,A1:] -defined Function-like total set
[:A1,A1,A1:] is set
B2 is Relation-like [:A2,A2:] -defined Function-like total set
(F,B2) is Relation-like Function-like set
G is Relation-like [:A2,A2:] -defined Function-like total set
(B1,G) is Relation-like Function-like set
{|B2,G|} is Relation-like [:A2,A2,A2:] -defined Function-like total set
[:A2,A2,A2:] is set
({|F,B1|},{|B2,G|}) is Relation-like Function-like set
dom B1 is Relation-like A1 -defined A1 -valued M2( bool [:A1,A1:])
bool [:A1,A1:] is non empty set
dom G is Relation-like A2 -defined A2 -valued M2( bool [:A2,A2:])
bool [:A2,A2:] is non empty set
[:A1,A1:] /\ [:A2,A2:] is Relation-like set
[:[:A1,A1:],A1:] is Relation-like set
[:[:A2,A2:],A2:] is Relation-like set
[:A1,A1,A1:] /\ [:A2,A2,A2:] is set
[:[:(A1 /\ A2),(A1 /\ A2):],(A1 /\ A2):] is Relation-like set
[:(A1 /\ A2),(A1 /\ A2),(A1 /\ A2):] is set
dom F is Relation-like A1 -defined A1 -valued M2( bool [:A1,A1:])
dom B2 is Relation-like A2 -defined A2 -valued M2( bool [:A2,A2:])
b1 is set
c1 is set
f is set
f1 is set
[c1,f,f1] is V15() V16() set
[c1,f] is V15() set
{c1,f} is set
{c1} is set
{{c1,f},{c1}} is set
[[c1,f],f1] is V15() set
{[c1,f],f1} is set
{[c1,f]} is Relation-like Function-like set
{{[c1,f],f1},{[c1,f]}} is set
[f,f1] is V15() set
{f,f1} is set
{f} is set
{{f,f1},{f}} is set
{|F,B1|} . (c1,f,f1) is set
B1 . (f,f1) is set
B1 . [f,f1] is set
F . (c1,f) is set
F . [c1,f] is set
[:(B1 . (f,f1)),(F . (c1,f)):] is Relation-like set
{|B2,G|} . (c1,f,f1) is set
G . (f,f1) is set
G . [f,f1] is set
B2 . (c1,f) is set
B2 . [c1,f] is set
[:(G . (f,f1)),(B2 . (c1,f)):] is Relation-like set
b is Relation-like [:(A1 /\ A2),(A1 /\ A2):] -defined Function-like total set
c is Relation-like [:(A1 /\ A2),(A1 /\ A2):] -defined Function-like total set
{|b,c|} is Relation-like [:(A1 /\ A2),(A1 /\ A2),(A1 /\ A2):] -defined Function-like total set
{|b,c|} . (c1,f,f1) is set
c . (f,f1) is set
c . [f,f1] is set
b . (c1,f) is set
b . [c1,f] is set
[:(c . (f,f1)),(b . (c1,f)):] is Relation-like set
{|b,c|} . b1 is set
(B1 . [f,f1]) /\ (G . [f,f1]) is set
[:((B1 . [f,f1]) /\ (G . [f,f1])),(b . (c1,f)):] is Relation-like set
(F . [c1,f]) /\ (B2 . [c1,f]) is set
[:((B1 . [f,f1]) /\ (G . [f,f1])),((F . [c1,f]) /\ (B2 . [c1,f])):] is Relation-like set
[:(B1 . [f,f1]),(F . [c1,f]):] is Relation-like set
[:(G . [f,f1]),(B2 . [c1,f]):] is Relation-like set
[:(B1 . [f,f1]),(F . [c1,f]):] /\ [:(G . [f,f1]),(B2 . [c1,f]):] is Relation-like set
{|F,B1|} . b1 is set
({|F,B1|} . b1) /\ [:(G . [f,f1]),(B2 . [c1,f]):] is Relation-like set
{|B2,G|} . b1 is set
({|F,B1|} . b1) /\ ({|B2,G|} . b1) is set
dom {|b,c|} is M2( bool [:(A1 /\ A2),(A1 /\ A2),(A1 /\ A2):])
bool [:(A1 /\ A2),(A1 /\ A2),(A1 /\ A2):] is non empty set
dom {|F,B1|} is M2( bool [:A1,A1,A1:])
bool [:A1,A1,A1:] is non empty set
dom {|B2,G|} is M2( bool [:A2,A2,A2:])
bool [:A2,A2,A2:] is non empty set
A1 is AltCatStr
A2 is AltCatStr
the carrier of A1 is set
the carrier of A2 is set
the carrier of A1 /\ the carrier of A2 is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like total set
[: the carrier of A1, the carrier of A1:] is Relation-like set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like total set
[: the carrier of A2, the carrier of A2:] is Relation-like set
( the Arrows of A1, the Arrows of A2) is Relation-like Function-like set
the Comp of A1 is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of A1, the Arrows of A1|},{| the Arrows of A1|}
[: the carrier of A1, the carrier of A1, the carrier of A1:] is set
{| the Arrows of A1, the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total set
{| the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total set
the Comp of A2 is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of A2, the Arrows of A2|},{| the Arrows of A2|}
[: the carrier of A2, the carrier of A2, the carrier of A2:] is set
{| the Arrows of A2, the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total set
{| the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total set
( the Comp of A1, the Comp of A2) is Relation-like Function-like set
F is set
dom the Comp of A1 is M2( bool [: the carrier of A1, the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1, the carrier of A1:] is non empty set
dom the Comp of A2 is M2( bool [: the carrier of A2, the carrier of A2, the carrier of A2:])
bool [: the carrier of A2, the carrier of A2, the carrier of A2:] is non empty set
the Comp of A1 . F is Relation-like Function-like set
the Comp of A2 . F is Relation-like Function-like set
B1 is set
B2 is set
G is set
[B1,B2,G] is V15() V16() set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
[[B1,B2],G] is V15() set
{[B1,B2],G} is set
{[B1,B2]} is Relation-like Function-like set
{{[B1,B2],G},{[B1,B2]}} is set
[:[: the carrier of A2, the carrier of A2:], the carrier of A2:] is Relation-like set
[:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] is Relation-like set
[: the carrier of A1, the carrier of A1:] /\ [: the carrier of A2, the carrier of A2:] is Relation-like set
[:[: the carrier of A1, the carrier of A1:], the carrier of A1:] is Relation-like set
[: the carrier of A1, the carrier of A1, the carrier of A1:] /\ [: the carrier of A2, the carrier of A2, the carrier of A2:] is set
[:[:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):],( the carrier of A1 /\ the carrier of A2):] is Relation-like set
[:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] is set
({| the Arrows of A1|},{| the Arrows of A2|}) is Relation-like Function-like set
B1 is Relation-like [:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] -defined Function-like total set
{|B1|} is Relation-like [:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] -defined Function-like total set
({| the Arrows of A1, the Arrows of A1|},{| the Arrows of A2, the Arrows of A2|}) is Relation-like Function-like set
{|B1,B1|} is Relation-like [:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] -defined Function-like total set
G is Relation-like [:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] -defined Function-like total set
b is Relation-like [:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] -defined Function-like total set
{|G,b|} is Relation-like [:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] -defined Function-like total set
B2 is Relation-like [:( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2),( the carrier of A1 /\ the carrier of A2):] -defined Function-like total Function-yielding V37() ManySortedFunction of {|B1,B1|},{|B1|}
AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #) is strict AltCatStr
the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #) is set
the Arrows of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #) is Relation-like [: the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #):] -defined Function-like total set
[: the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #):] is Relation-like set
the Comp of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #) is Relation-like [: the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #):] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the Arrows of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #)|},{| the Arrows of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #)|}
[: the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #):] is set
{| the Arrows of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the Arrows of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #)|} is Relation-like [: the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #):] -defined Function-like total set
{| the Arrows of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #)|} is Relation-like [: the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #), the carrier of AltCatStr(# ( the carrier of A1 /\ the carrier of A2),B1,B2 #):] -defined Function-like total set
F is strict AltCatStr
the carrier of F is set
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like total set
[: the carrier of F, the carrier of F:] is Relation-like set
the Comp of F is Relation-like [: the carrier of F, the carrier of F, the carrier of F:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of F, the Arrows of F|},{| the Arrows of F|}
[: the carrier of F, the carrier of F, the carrier of F:] is set
{| the Arrows of F, the Arrows of F|} is Relation-like [: the carrier of F, the carrier of F, the carrier of F:] -defined Function-like total set
{| the Arrows of F|} is Relation-like [: the carrier of F, the carrier of F, the carrier of F:] -defined Function-like total set
B1 is strict AltCatStr
the carrier of B1 is set
the Arrows of B1 is Relation-like [: the carrier of B1, the carrier of B1:] -defined Function-like total set
[: the carrier of B1, the carrier of B1:] is Relation-like set
the Comp of B1 is Relation-like [: the carrier of B1, the carrier of B1, the carrier of B1:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of B1, the Arrows of B1|},{| the Arrows of B1|}
[: the carrier of B1, the carrier of B1, the carrier of B1:] is set
{| the Arrows of B1, the Arrows of B1|} is Relation-like [: the carrier of B1, the carrier of B1, the carrier of B1:] -defined Function-like total set
{| the Arrows of B1|} is Relation-like [: the carrier of B1, the carrier of B1, the carrier of B1:] -defined Function-like total set
A1 is AltCatStr
A2 is AltCatStr
(A1,A2) is strict AltCatStr
(A2,A1) is strict AltCatStr
the Comp of (A1,A2) is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of (A1,A2), the Arrows of (A1,A2)|},{| the Arrows of (A1,A2)|}
the carrier of (A1,A2) is set
[: the carrier of (A1,A2), the carrier of (A1,A2), the carrier of (A1,A2):] is set
the Arrows of (A1,A2) is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
[: the carrier of (A1,A2), the carrier of (A1,A2):] is Relation-like set
{| the Arrows of (A1,A2), the Arrows of (A1,A2)|} is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
{| the Arrows of (A1,A2)|} is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
the Comp of A1 is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of A1, the Arrows of A1|},{| the Arrows of A1|}
the carrier of A1 is set
[: the carrier of A1, the carrier of A1, the carrier of A1:] is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like total set
[: the carrier of A1, the carrier of A1:] is Relation-like set
{| the Arrows of A1, the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total set
{| the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total set
the Comp of A2 is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of A2, the Arrows of A2|},{| the Arrows of A2|}
the carrier of A2 is set
[: the carrier of A2, the carrier of A2, the carrier of A2:] is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like total set
[: the carrier of A2, the carrier of A2:] is Relation-like set
{| the Arrows of A2, the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total set
{| the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total set
( the Comp of A1, the Comp of A2) is Relation-like Function-like set
the carrier of A1 /\ the carrier of A2 is set
( the Arrows of A1, the Arrows of A2) is Relation-like Function-like set
A1 is AltCatStr
A2 is AltCatStr
(A1,A2) is strict AltCatStr
the Comp of (A1,A2) is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of (A1,A2), the Arrows of (A1,A2)|},{| the Arrows of (A1,A2)|}
the carrier of (A1,A2) is set
[: the carrier of (A1,A2), the carrier of (A1,A2), the carrier of (A1,A2):] is set
the Arrows of (A1,A2) is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
[: the carrier of (A1,A2), the carrier of (A1,A2):] is Relation-like set
{| the Arrows of (A1,A2), the Arrows of (A1,A2)|} is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
{| the Arrows of (A1,A2)|} is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
the Comp of A1 is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of A1, the Arrows of A1|},{| the Arrows of A1|}
the carrier of A1 is set
[: the carrier of A1, the carrier of A1, the carrier of A1:] is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like total set
[: the carrier of A1, the carrier of A1:] is Relation-like set
{| the Arrows of A1, the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total set
{| the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like total set
the Comp of A2 is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total Function-yielding V37() ManySortedFunction of {| the Arrows of A2, the Arrows of A2|},{| the Arrows of A2|}
the carrier of A2 is set
[: the carrier of A2, the carrier of A2, the carrier of A2:] is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like total set
[: the carrier of A2, the carrier of A2:] is Relation-like set
{| the Arrows of A2, the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total set
{| the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like total set
( the Comp of A1, the Comp of A2) is Relation-like Function-like set
the carrier of A1 /\ the carrier of A2 is set
( the Arrows of A1, the Arrows of A2) is Relation-like Function-like set
A1 is AltCatStr
A2 is AltCatStr
the carrier of A1 is set
the carrier of A2 is set
(A1,A2) is strict AltCatStr
the carrier of (A1,A2) is set
the carrier of A1 /\ the carrier of A2 is set
[: the carrier of (A1,A2), the carrier of (A1,A2):] is Relation-like set
[: the carrier of A1, the carrier of A1:] is Relation-like set
[: the carrier of A2, the carrier of A2:] is Relation-like set
[: the carrier of A1, the carrier of A1:] /\ [: the carrier of A2, the carrier of A2:] is Relation-like set
F is M2( the carrier of A1)
B1 is M2( the carrier of A1)
<^F,B1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like total set
the Arrows of A1 . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of A1 . [F,B1] is set
B2 is M2( the carrier of A2)
G is M2( the carrier of A2)
<^B2,G^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like total set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
<^F,B1^> /\ <^B2,G^> is set
b is M2( the carrier of (A1,A2))
c is M2( the carrier of (A1,A2))
<^b,c^> is set
the Arrows of (A1,A2) is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
the Arrows of (A1,A2) . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of (A1,A2) . [b,c] is set
dom the Arrows of A1 is Relation-like the carrier of A1 -defined the carrier of A1 -valued M2( bool [: the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1:] is non empty set
dom the Arrows of A2 is Relation-like the carrier of A2 -defined the carrier of A2 -valued M2( bool [: the carrier of A2, the carrier of A2:])
bool [: the carrier of A2, the carrier of A2:] is non empty set
( the Arrows of A1 . [F,B1]) /\ ( the Arrows of A2 . [B2,G]) is set
( the Arrows of A1, the Arrows of A2) is Relation-like Function-like set
A1 is transitive AltCatStr
A2 is transitive AltCatStr
(A1,A2) is strict AltCatStr
the carrier of (A1,A2) is set
the carrier of A1 is set
the carrier of A2 is set
the carrier of A1 /\ the carrier of A2 is set
B1 is M2( the carrier of (A1,A2))
B2 is M2( the carrier of (A1,A2))
<^B1,B2^> is set
the Arrows of (A1,A2) is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
[: the carrier of (A1,A2), the carrier of (A1,A2):] is Relation-like set
the Arrows of (A1,A2) . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of (A1,A2) . [B1,B2] is set
G is M2( the carrier of (A1,A2))
<^B2,G^> is set
the Arrows of (A1,A2) . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of (A1,A2) . [B2,G] is set
<^B1,G^> is set
the Arrows of (A1,A2) . (B1,G) is set
[B1,G] is V15() set
{B1,G} is set
{{B1,G},{B1}} is set
the Arrows of (A1,A2) . [B1,G] is set
dom the Arrows of (A1,A2) is Relation-like the carrier of (A1,A2) -defined the carrier of (A1,A2) -valued M2( bool [: the carrier of (A1,A2), the carrier of (A1,A2):])
bool [: the carrier of (A1,A2), the carrier of (A1,A2):] is non empty set
c is non empty transitive AltCatStr
the carrier of c is non empty set
b is non empty transitive AltCatStr
the carrier of b is non empty set
the M2(<^B1,B2^>) is M2(<^B1,B2^>)
the M2(<^B2,G^>) is M2(<^B2,G^>)
c1 is M2( the carrier of b)
a9 is M2( the carrier of b)
<^c1,a9^> is set
the Arrows of b is Relation-like [: the carrier of b, the carrier of b:] -defined Function-like non empty total set
[: the carrier of b, the carrier of b:] is Relation-like non empty set
the Arrows of b . (c1,a9) is set
[c1,a9] is V15() set
{c1,a9} is set
{c1} is set
{{c1,a9},{c1}} is set
the Arrows of b . [c1,a9] is set
c1 is M2( the carrier of c)
f is M2( the carrier of c)
<^c1,f^> is set
the Arrows of c is Relation-like [: the carrier of c, the carrier of c:] -defined Function-like non empty total set
[: the carrier of c, the carrier of c:] is Relation-like non empty set
the Arrows of c . (c1,f) is set
[c1,f] is V15() set
{c1,f} is set
{c1} is set
{{c1,f},{c1}} is set
the Arrows of c . [c1,f] is set
<^c1,a9^> /\ <^c1,f^> is set
f1 is M2( the carrier of b)
<^f1,c1^> is set
the Arrows of b . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{f1} is set
{{f1,c1},{f1}} is set
the Arrows of b . [f1,c1] is set
b1 is M2( the carrier of c)
<^b1,c1^> is set
the Arrows of c . (b1,c1) is set
[b1,c1] is V15() set
{b1,c1} is set
{b1} is set
{{b1,c1},{b1}} is set
the Arrows of c . [b1,c1] is set
<^f1,c1^> /\ <^b1,c1^> is set
f9 is M2(<^f1,c1^>)
g1 is M2(<^c1,a9^>)
g1 * f9 is M2(<^f1,a9^>)
<^f1,a9^> is set
the Arrows of b . (f1,a9) is set
[f1,a9] is V15() set
{f1,a9} is set
{{f1,a9},{f1}} is set
the Arrows of b . [f1,a9] is set
f1 is M2(<^b1,c1^>)
g9 is M2(<^c1,f^>)
g9 * f1 is M2(<^b1,f^>)
<^b1,f^> is set
the Arrows of c . (b1,f) is set
[b1,f] is V15() set
{b1,f} is set
{{b1,f},{b1}} is set
the Arrows of c . [b1,f] is set
<^f1,a9^> /\ <^b1,f^> is set
A1 is AltCatStr
A2 is AltCatStr
the carrier of A1 is set
the carrier of A2 is set
(A1,A2) is strict AltCatStr
the carrier of (A1,A2) is set
F is M2( the carrier of A1)
B1 is M2( the carrier of A1)
<^F,B1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like total set
[: the carrier of A1, the carrier of A1:] is Relation-like set
the Arrows of A1 . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of A1 . [F,B1] is set
B2 is M2( the carrier of A2)
G is M2( the carrier of A2)
<^B2,G^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like total set
[: the carrier of A2, the carrier of A2:] is Relation-like set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
b is M2( the carrier of (A1,A2))
c is M2( the carrier of (A1,A2))
<^b,c^> is set
the Arrows of (A1,A2) is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
[: the carrier of (A1,A2), the carrier of (A1,A2):] is Relation-like set
the Arrows of (A1,A2) . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of (A1,A2) . [b,c] is set
<^F,B1^> /\ <^B2,G^> is set
b1 is M2(<^F,B1^>)
c1 is M2(<^B2,G^>)
A1 is non empty with_units reflexive AltCatStr
the carrier of A1 is non empty set
A2 is non empty with_units reflexive AltCatStr
the carrier of A2 is non empty set
(A1,A2) is strict AltCatStr
the carrier of (A1,A2) is set
B2 is M2( the carrier of (A1,A2))
F is M2( the carrier of A1)
B1 is M2( the carrier of A2)
idm F is M2(<^F,F^>)
<^F,F^> is non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (F,F) is set
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the Arrows of A1 . [F,F] is set
idm B1 is M2(<^B1,B1^>)
<^B1,B1^> is non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (B1,B1) is set
[B1,B1] is V15() set
{B1,B1} is set
{B1} is set
{{B1,B1},{B1}} is set
the Arrows of A2 . [B1,B1] is set
<^B2,B2^> is set
the Arrows of (A1,A2) is Relation-like [: the carrier of (A1,A2), the carrier of (A1,A2):] -defined Function-like total set
[: the carrier of (A1,A2), the carrier of (A1,A2):] is Relation-like set
the Arrows of (A1,A2) . (B2,B2) is set
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the Arrows of (A1,A2) . [B2,B2] is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
(A1,A2) is strict AltCatStr
the carrier of A1 is non empty set
the carrier of A2 is non empty set
F is non empty transitive V106() SubCatStr of A1
the carrier of F is non empty set
the carrier of A1 /\ the carrier of A2 is set
B1 is M2( the carrier of F)
B2 is M2( the carrier of A1)
idm B2 is M2(<^B2,B2^>)
<^B2,B2^> is non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (B2,B2) is set
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the Arrows of A1 . [B2,B2] is set
G is M2( the carrier of A2)
idm G is M2(<^G,G^>)
<^G,G^> is non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (G,G) is set
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the Arrows of A2 . [G,G] is set
<^B1,B1^> is set
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like non empty total set
[: the carrier of F, the carrier of F:] is Relation-like non empty set
the Arrows of F . (B1,B1) is set
[B1,B1] is V15() set
{B1,B1} is set
{B1} is set
{{B1,B1},{B1}} is set
the Arrows of F . [B1,B1] is set
F₁() is non empty transitive V106() with_units reflexive AltCatStr
the carrier of F₁() is non empty set
F₂() is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of F₁()
the carrier of F₂() is non empty set
F₃() is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of F₁()
the carrier of F₃() is non empty set
the Arrows of F₂() is Relation-like [: the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty total set
[: the carrier of F₂(), the carrier of F₂():] is Relation-like non empty set
the Comp of F₂() is Relation-like [: the carrier of F₂(), the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of F₂(), the Arrows of F₂()|},{| the Arrows of F₂()|}
[: the carrier of F₂(), the carrier of F₂(), the carrier of F₂():] is non empty set
{| the Arrows of F₂(), the Arrows of F₂()|} is Relation-like [: the carrier of F₂(), the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty total set
{| the Arrows of F₂()|} is Relation-like [: the carrier of F₂(), the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty total set
AltCatStr(# the carrier of F₂(), the Arrows of F₂(), the Comp of F₂() #) is strict AltCatStr
the Arrows of F₃() is Relation-like [: the carrier of F₃(), the carrier of F₃():] -defined Function-like non empty total set
[: the carrier of F₃(), the carrier of F₃():] is Relation-like non empty set
the Comp of F₃() is Relation-like [: the carrier of F₃(), the carrier of F₃(), the carrier of F₃():] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of F₃(), the Arrows of F₃()|},{| the Arrows of F₃()|}
[: the carrier of F₃(), the carrier of F₃(), the carrier of F₃():] is non empty set
{| the Arrows of F₃(), the Arrows of F₃()|} is Relation-like [: the carrier of F₃(), the carrier of F₃(), the carrier of F₃():] -defined Function-like non empty total set
{| the Arrows of F₃()|} is Relation-like [: the carrier of F₃(), the carrier of F₃(), the carrier of F₃():] -defined Function-like non empty total set
AltCatStr(# the carrier of F₃(), the Arrows of F₃(), the Comp of F₃() #) is strict AltCatStr
A1 is set
A2 is M2( the carrier of F₂())
F is M2( the carrier of F₁())
A1 is set
A2 is M2( the carrier of F₃())
F is M2( the carrier of F₁())
A1 is M2( the carrier of F₂())
A2 is M2( the carrier of F₂())
F is M2( the carrier of F₂())
B1 is M2( the carrier of F₂())
B2 is M2( the carrier of F₃())
G is M2( the carrier of F₃())
<^B2,G^> is set
the Arrows of F₃() . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of F₃() . [B2,G] is set
b is M2( the carrier of F₁())
c is M2( the carrier of F₁())
<^b,c^> is set
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty total set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
the Arrows of F₁() . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of F₁() . [b,c] is set
<^F,B1^> is set
the Arrows of F₂() . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of F₂() . [F,B1] is set
b1 is set
c1 is M2(<^b,c^>)
b1 is set
c1 is M2(<^b,c^>)
the Arrows of F₂() . (A1,A2) is set
[A1,A2] is V15() set
{A1,A2} is set
{A1} is set
{{A1,A2},{A1}} is set
the Arrows of F₂() . [A1,A2] is set
the Arrows of F₃() . (A1,A2) is set
the Arrows of F₃() . [A1,A2] is set
A1 is non empty AltCatStr
the carrier of A1 is non empty set
A2 is non empty SubCatStr of A1
the carrier of A2 is non empty set
B2 is M2( the carrier of A2)
F is M2( the carrier of A1)
G is M2( the carrier of A2)
B1 is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
<^F,B1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of A1 . [F,B1] is set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
dom the Arrows of A2 is Relation-like the carrier of A2 -defined the carrier of A2 -valued non empty M2( bool [: the carrier of A2, the carrier of A2:])
bool [: the carrier of A2, the carrier of A2:] is non empty set
F is set
B1 is set
B2 is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
G is M2( the carrier of A2)
b is M2( the carrier of A2)
the Arrows of A2 . F is set
<^G,b^> is set
the Arrows of A2 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of A2 . [G,b] is set
c is M2( the carrier of A1)
b1 is M2( the carrier of A1)
<^c,b1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (c,b1) is set
[c,b1] is V15() set
{c,b1} is set
{c} is set
{{c,b1},{c}} is set
the Arrows of A1 . [c,b1] is set
the Arrows of A1 . F is set
dom the Arrows of A1 is Relation-like the carrier of A1 -defined the carrier of A1 -valued non empty M2( bool [: the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1:] is non empty set
[: the carrier of A1, the carrier of A1:] /\ [: the carrier of A2, the carrier of A2:] is Relation-like set
the Arrows of A1 || the carrier of A2 is set
the Arrows of A1 | [: the carrier of A2, the carrier of A2:] is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -defined Function-like set
F₁() is non empty transitive V106() with_units reflexive AltCatStr
the carrier of F₁() is non empty set
A1 is M2( the carrier of F₁())
A2 is M2( the carrier of F₁())
<^A1,A2^> is set
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty total set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
the Arrows of F₁() . (A1,A2) is set
[A1,A2] is V15() set
{A1,A2} is set
{A1} is set
{{A1,A2},{A1}} is set
the Arrows of F₁() . [A1,A2] is set
F is M2( the carrier of F₁())
<^A2,F^> is set
the Arrows of F₁() . (A2,F) is set
[A2,F] is V15() set
{A2,F} is set
{A2} is set
{{A2,F},{A2}} is set
the Arrows of F₁() . [A2,F] is set
A1 is M2( the carrier of F₁())
A1 is M2( the carrier of F₁())
A1 is non empty transitive strict V106() with_units reflexive id-inheriting SubCatStr of F₁()
the carrier of A1 is non empty set
B1 is M2( the carrier of A1)
A2 is M2( the carrier of F₁())
B2 is M2( the carrier of A1)
F is M2( the carrier of F₁())
<^A2,F^> is set
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty total set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
the Arrows of F₁() . (A2,F) is set
[A2,F] is V15() set
{A2,F} is set
{A2} is set
{{A2,F},{A2}} is set
the Arrows of F₁() . [A2,F] is set
<^B1,B2^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of A1 . [B1,B2] is set
G is set
F₁() is non empty transitive V106() with_units reflexive AltCatStr
the carrier of F₁() is non empty set
F₂() is non empty transitive V106() with_units reflexive full id-inheriting SubCatStr of F₁()
the carrier of F₂() is non empty set
F₃() is non empty transitive V106() with_units reflexive full id-inheriting SubCatStr of F₁()
the carrier of F₃() is non empty set
the Arrows of F₂() is Relation-like [: the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty total set
[: the carrier of F₂(), the carrier of F₂():] is Relation-like non empty set
the Comp of F₂() is Relation-like [: the carrier of F₂(), the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of F₂(), the Arrows of F₂()|},{| the Arrows of F₂()|}
[: the carrier of F₂(), the carrier of F₂(), the carrier of F₂():] is non empty set
{| the Arrows of F₂(), the Arrows of F₂()|} is Relation-like [: the carrier of F₂(), the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty total set
{| the Arrows of F₂()|} is Relation-like [: the carrier of F₂(), the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty total set
AltCatStr(# the carrier of F₂(), the Arrows of F₂(), the Comp of F₂() #) is strict AltCatStr
the Arrows of F₃() is Relation-like [: the carrier of F₃(), the carrier of F₃():] -defined Function-like non empty total set
[: the carrier of F₃(), the carrier of F₃():] is Relation-like non empty set
the Comp of F₃() is Relation-like [: the carrier of F₃(), the carrier of F₃(), the carrier of F₃():] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of F₃(), the Arrows of F₃()|},{| the Arrows of F₃()|}
[: the carrier of F₃(), the carrier of F₃(), the carrier of F₃():] is non empty set
{| the Arrows of F₃(), the Arrows of F₃()|} is Relation-like [: the carrier of F₃(), the carrier of F₃(), the carrier of F₃():] -defined Function-like non empty total set
{| the Arrows of F₃()|} is Relation-like [: the carrier of F₃(), the carrier of F₃(), the carrier of F₃():] -defined Function-like non empty total set
AltCatStr(# the carrier of F₃(), the Arrows of F₃(), the Comp of F₃() #) is strict AltCatStr
A1 is M2( the carrier of F₁())
A2 is M2( the carrier of F₁())
F is M2( the carrier of F₂())
A1 is M2( the carrier of F₁())
B1 is M2( the carrier of F₂())
A2 is M2( the carrier of F₁())
<^F,B1^> is set
the Arrows of F₂() . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of F₂() . [F,B1] is set
<^A1,A2^> is set
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty total set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
the Arrows of F₁() . (A1,A2) is set
[A1,A2] is V15() set
{A1,A2} is set
{A1} is set
{{A1,A2},{A1}} is set
the Arrows of F₁() . [A1,A2] is set
B2 is M2(<^A1,A2^>)
G is M2(<^A1,A2^>)
F is M2( the carrier of F₃())
A1 is M2( the carrier of F₁())
B1 is M2( the carrier of F₃())
A2 is M2( the carrier of F₁())
<^F,B1^> is set
the Arrows of F₃() . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of F₃() . [F,B1] is set
<^A1,A2^> is set
the Arrows of F₁() . (A1,A2) is set
[A1,A2] is V15() set
{A1,A2} is set
{A1} is set
{{A1,A2},{A1}} is set
the Arrows of F₁() . [A1,A2] is set
B2 is M2(<^A1,A2^>)
G is M2(<^A1,A2^>)
A1 is M2( the carrier of F₁())
A2 is M2( the carrier of F₁())
A1 is Relation-like Function-like Function-yielding V37() set
A2 is set
F is set
A1 . (A2,F) is set
[A2,F] is V15() set
{A2,F} is set
{A2} is set
{{A2,F},{A2}} is set
A1 . [A2,F] is Relation-like Function-like set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
the carrier of A2 is non empty set
incl A2 is reflexive feasible strict Covariant FunctorStr over A2,A1
F is M2( the carrier of A2)
B1 is M2( the carrier of A2)
<^F,B1^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of A2 . [F,B1] is set
B2 is M2(<^F,B1^>)
(incl A2) . B2 is M2(<^((incl A2) . F),((incl A2) . B1)^>)
(incl A2) . F is M2( the carrier of A1)
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the ObjectMap of (incl A2) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (incl A2) . (F,F) is M2([: the carrier of A1, the carrier of A1:])
[F,F] is V15() set
{F,F} is set
{{F,F},{F}} is set
the ObjectMap of (incl A2) . [F,F] is set
( the ObjectMap of (incl A2) . (F,F)) `1 is set
(incl A2) . B1 is M2( the carrier of A1)
the ObjectMap of (incl A2) . (B1,B1) is M2([: the carrier of A1, the carrier of A1:])
[B1,B1] is V15() set
{B1,B1} is set
{B1} is set
{{B1,B1},{B1}} is set
the ObjectMap of (incl A2) . [B1,B1] is set
( the ObjectMap of (incl A2) . (B1,B1)) `1 is set
<^((incl A2) . F),((incl A2) . B1)^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (((incl A2) . F),((incl A2) . B1)) is set
[((incl A2) . F),((incl A2) . B1)] is V15() set
{((incl A2) . F),((incl A2) . B1)} is set
{((incl A2) . F)} is set
{{((incl A2) . F),((incl A2) . B1)},{((incl A2) . F)}} is set
the Arrows of A1 . [((incl A2) . F),((incl A2) . B1)] is set
the MorphMap of (incl A2) is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (incl A2), the Arrows of A2, the Arrows of A1
id the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of the Arrows of A2, the Arrows of A2
Morph-Map ((incl A2),F,B1) is Relation-like <^F,B1^> -defined <^((incl A2) . F),((incl A2) . B1)^> -valued Function-like quasi_total M2( bool [:<^F,B1^>,<^((incl A2) . F),((incl A2) . B1)^>:])
[:<^F,B1^>,<^((incl A2) . F),((incl A2) . B1)^>:] is Relation-like set
bool [:<^F,B1^>,<^((incl A2) . F),((incl A2) . B1)^>:] is non empty set
the MorphMap of (incl A2) . (F,B1) is Relation-like Function-like set
the MorphMap of (incl A2) . [F,B1] is Relation-like Function-like set
(Morph-Map ((incl A2),F,B1)) . B2 is set
id ( the Arrows of A2 . (F,B1)) is Relation-like the Arrows of A2 . (F,B1) -defined the Arrows of A2 . (F,B1) -valued Function-like one-to-one total M2( bool [:( the Arrows of A2 . (F,B1)),( the Arrows of A2 . (F,B1)):])
[:( the Arrows of A2 . (F,B1)),( the Arrows of A2 . (F,B1)):] is Relation-like set
bool [:( the Arrows of A2 . (F,B1)),( the Arrows of A2 . (F,B1)):] is non empty set
(id ( the Arrows of A2 . (F,B1))) . B2 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
incl A2 is reflexive feasible strict Covariant FunctorStr over A2,A1
the carrier of A2 is non empty set
F is M2( the carrier of A2)
Morph-Map ((incl A2),F,F) is Relation-like Function-like set
the MorphMap of (incl A2) is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (incl A2), the Arrows of A2, the Arrows of A1
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the ObjectMap of (incl A2) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the MorphMap of (incl A2) . (F,F) is Relation-like Function-like set
[F,F] is V15() set
{F,F} is set
{F} is set
{{F,F},{F}} is set
the MorphMap of (incl A2) . [F,F] is Relation-like Function-like set
idm F is M2(<^F,F^>)
<^F,F^> is non empty set
the Arrows of A2 . (F,F) is set
the Arrows of A2 . [F,F] is set
(Morph-Map ((incl A2),F,F)) . (idm F) is set
(incl A2) . F is M2( the carrier of A1)
the ObjectMap of (incl A2) . (F,F) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (incl A2) . [F,F] is set
( the ObjectMap of (incl A2) . (F,F)) `1 is set
idm ((incl A2) . F) is M2(<^((incl A2) . F),((incl A2) . F)^>)
<^((incl A2) . F),((incl A2) . F)^> is non empty set
the Arrows of A1 . (((incl A2) . F),((incl A2) . F)) is set
[((incl A2) . F),((incl A2) . F)] is V15() set
{((incl A2) . F),((incl A2) . F)} is set
{((incl A2) . F)} is set
{{((incl A2) . F),((incl A2) . F)},{((incl A2) . F)}} is set
the Arrows of A1 . [((incl A2) . F),((incl A2) . F)] is set
Morph-Map ((incl A2),F,F) is Relation-like <^F,F^> -defined <^((incl A2) . F),((incl A2) . F)^> -valued Function-like quasi_total M2( bool [:<^F,F^>,<^((incl A2) . F),((incl A2) . F)^>:])
[:<^F,F^>,<^((incl A2) . F),((incl A2) . F)^>:] is Relation-like non empty set
bool [:<^F,F^>,<^((incl A2) . F),((incl A2) . F)^>:] is non empty set
(Morph-Map ((incl A2),F,F)) . (idm F) is M2(<^((incl A2) . F),((incl A2) . F)^>)
(incl A2) . (idm F) is M2(<^((incl A2) . F),((incl A2) . F)^>)
the carrier of A2 is non empty set
F is M2( the carrier of A2)
B1 is M2( the carrier of A2)
<^F,B1^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (F,B1) is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
the Arrows of A2 . [F,B1] is set
B2 is M2( the carrier of A2)
<^B1,B2^> is set
the Arrows of A2 . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of A2 . [B1,B2] is set
(incl A2) . F is M2( the carrier of A1)
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the ObjectMap of (incl A2) is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (incl A2) . (F,F) is M2([: the carrier of A1, the carrier of A1:])
[F,F] is V15() set
{F,F} is set
{{F,F},{F}} is set
the ObjectMap of (incl A2) . [F,F] is set
( the ObjectMap of (incl A2) . (F,F)) `1 is set
(incl A2) . B1 is M2( the carrier of A1)
the ObjectMap of (incl A2) . (B1,B1) is M2([: the carrier of A1, the carrier of A1:])
[B1,B1] is V15() set
{B1,B1} is set
{{B1,B1},{B1}} is set
the ObjectMap of (incl A2) . [B1,B1] is set
( the ObjectMap of (incl A2) . (B1,B1)) `1 is set
(incl A2) . B2 is M2( the carrier of A1)
the ObjectMap of (incl A2) . (B2,B2) is M2([: the carrier of A1, the carrier of A1:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of (incl A2) . [B2,B2] is set
( the ObjectMap of (incl A2) . (B2,B2)) `1 is set
G is M2(<^F,B1^>)
(incl A2) . G is M2(<^((incl A2) . F),((incl A2) . B1)^>)
<^((incl A2) . F),((incl A2) . B1)^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (((incl A2) . F),((incl A2) . B1)) is set
[((incl A2) . F),((incl A2) . B1)] is V15() set
{((incl A2) . F),((incl A2) . B1)} is set
{((incl A2) . F)} is set
{{((incl A2) . F),((incl A2) . B1)},{((incl A2) . F)}} is set
the Arrows of A1 . [((incl A2) . F),((incl A2) . B1)] is set
b is M2(<^B1,B2^>)
b * G is M2(<^F,B2^>)
<^F,B2^> is set
the Arrows of A2 . (F,B2) is set
[F,B2] is V15() set
{F,B2} is set
{{F,B2},{F}} is set
the Arrows of A2 . [F,B2] is set
(incl A2) . (b * G) is M2(<^((incl A2) . F),((incl A2) . B2)^>)
<^((incl A2) . F),((incl A2) . B2)^> is set
the Arrows of A1 . (((incl A2) . F),((incl A2) . B2)) is set
[((incl A2) . F),((incl A2) . B2)] is V15() set
{((incl A2) . F),((incl A2) . B2)} is set
{{((incl A2) . F),((incl A2) . B2)},{((incl A2) . F)}} is set
the Arrows of A1 . [((incl A2) . F),((incl A2) . B2)] is set
(incl A2) . b is M2(<^((incl A2) . B1),((incl A2) . B2)^>)
<^((incl A2) . B1),((incl A2) . B2)^> is set
the Arrows of A1 . (((incl A2) . B1),((incl A2) . B2)) is set
[((incl A2) . B1),((incl A2) . B2)] is V15() set
{((incl A2) . B1),((incl A2) . B2)} is set
{((incl A2) . B1)} is set
{{((incl A2) . B1),((incl A2) . B2)},{((incl A2) . B1)}} is set
the Arrows of A1 . [((incl A2) . B1),((incl A2) . B2)] is set
((incl A2) . b) * ((incl A2) . G) is M2(<^((incl A2) . F),((incl A2) . B2)^>)
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
incl A2 is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over A2,A1
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
incl A2 is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over A2,A1
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
B1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
B1 | F is FunctorStr over F,A2
incl F is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over F,A1
B1 * (incl F) is reflexive feasible strict Covariant id-preserving FunctorStr over F,A2
(A1,F) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F,A1
B1 * (A1,F) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F,A2
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
B1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
B1 | F is FunctorStr over F,A2
incl F is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over F,A1
B1 * (incl F) is reflexive feasible strict Contravariant id-preserving FunctorStr over F,A2
(A1,F) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F,A1
B1 * (A1,F) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of F,A2
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
the carrier of F is non empty set
B1 is FunctorStr over A1,A2
B1 | F is FunctorStr over F,A2
incl F is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over F,A1
B1 * (incl F) is strict FunctorStr over F,A2
B2 is M2( the carrier of A1)
B1 . B2 is M2( the carrier of A2)
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
G is M2( the carrier of F)
(B1 | F) . G is M2( the carrier of A2)
the ObjectMap of (B1 | F) is Relation-like [: the carrier of F, the carrier of F:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of F, the carrier of F:] is Relation-like non empty set
[:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (B1 | F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (B1 | F) . [G,G] is set
( the ObjectMap of (B1 | F) . (G,G)) `1 is set
(A1,F) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F,A1
(A1,F) . G is M2( the carrier of A1)
the ObjectMap of (A1,F) is Relation-like [: the carrier of F, the carrier of F:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (A1,F) . (G,G) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (A1,F) . [G,G] is set
( the ObjectMap of (A1,F) . (G,G)) `1 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
the carrier of F is non empty set
B1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
(A1,A2,F,B1) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F,A2
incl F is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over F,A1
B1 * (incl F) is reflexive feasible strict Covariant id-preserving FunctorStr over F,A2
B2 is M2( the carrier of A1)
G is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A1 . [B2,G] is set
b is M2( the carrier of F)
c is M2( the carrier of F)
<^b,c^> is set
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like non empty total set
[: the carrier of F, the carrier of F:] is Relation-like non empty set
the Arrows of F . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of F . [b,c] is set
b1 is M2(<^B2,G^>)
B1 . b1 is M2(<^(B1 . B2),(B1 . G)^>)
B1 . B2 is M2( the carrier of A2)
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
B1 . G is M2( the carrier of A2)
the ObjectMap of B1 . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of B1 . [G,G] is set
( the ObjectMap of B1 . (G,G)) `1 is set
<^(B1 . B2),(B1 . G)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((B1 . B2),(B1 . G)) is set
[(B1 . B2),(B1 . G)] is V15() set
{(B1 . B2),(B1 . G)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . G)},{(B1 . B2)}} is set
the Arrows of A2 . [(B1 . B2),(B1 . G)] is set
c1 is M2(<^b,c^>)
(A1,A2,F,B1) . c1 is M2(<^((A1,A2,F,B1) . b),((A1,A2,F,B1) . c)^>)
(A1,A2,F,B1) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,F,B1) is Relation-like [: the carrier of F, the carrier of F:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (A1,A2,F,B1) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,F,B1) . [b,b] is set
( the ObjectMap of (A1,A2,F,B1) . (b,b)) `1 is set
(A1,A2,F,B1) . c is M2( the carrier of A2)
the ObjectMap of (A1,A2,F,B1) . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of (A1,A2,F,B1) . [c,c] is set
( the ObjectMap of (A1,A2,F,B1) . (c,c)) `1 is set
<^((A1,A2,F,B1) . b),((A1,A2,F,B1) . c)^> is set
the Arrows of A2 . (((A1,A2,F,B1) . b),((A1,A2,F,B1) . c)) is set
[((A1,A2,F,B1) . b),((A1,A2,F,B1) . c)] is V15() set
{((A1,A2,F,B1) . b),((A1,A2,F,B1) . c)} is set
{((A1,A2,F,B1) . b)} is set
{{((A1,A2,F,B1) . b),((A1,A2,F,B1) . c)},{((A1,A2,F,B1) . b)}} is set
the Arrows of A2 . [((A1,A2,F,B1) . b),((A1,A2,F,B1) . c)] is set
(A1,F) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F,A1
(A1,F) . c1 is M2(<^((A1,F) . b),((A1,F) . c)^>)
(A1,F) . b is M2( the carrier of A1)
the ObjectMap of (A1,F) is Relation-like [: the carrier of F, the carrier of F:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (A1,F) . (b,b) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (A1,F) . [b,b] is set
( the ObjectMap of (A1,F) . (b,b)) `1 is set
(A1,F) . c is M2( the carrier of A1)
the ObjectMap of (A1,F) . (c,c) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (A1,F) . [c,c] is set
( the ObjectMap of (A1,F) . (c,c)) `1 is set
<^((A1,F) . b),((A1,F) . c)^> is set
the Arrows of A1 . (((A1,F) . b),((A1,F) . c)) is set
[((A1,F) . b),((A1,F) . c)] is V15() set
{((A1,F) . b),((A1,F) . c)} is set
{((A1,F) . b)} is set
{{((A1,F) . b),((A1,F) . c)},{((A1,F) . b)}} is set
the Arrows of A1 . [((A1,F) . b),((A1,F) . c)] is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
the carrier of F is non empty set
B1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
(A1,A2,F,B1) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of F,A2
incl F is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over F,A1
B1 * (incl F) is reflexive feasible strict Contravariant id-preserving FunctorStr over F,A2
B2 is M2( the carrier of A1)
G is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A1 . [B2,G] is set
b is M2( the carrier of F)
c is M2( the carrier of F)
<^b,c^> is set
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like non empty total set
[: the carrier of F, the carrier of F:] is Relation-like non empty set
the Arrows of F . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of F . [b,c] is set
b1 is M2(<^B2,G^>)
B1 . b1 is M2(<^(B1 . G),(B1 . B2)^>)
B1 . G is M2( the carrier of A2)
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of B1 . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of B1 . [G,G] is set
( the ObjectMap of B1 . (G,G)) `1 is set
B1 . B2 is M2( the carrier of A2)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
<^(B1 . G),(B1 . B2)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((B1 . G),(B1 . B2)) is set
[(B1 . G),(B1 . B2)] is V15() set
{(B1 . G),(B1 . B2)} is set
{(B1 . G)} is set
{{(B1 . G),(B1 . B2)},{(B1 . G)}} is set
the Arrows of A2 . [(B1 . G),(B1 . B2)] is set
c1 is M2(<^b,c^>)
(A1,A2,F,B1) . c1 is M2(<^((A1,A2,F,B1) . c),((A1,A2,F,B1) . b)^>)
(A1,A2,F,B1) . c is M2( the carrier of A2)
the ObjectMap of (A1,A2,F,B1) is Relation-like [: the carrier of F, the carrier of F:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of F, the carrier of F:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (A1,A2,F,B1) . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of (A1,A2,F,B1) . [c,c] is set
( the ObjectMap of (A1,A2,F,B1) . (c,c)) `1 is set
(A1,A2,F,B1) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,F,B1) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,F,B1) . [b,b] is set
( the ObjectMap of (A1,A2,F,B1) . (b,b)) `1 is set
<^((A1,A2,F,B1) . c),((A1,A2,F,B1) . b)^> is set
the Arrows of A2 . (((A1,A2,F,B1) . c),((A1,A2,F,B1) . b)) is set
[((A1,A2,F,B1) . c),((A1,A2,F,B1) . b)] is V15() set
{((A1,A2,F,B1) . c),((A1,A2,F,B1) . b)} is set
{((A1,A2,F,B1) . c)} is set
{{((A1,A2,F,B1) . c),((A1,A2,F,B1) . b)},{((A1,A2,F,B1) . c)}} is set
the Arrows of A2 . [((A1,A2,F,B1) . c),((A1,A2,F,B1) . b)] is set
(A1,F) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F,A1
(A1,F) . c1 is M2(<^((A1,F) . b),((A1,F) . c)^>)
(A1,F) . b is M2( the carrier of A1)
the ObjectMap of (A1,F) is Relation-like [: the carrier of F, the carrier of F:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of F, the carrier of F:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (A1,F) . (b,b) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (A1,F) . [b,b] is set
( the ObjectMap of (A1,F) . (b,b)) `1 is set
(A1,F) . c is M2( the carrier of A1)
the ObjectMap of (A1,F) . (c,c) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of (A1,F) . [c,c] is set
( the ObjectMap of (A1,F) . (c,c)) `1 is set
<^((A1,F) . b),((A1,F) . c)^> is set
the Arrows of A1 . (((A1,F) . b),((A1,F) . c)) is set
[((A1,F) . b),((A1,F) . c)] is V15() set
{((A1,F) . b),((A1,F) . c)} is set
{((A1,F) . b)} is set
{{((A1,F) . b),((A1,F) . c)},{((A1,F) . b)}} is set
the Arrows of A1 . [((A1,F) . b),((A1,F) . c)] is set
A1 is non empty AltGraph
A2 is non empty AltGraph
the carrier of A1 is non empty set
F is BimapStr over A1,A2
the carrier of A2 is non empty set
[: the carrier of A1, the carrier of A2:] is Relation-like non empty set
bool [: the carrier of A1, the carrier of A2:] is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
B1 is Relation-like the carrier of A1 -defined the carrier of A2 -valued Function-like quasi_total M2( bool [: the carrier of A1, the carrier of A2:])
[:B1,B1:] is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
B2 is M2( the carrier of A1)
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
G is M2( the carrier of A1)
F . G is M2( the carrier of A2)
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
B1 . B2 is M2( the carrier of A2)
[(B1 . B2),(B1 . B2)] is V15() set
{(B1 . B2),(B1 . B2)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . B2)},{(B1 . B2)}} is set
[(B1 . B2),(B1 . B2)] `1 is set
B1 . G is M2( the carrier of A2)
[(B1 . G),(B1 . G)] is V15() set
{(B1 . G),(B1 . G)} is set
{(B1 . G)} is set
{{(B1 . G),(B1 . G)},{(B1 . G)}} is set
[(B1 . G),(B1 . G)] `1 is set
A1 is non empty reflexive AltGraph
A2 is non empty reflexive AltGraph
the carrier of A1 is non empty set
F is reflexive feasible Covariant FunctorStr over A1,A2
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
dom the MorphMap of F is Relation-like the carrier of A1 -defined the carrier of A1 -valued non empty M2( bool [: the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1:] is non empty set
B1 is M2( the carrier of A1)
B2 is M2( the carrier of A1)
<^B1,B2^> is set
the Arrows of A1 . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of A1 . [B1,B2] is set
G is M2(<^B1,B2^>)
F . G is M2(<^(F . B1),(F . B2)^>)
F . B1 is M2( the carrier of A2)
the ObjectMap of F . (B1,B1) is M2([: the carrier of A2, the carrier of A2:])
[B1,B1] is V15() set
{B1,B1} is set
{{B1,B1},{B1}} is set
the ObjectMap of F . [B1,B1] is set
( the ObjectMap of F . (B1,B1)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
<^(F . B1),(F . B2)^> is set
the Arrows of A2 . ((F . B1),(F . B2)) is set
[(F . B1),(F . B2)] is V15() set
{(F . B1),(F . B2)} is set
{(F . B1)} is set
{{(F . B1),(F . B2)},{(F . B1)}} is set
the Arrows of A2 . [(F . B1),(F . B2)] is set
b is M2(<^B1,B2^>)
F . b is M2(<^(F . B1),(F . B2)^>)
Morph-Map (F,B1,B2) is Relation-like <^B1,B2^> -defined <^(F . B1),(F . B2)^> -valued Function-like quasi_total M2( bool [:<^B1,B2^>,<^(F . B1),(F . B2)^>:])
[:<^B1,B2^>,<^(F . B1),(F . B2)^>:] is Relation-like set
bool [:<^B1,B2^>,<^(F . B1),(F . B2)^>:] is non empty set
the MorphMap of F . (B1,B2) is Relation-like Function-like set
the MorphMap of F . [B1,B2] is Relation-like Function-like set
(Morph-Map (F,B1,B2)) . G is set
(Morph-Map (F,B1,B2)) . b is set
A1 is non empty AltGraph
A2 is non empty AltGraph
the carrier of A2 is non empty set
the carrier of A1 is non empty set
F is reflexive Covariant FunctorStr over A1,A2
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the ObjectMap of F * the Arrows of A2 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of the Arrows of A1, the ObjectMap of F * the Arrows of A2
rng the ObjectMap of F is Relation-like the carrier of A2 -defined the carrier of A2 -valued M2( bool [: the carrier of A2, the carrier of A2:])
bool [: the carrier of A2, the carrier of A2:] is non empty set
B2 is M2( the carrier of A2)
G is M2( the carrier of A2)
<^B2,G^> is set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
[: the carrier of A1, the carrier of A2:] is Relation-like non empty set
bool [: the carrier of A1, the carrier of A2:] is non empty set
b is Relation-like the carrier of A1 -defined the carrier of A2 -valued Function-like quasi_total M2( bool [: the carrier of A1, the carrier of A2:])
[:b,b:] is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
c is M2(<^B2,G^>)
dom the ObjectMap of F is Relation-like the carrier of A1 -defined the carrier of A1 -valued M2( bool [: the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1:] is non empty set
b1 is set
the ObjectMap of F . b1 is set
c1 is set
f is set
[c1,f] is V15() set
{c1,f} is set
{c1} is set
{{c1,f},{c1}} is set
c1 is M2( the carrier of A1)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
b . c1 is M2( the carrier of A2)
[(b . c1),(b . c1)] is V15() set
{(b . c1),(b . c1)} is set
{(b . c1)} is set
{{(b . c1),(b . c1)},{(b . c1)}} is set
F . c1 is M2( the carrier of A2)
( the ObjectMap of F . (c1,c1)) `1 is set
f1 is M2( the carrier of A1)
the ObjectMap of F . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of F . [f1,f1] is set
b . f1 is M2( the carrier of A2)
[(b . f1),(b . f1)] is V15() set
{(b . f1),(b . f1)} is set
{(b . f1)} is set
{{(b . f1),(b . f1)},{(b . f1)}} is set
F . f1 is M2( the carrier of A2)
( the ObjectMap of F . (f1,f1)) `1 is set
the ObjectMap of F . (f1,c1) is M2([: the carrier of A2, the carrier of A2:])
[f1,c1] is V15() set
{f1,c1} is set
{{f1,c1},{f1}} is set
the ObjectMap of F . [f1,c1] is set
[(F . f1),(F . c1)] is V15() set
{(F . f1),(F . c1)} is set
{(F . f1)} is set
{{(F . f1),(F . c1)},{(F . f1)}} is set
Morph-Map (F,f1,c1) is Relation-like <^f1,c1^> -defined <^(F . f1),(F . c1)^> -valued Function-like quasi_total M2( bool [:<^f1,c1^>,<^(F . f1),(F . c1)^>:])
<^f1,c1^> is set
the Arrows of A1 . (f1,c1) is set
the Arrows of A1 . [f1,c1] is set
<^(F . f1),(F . c1)^> is set
the Arrows of A2 . ((F . f1),(F . c1)) is set
the Arrows of A2 . [(F . f1),(F . c1)] is set
[:<^f1,c1^>,<^(F . f1),(F . c1)^>:] is Relation-like set
bool [:<^f1,c1^>,<^(F . f1),(F . c1)^>:] is non empty set
the MorphMap of F . (f1,c1) is Relation-like Function-like set
the MorphMap of F . [f1,c1] is Relation-like Function-like set
proj2 (Morph-Map (F,f1,c1)) is set
( the ObjectMap of F * the Arrows of A2) . [f1,c1] is set
dom (Morph-Map (F,f1,c1)) is M2( bool <^f1,c1^>)
bool <^f1,c1^> is non empty set
a9 is set
(Morph-Map (F,f1,c1)) . a9 is set
b9 is M2(<^f1,c1^>)
F . b9 is M2(<^(F . f1),(F . c1)^>)
A1 is non empty AltGraph
A2 is non empty AltGraph
the carrier of A1 is non empty set
F is BimapStr over A1,A2
the carrier of A2 is non empty set
[: the carrier of A1, the carrier of A2:] is Relation-like non empty set
bool [: the carrier of A1, the carrier of A2:] is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
B1 is Relation-like the carrier of A1 -defined the carrier of A2 -valued Function-like quasi_total M2( bool [: the carrier of A1, the carrier of A2:])
[:B1,B1:] is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
~ [:B1,B1:] is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
B2 is M2( the carrier of A1)
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
G is M2( the carrier of A1)
F . G is M2( the carrier of A2)
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
dom the ObjectMap of F is Relation-like the carrier of A1 -defined the carrier of A1 -valued M2( bool [: the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1:] is non empty set
[:B1,B1:] . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[:B1,B1:] . [G,G] is set
B1 . G is M2( the carrier of A2)
[(B1 . G),(B1 . G)] is V15() set
{(B1 . G),(B1 . G)} is set
{(B1 . G)} is set
{{(B1 . G),(B1 . G)},{(B1 . G)}} is set
[:B1,B1:] . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[:B1,B1:] . [B2,B2] is set
B1 . B2 is M2( the carrier of A2)
[(B1 . B2),(B1 . B2)] is V15() set
{(B1 . B2),(B1 . B2)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . B2)},{(B1 . B2)}} is set
[(B1 . B2),(B1 . B2)] `1 is set
[(B1 . G),(B1 . G)] `1 is set
A1 is non empty reflexive AltGraph
A2 is non empty reflexive AltGraph
the carrier of A1 is non empty set
F is reflexive feasible Contravariant FunctorStr over A1,A2
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
dom the MorphMap of F is Relation-like the carrier of A1 -defined the carrier of A1 -valued non empty M2( bool [: the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1:] is non empty set
B1 is M2( the carrier of A1)
B2 is M2( the carrier of A1)
<^B1,B2^> is set
the Arrows of A1 . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of A1 . [B1,B2] is set
G is M2(<^B1,B2^>)
F . G is M2(<^(F . B2),(F . B1)^>)
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
F . B1 is M2( the carrier of A2)
the ObjectMap of F . (B1,B1) is M2([: the carrier of A2, the carrier of A2:])
[B1,B1] is V15() set
{B1,B1} is set
{{B1,B1},{B1}} is set
the ObjectMap of F . [B1,B1] is set
( the ObjectMap of F . (B1,B1)) `1 is set
<^(F . B2),(F . B1)^> is set
the Arrows of A2 . ((F . B2),(F . B1)) is set
[(F . B2),(F . B1)] is V15() set
{(F . B2),(F . B1)} is set
{(F . B2)} is set
{{(F . B2),(F . B1)},{(F . B2)}} is set
the Arrows of A2 . [(F . B2),(F . B1)] is set
b is M2(<^B1,B2^>)
F . b is M2(<^(F . B2),(F . B1)^>)
Morph-Map (F,B1,B2) is Relation-like <^B1,B2^> -defined <^(F . B2),(F . B1)^> -valued Function-like quasi_total M2( bool [:<^B1,B2^>,<^(F . B2),(F . B1)^>:])
[:<^B1,B2^>,<^(F . B2),(F . B1)^>:] is Relation-like set
bool [:<^B1,B2^>,<^(F . B2),(F . B1)^>:] is non empty set
the MorphMap of F . (B1,B2) is Relation-like Function-like set
the MorphMap of F . [B1,B2] is Relation-like Function-like set
(Morph-Map (F,B1,B2)) . G is set
(Morph-Map (F,B1,B2)) . b is set
A1 is non empty AltGraph
A2 is non empty AltGraph
the carrier of A2 is non empty set
the carrier of A1 is non empty set
F is reflexive Contravariant FunctorStr over A1,A2
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the ObjectMap of F * the Arrows of A2 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of the Arrows of A1, the ObjectMap of F * the Arrows of A2
rng the ObjectMap of F is Relation-like the carrier of A2 -defined the carrier of A2 -valued M2( bool [: the carrier of A2, the carrier of A2:])
bool [: the carrier of A2, the carrier of A2:] is non empty set
B2 is M2( the carrier of A2)
G is M2( the carrier of A2)
<^B2,G^> is set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
b is M2(<^B2,G^>)
dom the ObjectMap of F is Relation-like the carrier of A1 -defined the carrier of A1 -valued M2( bool [: the carrier of A1, the carrier of A1:])
bool [: the carrier of A1, the carrier of A1:] is non empty set
c is set
the ObjectMap of F . c is set
[: the carrier of A1, the carrier of A2:] is Relation-like non empty set
bool [: the carrier of A1, the carrier of A2:] is non empty set
b1 is Relation-like the carrier of A1 -defined the carrier of A2 -valued Function-like quasi_total M2( bool [: the carrier of A1, the carrier of A2:])
[:b1,b1:] is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
~ [:b1,b1:] is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
c1 is set
f is set
[c1,f] is V15() set
{c1,f} is set
{c1} is set
{{c1,f},{c1}} is set
f1 is M2( the carrier of A1)
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of F . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [f1,f1] is set
[:b1,b1:] . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[:b1,b1:] . [f1,f1] is set
b1 . f1 is M2( the carrier of A2)
[(b1 . f1),(b1 . f1)] is V15() set
{(b1 . f1),(b1 . f1)} is set
{(b1 . f1)} is set
{{(b1 . f1),(b1 . f1)},{(b1 . f1)}} is set
F . f1 is M2( the carrier of A2)
( the ObjectMap of F . (f1,f1)) `1 is set
c1 is M2( the carrier of A1)
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [c1,c1] is set
[:b1,b1:] . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[:b1,b1:] . [c1,c1] is set
b1 . c1 is M2( the carrier of A2)
[(b1 . c1),(b1 . c1)] is V15() set
{(b1 . c1),(b1 . c1)} is set
{(b1 . c1)} is set
{{(b1 . c1),(b1 . c1)},{(b1 . c1)}} is set
F . c1 is M2( the carrier of A2)
( the ObjectMap of F . (c1,c1)) `1 is set
[c1,f1] is V15() set
{c1,f1} is set
{{c1,f1},{c1}} is set
the ObjectMap of F . (c1,f1) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [c1,f1] is set
[:b1,b1:] . (f1,c1) is M2([: the carrier of A2, the carrier of A2:])
[f1,c1] is V15() set
{f1,c1} is set
{{f1,c1},{f1}} is set
[:b1,b1:] . [f1,c1] is set
[(F . f1),(F . c1)] is V15() set
{(F . f1),(F . c1)} is set
{(F . f1)} is set
{{(F . f1),(F . c1)},{(F . f1)}} is set
Morph-Map (F,c1,f1) is Relation-like <^c1,f1^> -defined <^(F . f1),(F . c1)^> -valued Function-like quasi_total M2( bool [:<^c1,f1^>,<^(F . f1),(F . c1)^>:])
<^c1,f1^> is set
the Arrows of A1 . (c1,f1) is set
the Arrows of A1 . [c1,f1] is set
<^(F . f1),(F . c1)^> is set
the Arrows of A2 . ((F . f1),(F . c1)) is set
the Arrows of A2 . [(F . f1),(F . c1)] is set
[:<^c1,f1^>,<^(F . f1),(F . c1)^>:] is Relation-like set
bool [:<^c1,f1^>,<^(F . f1),(F . c1)^>:] is non empty set
the MorphMap of F . (c1,f1) is Relation-like Function-like set
the MorphMap of F . [c1,f1] is Relation-like Function-like set
proj2 (Morph-Map (F,c1,f1)) is set
( the ObjectMap of F * the Arrows of A2) . [c1,f1] is set
dom (Morph-Map (F,c1,f1)) is M2( bool <^c1,f1^>)
bool <^c1,f1^> is non empty set
a9 is set
(Morph-Map (F,c1,f1)) . a9 is set
b9 is M2(<^c1,f1^>)
F . b9 is M2(<^(F . f1),(F . c1)^>)
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is non empty transitive V106() with_units reflexive AltCatStr
B1 is non empty transitive V106() with_units reflexive AltCatStr
B2 is FunctorStr over A1,A2
the carrier of F is non empty set
the carrier of A1 is non empty set
G is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F,B1
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is non empty transitive V106() with_units reflexive AltCatStr
B1 is non empty transitive V106() with_units reflexive AltCatStr
B2 is FunctorStr over A1,A2
the carrier of F is non empty set
the carrier of A1 is non empty set
G is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of F,B1
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
the carrier of A1 is non empty set
B1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
B2 is M2( the carrier of A1)
G is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A1 . [B2,G] is set
F . B2 is M2( the carrier of A2)
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
F . G is M2( the carrier of A2)
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
<^(F . B2),(F . G)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((F . B2),(F . G)) is set
[(F . B2),(F . G)] is V15() set
{(F . B2),(F . G)} is set
{(F . B2)} is set
{{(F . B2),(F . G)},{(F . B2)}} is set
the Arrows of A2 . [(F . B2),(F . G)] is set
b is M2(<^B2,G^>)
F . b is M2(<^(F . B2),(F . G)^>)
Morph-Map (F,B2,G) is Relation-like <^B2,G^> -defined <^(F . B2),(F . G)^> -valued Function-like quasi_total M2( bool [:<^B2,G^>,<^(F . B2),(F . G)^>:])
[:<^B2,G^>,<^(F . B2),(F . G)^>:] is Relation-like set
bool [:<^B2,G^>,<^(F . B2),(F . G)^>:] is non empty set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the MorphMap of F . (B2,G) is Relation-like Function-like set
the MorphMap of F . [B2,G] is Relation-like Function-like set
(Morph-Map (F,B2,G)) . b is set
B1 . b is M2(<^(B1 . B2),(B1 . G)^>)
B1 . B2 is M2( the carrier of A2)
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
B1 . G is M2( the carrier of A2)
the ObjectMap of B1 . (G,G) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [G,G] is set
( the ObjectMap of B1 . (G,G)) `1 is set
<^(B1 . B2),(B1 . G)^> is set
the Arrows of A2 . ((B1 . B2),(B1 . G)) is set
[(B1 . B2),(B1 . G)] is V15() set
{(B1 . B2),(B1 . G)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . G)},{(B1 . B2)}} is set
the Arrows of A2 . [(B1 . B2),(B1 . G)] is set
B2 is M2( the carrier of A1)
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
B1 . B2 is M2( the carrier of A2)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
FunctorStr(# the ObjectMap of F, the MorphMap of F #) is strict FunctorStr over A1,A2
the MorphMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A1, the Arrows of A2
FunctorStr(# the ObjectMap of B1, the MorphMap of B1 #) is strict FunctorStr over A1,A2
the ObjectMap of F * the Arrows of A2 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
the carrier of A1 is non empty set
B1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
B2 is M2( the carrier of A1)
G is M2( the carrier of A1)
<^B2,G^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A1 . [B2,G] is set
F . G is M2( the carrier of A2)
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
<^(F . G),(F . B2)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((F . G),(F . B2)) is set
[(F . G),(F . B2)] is V15() set
{(F . G),(F . B2)} is set
{(F . G)} is set
{{(F . G),(F . B2)},{(F . G)}} is set
the Arrows of A2 . [(F . G),(F . B2)] is set
b is M2(<^B2,G^>)
F . b is M2(<^(F . G),(F . B2)^>)
Morph-Map (F,B2,G) is Relation-like <^B2,G^> -defined <^(F . G),(F . B2)^> -valued Function-like quasi_total M2( bool [:<^B2,G^>,<^(F . G),(F . B2)^>:])
[:<^B2,G^>,<^(F . G),(F . B2)^>:] is Relation-like set
bool [:<^B2,G^>,<^(F . G),(F . B2)^>:] is non empty set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the MorphMap of F . (B2,G) is Relation-like Function-like set
the MorphMap of F . [B2,G] is Relation-like Function-like set
(Morph-Map (F,B2,G)) . b is set
B1 . b is M2(<^(B1 . G),(B1 . B2)^>)
B1 . G is M2( the carrier of A2)
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
the ObjectMap of B1 . (G,G) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [G,G] is set
( the ObjectMap of B1 . (G,G)) `1 is set
B1 . B2 is M2( the carrier of A2)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
<^(B1 . G),(B1 . B2)^> is set
the Arrows of A2 . ((B1 . G),(B1 . B2)) is set
[(B1 . G),(B1 . B2)] is V15() set
{(B1 . G),(B1 . B2)} is set
{(B1 . G)} is set
{{(B1 . G),(B1 . B2)},{(B1 . G)}} is set
the Arrows of A2 . [(B1 . G),(B1 . B2)] is set
B2 is M2( the carrier of A1)
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
B1 . B2 is M2( the carrier of A2)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
FunctorStr(# the ObjectMap of F, the MorphMap of F #) is strict FunctorStr over A1,A2
the MorphMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A1, the Arrows of A2
FunctorStr(# the ObjectMap of B1, the MorphMap of B1 #) is strict FunctorStr over A1,A2
the ObjectMap of F * the Arrows of A2 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
B1 is M2( the carrier of A1)
B2 is M2( the carrier of A1)
F . B1 is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (B1,B1) is M2([: the carrier of A2, the carrier of A2:])
[B1,B1] is V15() set
{B1,B1} is set
{B1} is set
{{B1,B1},{B1}} is set
the ObjectMap of F . [B1,B1] is set
( the ObjectMap of F . (B1,B1)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
B1 is M2( the carrier of A1)
B2 is M2( the carrier of A1)
<^B1,B2^> is set
the Arrows of A1 . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of A1 . [B1,B2] is set
G is M2( the carrier of A1)
b is M2( the carrier of A1)
<^G,b^> is set
the Arrows of A1 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of A1 . [G,b] is set
Morph-Map (F,G,b) is Relation-like Function-like set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the MorphMap of F . (G,b) is Relation-like Function-like set
the MorphMap of F . [G,b] is Relation-like Function-like set
F . G is M2( the carrier of A2)
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{{G,G},{G}} is set
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
F . b is M2( the carrier of A2)
the ObjectMap of F . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of F . [b,b] is set
( the ObjectMap of F . (b,b)) `1 is set
<^(F . G),(F . b)^> is set
the Arrows of A2 . ((F . G),(F . b)) is set
[(F . G),(F . b)] is V15() set
{(F . G),(F . b)} is set
{(F . G)} is set
{{(F . G),(F . b)},{(F . G)}} is set
the Arrows of A2 . [(F . G),(F . b)] is set
c is M2(<^B1,B2^>)
b1 is M2(<^G,b^>)
F . c is M2(<^(F . B1),(F . B2)^>)
F . B1 is M2( the carrier of A2)
the ObjectMap of F . (B1,B1) is M2([: the carrier of A2, the carrier of A2:])
[B1,B1] is V15() set
{B1,B1} is set
{{B1,B1},{B1}} is set
the ObjectMap of F . [B1,B1] is set
( the ObjectMap of F . (B1,B1)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
<^(F . B1),(F . B2)^> is set
the Arrows of A2 . ((F . B1),(F . B2)) is set
[(F . B1),(F . B2)] is V15() set
{(F . B1),(F . B2)} is set
{(F . B1)} is set
{{(F . B1),(F . B2)},{(F . B1)}} is set
the Arrows of A2 . [(F . B1),(F . B2)] is set
(Morph-Map (F,G,b)) . b1 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
the carrier of A1 is non empty set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the carrier of A2 is non empty set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
B1 is M2( the carrier of A1)
B2 is M2( the carrier of A1)
F . B1 is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (B1,B1) is M2([: the carrier of A2, the carrier of A2:])
[B1,B1] is V15() set
{B1,B1} is set
{B1} is set
{{B1,B1},{B1}} is set
the ObjectMap of F . [B1,B1] is set
( the ObjectMap of F . (B1,B1)) `1 is set
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
B1 is M2( the carrier of A1)
B2 is M2( the carrier of A1)
<^B1,B2^> is set
the Arrows of A1 . (B1,B2) is set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
the Arrows of A1 . [B1,B2] is set
G is M2( the carrier of A1)
b is M2( the carrier of A1)
<^G,b^> is set
the Arrows of A1 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of A1 . [G,b] is set
Morph-Map (F,G,b) is Relation-like Function-like set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the MorphMap of F . (G,b) is Relation-like Function-like set
the MorphMap of F . [G,b] is Relation-like Function-like set
F . b is M2( the carrier of A2)
the ObjectMap of F . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of F . [b,b] is set
( the ObjectMap of F . (b,b)) `1 is set
F . G is M2( the carrier of A2)
the ObjectMap of F . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{{G,G},{G}} is set
the ObjectMap of F . [G,G] is set
( the ObjectMap of F . (G,G)) `1 is set
<^(F . b),(F . G)^> is set
the Arrows of A2 . ((F . b),(F . G)) is set
[(F . b),(F . G)] is V15() set
{(F . b),(F . G)} is set
{(F . b)} is set
{{(F . b),(F . G)},{(F . b)}} is set
the Arrows of A2 . [(F . b),(F . G)] is set
c is M2(<^B1,B2^>)
b1 is M2(<^G,b^>)
F . c is M2(<^(F . B2),(F . B1)^>)
F . B2 is M2( the carrier of A2)
the ObjectMap of F . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of F . [B2,B2] is set
( the ObjectMap of F . (B2,B2)) `1 is set
F . B1 is M2( the carrier of A2)
the ObjectMap of F . (B1,B1) is M2([: the carrier of A2, the carrier of A2:])
[B1,B1] is V15() set
{B1,B1} is set
{{B1,B1},{B1}} is set
the ObjectMap of F . [B1,B1] is set
( the ObjectMap of F . (B1,B1)) `1 is set
<^(F . B2),(F . B1)^> is set
the Arrows of A2 . ((F . B2),(F . B1)) is set
[(F . B2),(F . B1)] is V15() set
{(F . B2),(F . B1)} is set
{(F . B2)} is set
{{(F . B2),(F . B1)},{(F . B2)}} is set
the Arrows of A2 . [(F . B2),(F . B1)] is set
(Morph-Map (F,G,b)) . b1 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
id A1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A1,A1
A2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
the carrier of A2 is non empty set
the carrier of A1 is non empty set
id A2 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
B1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A2,A2
B2 is M2( the carrier of A2)
G is M2( the carrier of A1)
B1 . B2 is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
(id A1) . G is M2( the carrier of A1)
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the ObjectMap of (id A1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (id A1) . (G,G) is M2([: the carrier of A1, the carrier of A1:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (id A1) . [G,G] is set
( the ObjectMap of (id A1) . (G,G)) `1 is set
B2 is M2( the carrier of A2)
G is M2( the carrier of A2)
<^B2,G^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
b is M2( the carrier of A1)
c is M2( the carrier of A1)
<^b,c^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of A1 . [b,c] is set
Morph-Map ((id A1),b,c) is Relation-like Function-like set
the MorphMap of (id A1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (id A1), the Arrows of A1, the Arrows of A1
the MorphMap of (id A1) . (b,c) is Relation-like Function-like set
the MorphMap of (id A1) . [b,c] is Relation-like Function-like set
b1 is M2(<^B2,G^>)
B1 . b1 is M2(<^(B1 . B2),(B1 . G)^>)
B1 . B2 is M2( the carrier of A2)
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of A2, the carrier of A2:])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
B1 . G is M2( the carrier of A2)
the ObjectMap of B1 . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of B1 . [G,G] is set
( the ObjectMap of B1 . (G,G)) `1 is set
<^(B1 . B2),(B1 . G)^> is set
the Arrows of A2 . ((B1 . B2),(B1 . G)) is set
[(B1 . B2),(B1 . G)] is V15() set
{(B1 . B2),(B1 . G)} is set
{(B1 . B2)} is set
{{(B1 . B2),(B1 . G)},{(B1 . B2)}} is set
the Arrows of A2 . [(B1 . B2),(B1 . G)] is set
c1 is M2(<^b,c^>)
(Morph-Map ((id A1),b,c)) . c1 is set
(id A1) . b is M2( the carrier of A1)
the ObjectMap of (id A1) . (b,b) is M2([: the carrier of A1, the carrier of A1:])
[b,b] is V15() set
{b,b} is set
{{b,b},{b}} is set
the ObjectMap of (id A1) . [b,b] is set
( the ObjectMap of (id A1) . (b,b)) `1 is set
(id A1) . c is M2( the carrier of A1)
the ObjectMap of (id A1) . (c,c) is M2([: the carrier of A1, the carrier of A1:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of (id A1) . [c,c] is set
( the ObjectMap of (id A1) . (c,c)) `1 is set
(id A1) . c1 is M2(<^((id A1) . b),((id A1) . c)^>)
<^((id A1) . b),((id A1) . c)^> is set
the Arrows of A1 . (((id A1) . b),((id A1) . c)) is set
[((id A1) . b),((id A1) . c)] is V15() set
{((id A1) . b),((id A1) . c)} is set
{((id A1) . b)} is set
{{((id A1) . b),((id A1) . c)},{((id A1) . b)}} is set
the Arrows of A1 . [((id A1) . b),((id A1) . c)] is set
Morph-Map ((id A1),b,c) is Relation-like <^b,c^> -defined <^((id A1) . b),((id A1) . c)^> -valued Function-like quasi_total M2( bool [:<^b,c^>,<^((id A1) . b),((id A1) . c)^>:])
[:<^b,c^>,<^((id A1) . b),((id A1) . c)^>:] is Relation-like set
bool [:<^b,c^>,<^((id A1) . b),((id A1) . c)^>:] is non empty set
(Morph-Map ((id A1),b,c)) . c1 is set
A1 is Relation-like Function-like set
A2 is Relation-like Function-like set
~ A1 is Relation-like Function-like set
~ A2 is Relation-like Function-like set
F is set
B1 is set
[F,B1] is V15() set
{F,B1} is set
{F} is set
{{F,B1},{F}} is set
proj1 (~ A1) is set
proj1 A1 is set
G is set
B2 is set
[G,B2] is V15() set
{G,B2} is set
{G} is set
{{G,B2},{G}} is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
(~ A1) . (G,B2) is set
(~ A1) . [G,B2] is set
A1 . (B2,G) is set
A1 . [B2,G] is set
[[B2,G],B1] is V15() set
{[B2,G],B1} is set
{[B2,G]} is Relation-like Function-like set
{{[B2,G],B1},{[B2,G]}} is set
proj1 A2 is set
A2 . (B2,G) is set
A2 . [B2,G] is set
(~ A2) . (G,B2) is set
(~ A2) . [G,B2] is set
proj1 (~ A2) is set
A1 is Relation-like Function-like set
proj1 A1 is set
~ A1 is Relation-like Function-like set
A2 is Relation-like Function-like set
~ A2 is Relation-like Function-like set
F is Relation-like set
proj1 F is set
proj2 F is set
[:(proj1 F),(proj2 F):] is Relation-like set
~ (~ A1) is Relation-like Function-like set
~ (~ A2) is Relation-like Function-like set
A1 is set
[:A1,A1:] is Relation-like set
A2 is set
[:A2,A2:] is Relation-like set
F is Relation-like [:A1,A1:] -defined Function-like total set
~ F is Relation-like [:A1,A1:] -defined Function-like total set
B1 is Relation-like [:A2,A2:] -defined Function-like total set
~ B1 is Relation-like [:A2,A2:] -defined Function-like total set
B2 is set
(~ F) . B2 is set
(~ B1) . B2 is set
G is set
b is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
[b,G] is V15() set
{b,G} is set
{b} is set
{{b,G},{b}} is set
dom F is Relation-like A1 -defined A1 -valued M2( bool [:A1,A1:])
bool [:A1,A1:] is non empty set
(~ F) . (G,b) is set
(~ F) . [G,b] is set
F . (b,G) is set
F . [b,G] is set
dom B1 is Relation-like A2 -defined A2 -valued M2( bool [:A2,A2:])
bool [:A2,A2:] is non empty set
(~ B1) . (G,b) is set
(~ B1) . [G,b] is set
B1 . (b,G) is set
B1 . [b,G] is set
A1 is non empty transitive AltCatStr
A1 opp is non empty transitive strict AltCatStr
A2 is non empty transitive SubCatStr of A1
A2 opp is non empty transitive strict AltCatStr
the carrier of (A2 opp) is non empty set
the carrier of A2 is non empty set
the Arrows of (A2 opp) is Relation-like [: the carrier of (A2 opp), the carrier of (A2 opp):] -defined Function-like non empty total set
[: the carrier of (A2 opp), the carrier of (A2 opp):] is Relation-like non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
~ the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the carrier of (A1 opp) is non empty set
the carrier of A1 is non empty set
[: the carrier of (A1 opp), the carrier of (A1 opp):] is Relation-like non empty set
the Arrows of (A1 opp) is Relation-like [: the carrier of (A1 opp), the carrier of (A1 opp):] -defined Function-like non empty total set
[: the carrier of (A2 opp), the carrier of (A2 opp), the carrier of (A2 opp):] is non empty set
[: the carrier of (A1 opp), the carrier of (A1 opp), the carrier of (A1 opp):] is non empty set
the Comp of (A2 opp) is Relation-like [: the carrier of (A2 opp), the carrier of (A2 opp), the carrier of (A2 opp):] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of (A2 opp), the Arrows of (A2 opp)|},{| the Arrows of (A2 opp)|}
{| the Arrows of (A2 opp), the Arrows of (A2 opp)|} is Relation-like [: the carrier of (A2 opp), the carrier of (A2 opp), the carrier of (A2 opp):] -defined Function-like non empty total set
{| the Arrows of (A2 opp)|} is Relation-like [: the carrier of (A2 opp), the carrier of (A2 opp), the carrier of (A2 opp):] -defined Function-like non empty total set
the Comp of (A1 opp) is Relation-like [: the carrier of (A1 opp), the carrier of (A1 opp), the carrier of (A1 opp):] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of (A1 opp), the Arrows of (A1 opp)|},{| the Arrows of (A1 opp)|}
{| the Arrows of (A1 opp), the Arrows of (A1 opp)|} is Relation-like [: the carrier of (A1 opp), the carrier of (A1 opp), the carrier of (A1 opp):] -defined Function-like non empty total set
{| the Arrows of (A1 opp)|} is Relation-like [: the carrier of (A1 opp), the carrier of (A1 opp), the carrier of (A1 opp):] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
~ the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
F is set
the Comp of (A2 opp) . F is Relation-like Function-like set
the Comp of (A1 opp) . F is Relation-like Function-like set
B1 is set
B2 is set
G is set
[B1,B2,G] is V15() V16() set
[B1,B2] is V15() set
{B1,B2} is set
{B1} is set
{{B1,B2},{B1}} is set
[[B1,B2],G] is V15() set
{[B1,B2],G} is set
{[B1,B2]} is Relation-like Function-like set
{{[B1,B2],G},{[B1,B2]}} is set
b is M2( the carrier of A2)
c is M2( the carrier of A2)
b1 is M2( the carrier of A2)
c1 is M2( the carrier of A1)
f is M2( the carrier of A1)
f1 is M2( the carrier of A1)
[: the carrier of A2, the carrier of A2, the carrier of A2:] is non empty set
[: the carrier of A1, the carrier of A1, the carrier of A1:] is non empty set
the Comp of A2 is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of A2, the Arrows of A2|},{| the Arrows of A2|}
{| the Arrows of A2, the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
{| the Arrows of A2|} is Relation-like [: the carrier of A2, the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Comp of A1 is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() ManySortedFunction of {| the Arrows of A1, the Arrows of A1|},{| the Arrows of A1|}
{| the Arrows of A1, the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
{| the Arrows of A1|} is Relation-like [: the carrier of A1, the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Comp of A2 . (b1,c,b) is Relation-like [:( the Arrows of A2 . (c,b)),( the Arrows of A2 . (b1,c)):] -defined the Arrows of A2 . (b1,b) -valued Function-like quasi_total M2( bool [:[:( the Arrows of A2 . (c,b)),( the Arrows of A2 . (b1,c)):],( the Arrows of A2 . (b1,b)):])
the Arrows of A2 . (c,b) is set
[c,b] is V15() set
{c,b} is set
{c} is set
{{c,b},{c}} is set
the Arrows of A2 . [c,b] is set
the Arrows of A2 . (b1,c) is set
[b1,c] is V15() set
{b1,c} is set
{b1} is set
{{b1,c},{b1}} is set
the Arrows of A2 . [b1,c] is set
[:( the Arrows of A2 . (c,b)),( the Arrows of A2 . (b1,c)):] is Relation-like set
the Arrows of A2 . (b1,b) is set
[b1,b] is V15() set
{b1,b} is set
{{b1,b},{b1}} is set
the Arrows of A2 . [b1,b] is set
[:[:( the Arrows of A2 . (c,b)),( the Arrows of A2 . (b1,c)):],( the Arrows of A2 . (b1,b)):] is Relation-like set
bool [:[:( the Arrows of A2 . (c,b)),( the Arrows of A2 . (b1,c)):],( the Arrows of A2 . (b1,b)):] is non empty set
[b1,c,b] is V15() V16() set
[[b1,c],b] is V15() set
{[b1,c],b} is set
{[b1,c]} is Relation-like Function-like set
{{[b1,c],b},{[b1,c]}} is set
the Comp of A2 . [b1,c,b] is Relation-like Function-like set
the Comp of A1 . (f1,f,c1) is Relation-like [:( the Arrows of A1 . (f,c1)),( the Arrows of A1 . (f1,f)):] -defined the Arrows of A1 . (f1,c1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of A1 . (f,c1)),( the Arrows of A1 . (f1,f)):],( the Arrows of A1 . (f1,c1)):])
the Arrows of A1 . (f,c1) is set
[f,c1] is V15() set
{f,c1} is set
{f} is set
{{f,c1},{f}} is set
the Arrows of A1 . [f,c1] is set
the Arrows of A1 . (f1,f) is set
[f1,f] is V15() set
{f1,f} is set
{f1} is set
{{f1,f},{f1}} is set
the Arrows of A1 . [f1,f] is set
[:( the Arrows of A1 . (f,c1)),( the Arrows of A1 . (f1,f)):] is Relation-like set
the Arrows of A1 . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{{f1,c1},{f1}} is set
the Arrows of A1 . [f1,c1] is set
[:[:( the Arrows of A1 . (f,c1)),( the Arrows of A1 . (f1,f)):],( the Arrows of A1 . (f1,c1)):] is Relation-like set
bool [:[:( the Arrows of A1 . (f,c1)),( the Arrows of A1 . (f1,f)):],( the Arrows of A1 . (f1,c1)):] is non empty set
[f1,f,c1] is V15() V16() set
[[f1,f],c1] is V15() set
{[f1,f],c1} is set
{[f1,f]} is Relation-like Function-like set
{{[f1,f],c1},{[f1,f]}} is set
the Comp of A1 . [f1,f,c1] is Relation-like Function-like set
[G,B2,B1] is V15() V16() set
[G,B2] is V15() set
{G,B2} is set
{G} is set
{{G,B2},{G}} is set
[[G,B2],B1] is V15() set
{[G,B2],B1} is set
{[G,B2]} is Relation-like Function-like set
{{[G,B2],B1},{[G,B2]}} is set
c9 is M2( the carrier of (A2 opp))
f9 is M2( the carrier of (A2 opp))
g9 is M2( the carrier of (A2 opp))
the Comp of (A2 opp) . (c9,f9,g9) is Relation-like [:( the Arrows of (A2 opp) . (f9,g9)),( the Arrows of (A2 opp) . (c9,f9)):] -defined the Arrows of (A2 opp) . (c9,g9) -valued Function-like quasi_total M2( bool [:[:( the Arrows of (A2 opp) . (f9,g9)),( the Arrows of (A2 opp) . (c9,f9)):],( the Arrows of (A2 opp) . (c9,g9)):])
the Arrows of (A2 opp) . (f9,g9) is set
[f9,g9] is V15() set
{f9,g9} is set
{f9} is set
{{f9,g9},{f9}} is set
the Arrows of (A2 opp) . [f9,g9] is set
the Arrows of (A2 opp) . (c9,f9) is set
[c9,f9] is V15() set
{c9,f9} is set
{c9} is set
{{c9,f9},{c9}} is set
the Arrows of (A2 opp) . [c9,f9] is set
[:( the Arrows of (A2 opp) . (f9,g9)),( the Arrows of (A2 opp) . (c9,f9)):] is Relation-like set
the Arrows of (A2 opp) . (c9,g9) is set
[c9,g9] is V15() set
{c9,g9} is set
{{c9,g9},{c9}} is set
the Arrows of (A2 opp) . [c9,g9] is set
[:[:( the Arrows of (A2 opp) . (f9,g9)),( the Arrows of (A2 opp) . (c9,f9)):],( the Arrows of (A2 opp) . (c9,g9)):] is Relation-like set
bool [:[:( the Arrows of (A2 opp) . (f9,g9)),( the Arrows of (A2 opp) . (c9,f9)):],( the Arrows of (A2 opp) . (c9,g9)):] is non empty set
c1 is M2( the carrier of (A1 opp))
a9 is M2( the carrier of (A1 opp))
b9 is M2( the carrier of (A1 opp))
the Comp of (A1 opp) . (c1,a9,b9) is Relation-like [:( the Arrows of (A1 opp) . (a9,b9)),( the Arrows of (A1 opp) . (c1,a9)):] -defined the Arrows of (A1 opp) . (c1,b9) -valued Function-like quasi_total M2( bool [:[:( the Arrows of (A1 opp) . (a9,b9)),( the Arrows of (A1 opp) . (c1,a9)):],( the Arrows of (A1 opp) . (c1,b9)):])
the Arrows of (A1 opp) . (a9,b9) is set
[a9,b9] is V15() set
{a9,b9} is set
{a9} is set
{{a9,b9},{a9}} is set
the Arrows of (A1 opp) . [a9,b9] is set
the Arrows of (A1 opp) . (c1,a9) is set
[c1,a9] is V15() set
{c1,a9} is set
{c1} is set
{{c1,a9},{c1}} is set
the Arrows of (A1 opp) . [c1,a9] is set
[:( the Arrows of (A1 opp) . (a9,b9)),( the Arrows of (A1 opp) . (c1,a9)):] is Relation-like set
the Arrows of (A1 opp) . (c1,b9) is set
[c1,b9] is V15() set
{c1,b9} is set
{{c1,b9},{c1}} is set
the Arrows of (A1 opp) . [c1,b9] is set
[:[:( the Arrows of (A1 opp) . (a9,b9)),( the Arrows of (A1 opp) . (c1,a9)):],( the Arrows of (A1 opp) . (c1,b9)):] is Relation-like set
bool [:[:( the Arrows of (A1 opp) . (a9,b9)),( the Arrows of (A1 opp) . (c1,a9)):],( the Arrows of (A1 opp) . (c1,b9)):] is non empty set
~ ( the Comp of A1 . (f1,f,c1)) is Relation-like [:( the Arrows of A1 . (f1,f)),( the Arrows of A1 . (f,c1)):] -defined the Arrows of A1 . (f1,c1) -valued Function-like quasi_total M2( bool [:[:( the Arrows of A1 . (f1,f)),( the Arrows of A1 . (f,c1)):],( the Arrows of A1 . (f1,c1)):])
[:( the Arrows of A1 . (f1,f)),( the Arrows of A1 . (f,c1)):] is Relation-like set
[:[:( the Arrows of A1 . (f1,f)),( the Arrows of A1 . (f,c1)):],( the Arrows of A1 . (f1,c1)):] is Relation-like set
bool [:[:( the Arrows of A1 . (f1,f)),( the Arrows of A1 . (f,c1)):],( the Arrows of A1 . (f1,c1)):] is non empty set
~ ( the Comp of A2 . (b1,c,b)) is Relation-like [:( the Arrows of A2 . (b1,c)),( the Arrows of A2 . (c,b)):] -defined the Arrows of A2 . (b1,b) -valued Function-like quasi_total M2( bool [:[:( the Arrows of A2 . (b1,c)),( the Arrows of A2 . (c,b)):],( the Arrows of A2 . (b1,b)):])
[:( the Arrows of A2 . (b1,c)),( the Arrows of A2 . (c,b)):] is Relation-like set
[:[:( the Arrows of A2 . (b1,c)),( the Arrows of A2 . (c,b)):],( the Arrows of A2 . (b1,b)):] is Relation-like set
bool [:[:( the Arrows of A2 . (b1,c)),( the Arrows of A2 . (c,b)):],( the Arrows of A2 . (b1,b)):] is non empty set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A1 opp is non empty transitive strict V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
A2 opp is non empty transitive strict V106() with_units reflexive AltCatStr
F is non empty transitive V106() SubCatStr of A1 opp
the carrier of F is non empty set
the carrier of (A1 opp) is non empty set
B1 is M2( the carrier of F)
<^B1,B1^> is set
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like non empty total set
[: the carrier of F, the carrier of F:] is Relation-like non empty set
the Arrows of F . (B1,B1) is set
[B1,B1] is V15() set
{B1,B1} is set
{B1} is set
{{B1,B1},{B1}} is set
the Arrows of F . [B1,B1] is set
B2 is M2( the carrier of (A1 opp))
idm B2 is M2(<^B2,B2^>)
<^B2,B2^> is non empty set
the Arrows of (A1 opp) is Relation-like [: the carrier of (A1 opp), the carrier of (A1 opp):] -defined Function-like non empty total set
[: the carrier of (A1 opp), the carrier of (A1 opp):] is Relation-like non empty set
the Arrows of (A1 opp) . (B2,B2) is set
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the Arrows of (A1 opp) . [B2,B2] is set
the carrier of A1 is non empty set
the carrier of A2 is non empty set
G is M2( the carrier of A1)
idm G is M2(<^G,G^>)
<^G,G^> is non empty set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (G,G) is set
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the Arrows of A1 . [G,G] is set
b is M2( the carrier of A2)
<^b,b^> is non empty set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (b,b) is set
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the Arrows of A2 . [b,b] is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A1 opp is non empty transitive strict V106() with_units reflexive AltCatStr
dualizing-func (A1,(A1 opp)) is reflexive reflexive feasible feasible strict strict Contravariant Contravariant id-preserving id-preserving comp-reversing comp-reversing contravariant contravariant bijective Functor of A1,A1 opp
A2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
A2 opp is non empty transitive strict V106() with_units reflexive AltCatStr
the carrier of A2 is non empty set
the carrier of A1 is non empty set
dualizing-func (A2,(A2 opp)) is reflexive reflexive feasible feasible strict strict Contravariant Contravariant id-preserving id-preserving comp-reversing comp-reversing contravariant contravariant bijective Functor of A2,A2 opp
B1 is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant bijective Functor of A2,A2 opp
B2 is M2( the carrier of A2)
G is M2( the carrier of A1)
B1 . B2 is M2( the carrier of (A2 opp))
the carrier of (A2 opp) is non empty set
[: the carrier of (A2 opp), the carrier of (A2 opp):] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of (A2 opp), the carrier of (A2 opp):] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of (A2 opp), the carrier of (A2 opp):]:])
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
[:[: the carrier of A2, the carrier of A2:],[: the carrier of (A2 opp), the carrier of (A2 opp):]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of (A2 opp), the carrier of (A2 opp):]:] is non empty set
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of (A2 opp), the carrier of (A2 opp):])
[B2,B2] is V15() set
{B2,B2} is set
{B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
(dualizing-func (A1,(A1 opp))) . G is M2( the carrier of (A1 opp))
the carrier of (A1 opp) is non empty set
[: the carrier of (A1 opp), the carrier of (A1 opp):] is Relation-like non empty set
the ObjectMap of (dualizing-func (A1,(A1 opp))) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of (A1 opp), the carrier of (A1 opp):] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of (A1 opp), the carrier of (A1 opp):]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of (A1 opp), the carrier of (A1 opp):]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of (A1 opp), the carrier of (A1 opp):]:] is non empty set
the ObjectMap of (dualizing-func (A1,(A1 opp))) . (G,G) is M2([: the carrier of (A1 opp), the carrier of (A1 opp):])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (dualizing-func (A1,(A1 opp))) . [G,G] is set
( the ObjectMap of (dualizing-func (A1,(A1 opp))) . (G,G)) `1 is set
B2 is M2( the carrier of A2)
G is M2( the carrier of A2)
<^B2,G^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . (B2,G) is set
[B2,G] is V15() set
{B2,G} is set
{B2} is set
{{B2,G},{B2}} is set
the Arrows of A2 . [B2,G] is set
b is M2( the carrier of A1)
c is M2( the carrier of A1)
<^b,c^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of A1 . [b,c] is set
Morph-Map ((dualizing-func (A1,(A1 opp))),b,c) is Relation-like Function-like set
the MorphMap of (dualizing-func (A1,(A1 opp))) is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (dualizing-func (A1,(A1 opp))), the Arrows of A1, the Arrows of (A1 opp)
the Arrows of (A1 opp) is Relation-like [: the carrier of (A1 opp), the carrier of (A1 opp):] -defined Function-like non empty total set
the MorphMap of (dualizing-func (A1,(A1 opp))) . (b,c) is Relation-like Function-like set
the MorphMap of (dualizing-func (A1,(A1 opp))) . [b,c] is Relation-like Function-like set
b1 is M2(<^B2,G^>)
B1 . b1 is M2(<^(B1 . G),(B1 . B2)^>)
B1 . G is M2( the carrier of (A2 opp))
the ObjectMap of B1 . (G,G) is M2([: the carrier of (A2 opp), the carrier of (A2 opp):])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of B1 . [G,G] is set
( the ObjectMap of B1 . (G,G)) `1 is set
B1 . B2 is M2( the carrier of (A2 opp))
the ObjectMap of B1 . (B2,B2) is M2([: the carrier of (A2 opp), the carrier of (A2 opp):])
[B2,B2] is V15() set
{B2,B2} is set
{{B2,B2},{B2}} is set
the ObjectMap of B1 . [B2,B2] is set
( the ObjectMap of B1 . (B2,B2)) `1 is set
<^(B1 . G),(B1 . B2)^> is set
the Arrows of (A2 opp) is Relation-like [: the carrier of (A2 opp), the carrier of (A2 opp):] -defined Function-like non empty total set
the Arrows of (A2 opp) . ((B1 . G),(B1 . B2)) is set
[(B1 . G),(B1 . B2)] is V15() set
{(B1 . G),(B1 . B2)} is set
{(B1 . G)} is set
{{(B1 . G),(B1 . B2)},{(B1 . G)}} is set
the Arrows of (A2 opp) . [(B1 . G),(B1 . B2)] is set
c1 is M2(<^b,c^>)
(Morph-Map ((dualizing-func (A1,(A1 opp))),b,c)) . c1 is set
(dualizing-func (A1,(A1 opp))) . c is M2( the carrier of (A1 opp))
the ObjectMap of (dualizing-func (A1,(A1 opp))) . (c,c) is M2([: the carrier of (A1 opp), the carrier of (A1 opp):])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of (dualizing-func (A1,(A1 opp))) . [c,c] is set
( the ObjectMap of (dualizing-func (A1,(A1 opp))) . (c,c)) `1 is set
(dualizing-func (A1,(A1 opp))) . b is M2( the carrier of (A1 opp))
the ObjectMap of (dualizing-func (A1,(A1 opp))) . (b,b) is M2([: the carrier of (A1 opp), the carrier of (A1 opp):])
[b,b] is V15() set
{b,b} is set
{{b,b},{b}} is set
the ObjectMap of (dualizing-func (A1,(A1 opp))) . [b,b] is set
( the ObjectMap of (dualizing-func (A1,(A1 opp))) . (b,b)) `1 is set
<^((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)^> is set
the Arrows of (A1 opp) . (((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)) is set
[((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)] is V15() set
{((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)} is set
{((dualizing-func (A1,(A1 opp))) . c)} is set
{{((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)},{((dualizing-func (A1,(A1 opp))) . c)}} is set
the Arrows of (A1 opp) . [((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)] is set
(dualizing-func (A1,(A1 opp))) . c1 is M2(<^((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)^>)
Morph-Map ((dualizing-func (A1,(A1 opp))),b,c) is Relation-like <^b,c^> -defined <^((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)^> -valued Function-like quasi_total M2( bool [:<^b,c^>,<^((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)^>:])
[:<^b,c^>,<^((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)^>:] is Relation-like set
bool [:<^b,c^>,<^((dualizing-func (A1,(A1 opp))) . c),((dualizing-func (A1,(A1 opp))) . b)^>:] is non empty set
(Morph-Map ((dualizing-func (A1,(A1 opp))),b,c)) . c1 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
F " is strict FunctorStr over A2,A1
B2 is feasible id-preserving Functor of A2,A1
B2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
G is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A2
the carrier of B2 is non empty set
the carrier of A1 is non empty set
b is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of B2,G
the carrier of G is non empty set
the carrier of A2 is non empty set
b " is strict FunctorStr over G,B2
c is feasible id-preserving Functor of G,B2
b1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of G,B2
c1 is M2( the carrier of G)
b1 . c1 is M2( the carrier of B2)
[: the carrier of B2, the carrier of B2:] is Relation-like non empty set
the ObjectMap of b1 is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of B2, the carrier of B2:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of B2, the carrier of B2:]:])
[: the carrier of G, the carrier of G:] is Relation-like non empty set
[:[: the carrier of G, the carrier of G:],[: the carrier of B2, the carrier of B2:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of B2, the carrier of B2:]:] is non empty set
the ObjectMap of b1 . (c1,c1) is M2([: the carrier of B2, the carrier of B2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of b1 . [c1,c1] is set
( the ObjectMap of b1 . (c1,c1)) `1 is set
b . (b1 . c1) is M2( the carrier of G)
the ObjectMap of b is Relation-like [: the carrier of B2, the carrier of B2:] -defined [: the carrier of G, the carrier of G:] -valued Function-like quasi_total M2( bool [:[: the carrier of B2, the carrier of B2:],[: the carrier of G, the carrier of G:]:])
[:[: the carrier of B2, the carrier of B2:],[: the carrier of G, the carrier of G:]:] is Relation-like non empty set
bool [:[: the carrier of B2, the carrier of B2:],[: the carrier of G, the carrier of G:]:] is non empty set
the ObjectMap of b . ((b1 . c1),(b1 . c1)) is M2([: the carrier of G, the carrier of G:])
[(b1 . c1),(b1 . c1)] is V15() set
{(b1 . c1),(b1 . c1)} is set
{(b1 . c1)} is set
{{(b1 . c1),(b1 . c1)},{(b1 . c1)}} is set
the ObjectMap of b . [(b1 . c1),(b1 . c1)] is set
( the ObjectMap of b . ((b1 . c1),(b1 . c1))) `1 is set
f1 is M2( the carrier of A1)
F . f1 is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of F . [f1,f1] is set
( the ObjectMap of F . (f1,f1)) `1 is set
f is M2( the carrier of A2)
(F ") . f is M2( the carrier of A1)
the ObjectMap of (F ") is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (F ") . (f,f) is M2([: the carrier of A1, the carrier of A1:])
[f,f] is V15() set
{f,f} is set
{f} is set
{{f,f},{f}} is set
the ObjectMap of (F ") . [f,f] is set
( the ObjectMap of (F ") . (f,f)) `1 is set
c1 is M2( the carrier of G)
f is M2( the carrier of G)
<^c1,f^> is set
the Arrows of G is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty total set
the Arrows of G . (c1,f) is set
[c1,f] is V15() set
{c1,f} is set
{c1} is set
{{c1,f},{c1}} is set
the Arrows of G . [c1,f] is set
f1 is M2( the carrier of A2)
c1 is M2( the carrier of A2)
<^f1,c1^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{f1} is set
{{f1,c1},{f1}} is set
the Arrows of A2 . [f1,c1] is set
Morph-Map ((F "),f1,c1) is Relation-like Function-like set
the MorphMap of (F ") is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (F "), the Arrows of A2, the Arrows of A1
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the MorphMap of (F ") . (f1,c1) is Relation-like Function-like set
the MorphMap of (F ") . [f1,c1] is Relation-like Function-like set
a9 is M2(<^c1,f^>)
b1 . a9 is M2(<^(b1 . c1),(b1 . f)^>)
b1 . c1 is M2( the carrier of B2)
the ObjectMap of b1 . (c1,c1) is M2([: the carrier of B2, the carrier of B2:])
[c1,c1] is V15() set
{c1,c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of b1 . [c1,c1] is set
( the ObjectMap of b1 . (c1,c1)) `1 is set
b1 . f is M2( the carrier of B2)
the ObjectMap of b1 . (f,f) is M2([: the carrier of B2, the carrier of B2:])
[f,f] is V15() set
{f,f} is set
{f} is set
{{f,f},{f}} is set
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
<^(b1 . c1),(b1 . f)^> is set
the Arrows of B2 is Relation-like [: the carrier of B2, the carrier of B2:] -defined Function-like non empty total set
the Arrows of B2 . ((b1 . c1),(b1 . f)) is set
[(b1 . c1),(b1 . f)] is V15() set
{(b1 . c1),(b1 . f)} is set
{(b1 . c1)} is set
{{(b1 . c1),(b1 . f)},{(b1 . c1)}} is set
the Arrows of B2 . [(b1 . c1),(b1 . f)] is set
b9 is M2(<^f1,c1^>)
(Morph-Map ((F "),f1,c1)) . b9 is set
b . (b1 . c1) is M2( the carrier of G)
the ObjectMap of b . ((b1 . c1),(b1 . c1)) is M2([: the carrier of G, the carrier of G:])
[(b1 . c1),(b1 . c1)] is V15() set
{(b1 . c1),(b1 . c1)} is set
{{(b1 . c1),(b1 . c1)},{(b1 . c1)}} is set
the ObjectMap of b . [(b1 . c1),(b1 . c1)] is set
( the ObjectMap of b . ((b1 . c1),(b1 . c1))) `1 is set
b . (b1 . f) is M2( the carrier of G)
the ObjectMap of b . ((b1 . f),(b1 . f)) is M2([: the carrier of G, the carrier of G:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of b . [(b1 . f),(b1 . f)] is set
( the ObjectMap of b . ((b1 . f),(b1 . f))) `1 is set
(F ") . f1 is M2( the carrier of A1)
the ObjectMap of (F ") . (f1,f1) is M2([: the carrier of A1, the carrier of A1:])
[f1,f1] is V15() set
{f1,f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of (F ") . [f1,f1] is set
( the ObjectMap of (F ") . (f1,f1)) `1 is set
F . ((F ") . f1) is M2( the carrier of A2)
the ObjectMap of F . (((F ") . f1),((F ") . f1)) is M2([: the carrier of A2, the carrier of A2:])
[((F ") . f1),((F ") . f1)] is V15() set
{((F ") . f1),((F ") . f1)} is set
{((F ") . f1)} is set
{{((F ") . f1),((F ") . f1)},{((F ") . f1)}} is set
the ObjectMap of F . [((F ") . f1),((F ") . f1)] is set
( the ObjectMap of F . (((F ") . f1),((F ") . f1))) `1 is set
(F ") . c1 is M2( the carrier of A1)
the ObjectMap of (F ") . (c1,c1) is M2([: the carrier of A1, the carrier of A1:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of (F ") . [c1,c1] is set
( the ObjectMap of (F ") . (c1,c1)) `1 is set
F . ((F ") . c1) is M2( the carrier of A2)
the ObjectMap of F . (((F ") . c1),((F ") . c1)) is M2([: the carrier of A2, the carrier of A2:])
[((F ") . c1),((F ") . c1)] is V15() set
{((F ") . c1),((F ") . c1)} is set
{((F ") . c1)} is set
{{((F ") . c1),((F ") . c1)},{((F ") . c1)}} is set
the ObjectMap of F . [((F ") . c1),((F ") . c1)] is set
( the ObjectMap of F . (((F ") . c1),((F ") . c1))) `1 is set
<^((F ") . f1),((F ") . c1)^> is set
the Arrows of A1 . (((F ") . f1),((F ") . c1)) is set
[((F ") . f1),((F ") . c1)] is V15() set
{((F ") . f1),((F ") . c1)} is set
{{((F ") . f1),((F ") . c1)},{((F ") . f1)}} is set
the Arrows of A1 . [((F ") . f1),((F ") . c1)] is set
b . (b1 . a9) is M2(<^(b . (b1 . c1)),(b . (b1 . f))^>)
<^(b . (b1 . c1)),(b . (b1 . f))^> is set
the Arrows of G . ((b . (b1 . c1)),(b . (b1 . f))) is set
[(b . (b1 . c1)),(b . (b1 . f))] is V15() set
{(b . (b1 . c1)),(b . (b1 . f))} is set
{(b . (b1 . c1))} is set
{{(b . (b1 . c1)),(b . (b1 . f))},{(b . (b1 . c1))}} is set
the Arrows of G . [(b . (b1 . c1)),(b . (b1 . f))] is set
Morph-Map (F,((F ") . f1),((F ") . c1)) is Relation-like <^((F ") . f1),((F ") . c1)^> -defined <^(F . ((F ") . f1)),(F . ((F ") . c1))^> -valued Function-like quasi_total M2( bool [:<^((F ") . f1),((F ") . c1)^>,<^(F . ((F ") . f1)),(F . ((F ") . c1))^>:])
<^(F . ((F ") . f1)),(F . ((F ") . c1))^> is set
the Arrows of A2 . ((F . ((F ") . f1)),(F . ((F ") . c1))) is set
[(F . ((F ") . f1)),(F . ((F ") . c1))] is V15() set
{(F . ((F ") . f1)),(F . ((F ") . c1))} is set
{(F . ((F ") . f1))} is set
{{(F . ((F ") . f1)),(F . ((F ") . c1))},{(F . ((F ") . f1))}} is set
the Arrows of A2 . [(F . ((F ") . f1)),(F . ((F ") . c1))] is set
[:<^((F ") . f1),((F ") . c1)^>,<^(F . ((F ") . f1)),(F . ((F ") . c1))^>:] is Relation-like set
bool [:<^((F ") . f1),((F ") . c1)^>,<^(F . ((F ") . f1)),(F . ((F ") . c1))^>:] is non empty set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the MorphMap of F . (((F ") . f1),((F ") . c1)) is Relation-like Function-like set
the MorphMap of F . [((F ") . f1),((F ") . c1)] is Relation-like Function-like set
c9 is M2(<^((F ") . f1),((F ") . c1)^>)
(Morph-Map (F,((F ") . f1),((F ") . c1))) . c9 is set
F . c9 is M2(<^(F . ((F ") . f1)),(F . ((F ") . c1))^>)
B1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A2,A1
B1 . b9 is M2(<^(B1 . f1),(B1 . c1)^>)
B1 . f1 is M2( the carrier of A1)
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
the ObjectMap of B1 . (f1,f1) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [f1,f1] is set
( the ObjectMap of B1 . (f1,f1)) `1 is set
B1 . c1 is M2( the carrier of A1)
the ObjectMap of B1 . (c1,c1) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [c1,c1] is set
( the ObjectMap of B1 . (c1,c1)) `1 is set
<^(B1 . f1),(B1 . c1)^> is set
the Arrows of A1 . ((B1 . f1),(B1 . c1)) is set
[(B1 . f1),(B1 . c1)] is V15() set
{(B1 . f1),(B1 . c1)} is set
{(B1 . f1)} is set
{{(B1 . f1),(B1 . c1)},{(B1 . f1)}} is set
the Arrows of A1 . [(B1 . f1),(B1 . c1)] is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
F " is strict FunctorStr over A2,A1
B2 is feasible id-preserving Functor of A2,A1
B2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
G is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A2
the carrier of B2 is non empty set
the carrier of A1 is non empty set
b is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of B2,G
the carrier of G is non empty set
the carrier of A2 is non empty set
b " is strict FunctorStr over G,B2
c is feasible id-preserving Functor of G,B2
b1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of G,B2
c1 is M2( the carrier of G)
b1 . c1 is M2( the carrier of B2)
[: the carrier of B2, the carrier of B2:] is Relation-like non empty set
the ObjectMap of b1 is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of B2, the carrier of B2:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of B2, the carrier of B2:]:])
[: the carrier of G, the carrier of G:] is Relation-like non empty set
[:[: the carrier of G, the carrier of G:],[: the carrier of B2, the carrier of B2:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of B2, the carrier of B2:]:] is non empty set
the ObjectMap of b1 . (c1,c1) is M2([: the carrier of B2, the carrier of B2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of b1 . [c1,c1] is set
( the ObjectMap of b1 . (c1,c1)) `1 is set
b . (b1 . c1) is M2( the carrier of G)
the ObjectMap of b is Relation-like [: the carrier of B2, the carrier of B2:] -defined [: the carrier of G, the carrier of G:] -valued Function-like quasi_total M2( bool [:[: the carrier of B2, the carrier of B2:],[: the carrier of G, the carrier of G:]:])
[:[: the carrier of B2, the carrier of B2:],[: the carrier of G, the carrier of G:]:] is Relation-like non empty set
bool [:[: the carrier of B2, the carrier of B2:],[: the carrier of G, the carrier of G:]:] is non empty set
the ObjectMap of b . ((b1 . c1),(b1 . c1)) is M2([: the carrier of G, the carrier of G:])
[(b1 . c1),(b1 . c1)] is V15() set
{(b1 . c1),(b1 . c1)} is set
{(b1 . c1)} is set
{{(b1 . c1),(b1 . c1)},{(b1 . c1)}} is set
the ObjectMap of b . [(b1 . c1),(b1 . c1)] is set
( the ObjectMap of b . ((b1 . c1),(b1 . c1))) `1 is set
f1 is M2( the carrier of A1)
F . f1 is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of F . [f1,f1] is set
( the ObjectMap of F . (f1,f1)) `1 is set
f is M2( the carrier of A2)
(F ") . f is M2( the carrier of A1)
the ObjectMap of (F ") is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:] is non empty set
the ObjectMap of (F ") . (f,f) is M2([: the carrier of A1, the carrier of A1:])
[f,f] is V15() set
{f,f} is set
{f} is set
{{f,f},{f}} is set
the ObjectMap of (F ") . [f,f] is set
( the ObjectMap of (F ") . (f,f)) `1 is set
c1 is M2( the carrier of G)
f is M2( the carrier of G)
<^c1,f^> is set
the Arrows of G is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty total set
the Arrows of G . (c1,f) is set
[c1,f] is V15() set
{c1,f} is set
{c1} is set
{{c1,f},{c1}} is set
the Arrows of G . [c1,f] is set
f1 is M2( the carrier of A2)
c1 is M2( the carrier of A2)
<^f1,c1^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{f1} is set
{{f1,c1},{f1}} is set
the Arrows of A2 . [f1,c1] is set
Morph-Map ((F "),f1,c1) is Relation-like Function-like set
the MorphMap of (F ") is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (F "), the Arrows of A2, the Arrows of A1
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the MorphMap of (F ") . (f1,c1) is Relation-like Function-like set
the MorphMap of (F ") . [f1,c1] is Relation-like Function-like set
a9 is M2(<^c1,f^>)
b1 . a9 is M2(<^(b1 . f),(b1 . c1)^>)
b1 . f is M2( the carrier of B2)
the ObjectMap of b1 . (f,f) is M2([: the carrier of B2, the carrier of B2:])
[f,f] is V15() set
{f,f} is set
{f} is set
{{f,f},{f}} is set
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
b1 . c1 is M2( the carrier of B2)
the ObjectMap of b1 . (c1,c1) is M2([: the carrier of B2, the carrier of B2:])
[c1,c1] is V15() set
{c1,c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of b1 . [c1,c1] is set
( the ObjectMap of b1 . (c1,c1)) `1 is set
<^(b1 . f),(b1 . c1)^> is set
the Arrows of B2 is Relation-like [: the carrier of B2, the carrier of B2:] -defined Function-like non empty total set
the Arrows of B2 . ((b1 . f),(b1 . c1)) is set
[(b1 . f),(b1 . c1)] is V15() set
{(b1 . f),(b1 . c1)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . c1)},{(b1 . f)}} is set
the Arrows of B2 . [(b1 . f),(b1 . c1)] is set
b9 is M2(<^f1,c1^>)
(Morph-Map ((F "),f1,c1)) . b9 is set
b . (b1 . c1) is M2( the carrier of G)
the ObjectMap of b . ((b1 . c1),(b1 . c1)) is M2([: the carrier of G, the carrier of G:])
[(b1 . c1),(b1 . c1)] is V15() set
{(b1 . c1),(b1 . c1)} is set
{(b1 . c1)} is set
{{(b1 . c1),(b1 . c1)},{(b1 . c1)}} is set
the ObjectMap of b . [(b1 . c1),(b1 . c1)] is set
( the ObjectMap of b . ((b1 . c1),(b1 . c1))) `1 is set
b . (b1 . f) is M2( the carrier of G)
the ObjectMap of b . ((b1 . f),(b1 . f)) is M2([: the carrier of G, the carrier of G:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of b . [(b1 . f),(b1 . f)] is set
( the ObjectMap of b . ((b1 . f),(b1 . f))) `1 is set
(F ") . f1 is M2( the carrier of A1)
the ObjectMap of (F ") . (f1,f1) is M2([: the carrier of A1, the carrier of A1:])
[f1,f1] is V15() set
{f1,f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of (F ") . [f1,f1] is set
( the ObjectMap of (F ") . (f1,f1)) `1 is set
F . ((F ") . f1) is M2( the carrier of A2)
the ObjectMap of F . (((F ") . f1),((F ") . f1)) is M2([: the carrier of A2, the carrier of A2:])
[((F ") . f1),((F ") . f1)] is V15() set
{((F ") . f1),((F ") . f1)} is set
{((F ") . f1)} is set
{{((F ") . f1),((F ") . f1)},{((F ") . f1)}} is set
the ObjectMap of F . [((F ") . f1),((F ") . f1)] is set
( the ObjectMap of F . (((F ") . f1),((F ") . f1))) `1 is set
(F ") . c1 is M2( the carrier of A1)
the ObjectMap of (F ") . (c1,c1) is M2([: the carrier of A1, the carrier of A1:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of (F ") . [c1,c1] is set
( the ObjectMap of (F ") . (c1,c1)) `1 is set
F . ((F ") . c1) is M2( the carrier of A2)
the ObjectMap of F . (((F ") . c1),((F ") . c1)) is M2([: the carrier of A2, the carrier of A2:])
[((F ") . c1),((F ") . c1)] is V15() set
{((F ") . c1),((F ") . c1)} is set
{((F ") . c1)} is set
{{((F ") . c1),((F ") . c1)},{((F ") . c1)}} is set
the ObjectMap of F . [((F ") . c1),((F ") . c1)] is set
( the ObjectMap of F . (((F ") . c1),((F ") . c1))) `1 is set
<^((F ") . c1),((F ") . f1)^> is set
the Arrows of A1 . (((F ") . c1),((F ") . f1)) is set
[((F ") . c1),((F ") . f1)] is V15() set
{((F ") . c1),((F ") . f1)} is set
{{((F ") . c1),((F ") . f1)},{((F ") . c1)}} is set
the Arrows of A1 . [((F ") . c1),((F ") . f1)] is set
b . (b1 . a9) is M2(<^(b . (b1 . c1)),(b . (b1 . f))^>)
<^(b . (b1 . c1)),(b . (b1 . f))^> is set
the Arrows of G . ((b . (b1 . c1)),(b . (b1 . f))) is set
[(b . (b1 . c1)),(b . (b1 . f))] is V15() set
{(b . (b1 . c1)),(b . (b1 . f))} is set
{(b . (b1 . c1))} is set
{{(b . (b1 . c1)),(b . (b1 . f))},{(b . (b1 . c1))}} is set
the Arrows of G . [(b . (b1 . c1)),(b . (b1 . f))] is set
Morph-Map (F,((F ") . c1),((F ") . f1)) is Relation-like <^((F ") . c1),((F ") . f1)^> -defined <^(F . ((F ") . f1)),(F . ((F ") . c1))^> -valued Function-like quasi_total M2( bool [:<^((F ") . c1),((F ") . f1)^>,<^(F . ((F ") . f1)),(F . ((F ") . c1))^>:])
<^(F . ((F ") . f1)),(F . ((F ") . c1))^> is set
the Arrows of A2 . ((F . ((F ") . f1)),(F . ((F ") . c1))) is set
[(F . ((F ") . f1)),(F . ((F ") . c1))] is V15() set
{(F . ((F ") . f1)),(F . ((F ") . c1))} is set
{(F . ((F ") . f1))} is set
{{(F . ((F ") . f1)),(F . ((F ") . c1))},{(F . ((F ") . f1))}} is set
the Arrows of A2 . [(F . ((F ") . f1)),(F . ((F ") . c1))] is set
[:<^((F ") . c1),((F ") . f1)^>,<^(F . ((F ") . f1)),(F . ((F ") . c1))^>:] is Relation-like set
bool [:<^((F ") . c1),((F ") . f1)^>,<^(F . ((F ") . f1)),(F . ((F ") . c1))^>:] is non empty set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the MorphMap of F . (((F ") . c1),((F ") . f1)) is Relation-like Function-like set
the MorphMap of F . [((F ") . c1),((F ") . f1)] is Relation-like Function-like set
c9 is M2(<^((F ") . c1),((F ") . f1)^>)
(Morph-Map (F,((F ") . c1),((F ") . f1))) . c9 is set
F . c9 is M2(<^(F . ((F ") . f1)),(F . ((F ") . c1))^>)
B1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A2,A1
B1 . b9 is M2(<^(B1 . c1),(B1 . f1)^>)
B1 . c1 is M2( the carrier of A1)
the ObjectMap of B1 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of A1, the carrier of A1:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of A1, the carrier of A1:]:])
the ObjectMap of B1 . (c1,c1) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [c1,c1] is set
( the ObjectMap of B1 . (c1,c1)) `1 is set
B1 . f1 is M2( the carrier of A1)
the ObjectMap of B1 . (f1,f1) is M2([: the carrier of A1, the carrier of A1:])
the ObjectMap of B1 . [f1,f1] is set
( the ObjectMap of B1 . (f1,f1)) `1 is set
<^(B1 . c1),(B1 . f1)^> is set
the Arrows of A1 . ((B1 . c1),(B1 . f1)) is set
[(B1 . c1),(B1 . f1)] is V15() set
{(B1 . c1),(B1 . f1)} is set
{(B1 . c1)} is set
{{(B1 . c1),(B1 . f1)},{(B1 . c1)}} is set
the Arrows of A1 . [(B1 . c1),(B1 . f1)] is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is non empty transitive V106() with_units reflexive AltCatStr
B1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
B2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A2,F
B2 * B1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A1,F
G is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
b is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A2
c is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of F
the carrier of G is non empty set
the carrier of A1 is non empty set
b1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of G,b
the carrier of b is non empty set
the carrier of A2 is non empty set
c1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of b,c
c1 * b1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of G,c
f is M2( the carrier of G)
f1 is M2( the carrier of A1)
b1 . f is M2( the carrier of b)
[: the carrier of b, the carrier of b:] is Relation-like non empty set
the ObjectMap of b1 is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of b, the carrier of b:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:])
[: the carrier of G, the carrier of G:] is Relation-like non empty set
[:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:] is non empty set
the ObjectMap of b1 . (f,f) is M2([: the carrier of b, the carrier of b:])
[f,f] is V15() set
{f,f} is set
{f} is set
{{f,f},{f}} is set
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
c1 . (b1 . f) is M2( the carrier of c)
the carrier of c is non empty set
[: the carrier of c, the carrier of c:] is Relation-like non empty set
the ObjectMap of c1 is Relation-like [: the carrier of b, the carrier of b:] -defined [: the carrier of c, the carrier of c:] -valued Function-like quasi_total M2( bool [:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:])
[:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:] is Relation-like non empty set
bool [:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:] is non empty set
the ObjectMap of c1 . ((b1 . f),(b1 . f)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of c1 . [(b1 . f),(b1 . f)] is set
( the ObjectMap of c1 . ((b1 . f),(b1 . f))) `1 is set
B1 . f1 is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of B1 . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of B1 . [f1,f1] is set
( the ObjectMap of B1 . (f1,f1)) `1 is set
B2 . (B1 . f1) is M2( the carrier of F)
the carrier of F is non empty set
[: the carrier of F, the carrier of F:] is Relation-like non empty set
the ObjectMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of F, the carrier of F:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:] is non empty set
the ObjectMap of B2 . ((B1 . f1),(B1 . f1)) is M2([: the carrier of F, the carrier of F:])
[(B1 . f1),(B1 . f1)] is V15() set
{(B1 . f1),(B1 . f1)} is set
{(B1 . f1)} is set
{{(B1 . f1),(B1 . f1)},{(B1 . f1)}} is set
the ObjectMap of B2 . [(B1 . f1),(B1 . f1)] is set
( the ObjectMap of B2 . ((B1 . f1),(B1 . f1))) `1 is set
(c1 * b1) . f is M2( the carrier of c)
the ObjectMap of (c1 * b1) is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of c, the carrier of c:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:])
[:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:] is non empty set
the ObjectMap of (c1 * b1) . (f,f) is M2([: the carrier of c, the carrier of c:])
the ObjectMap of (c1 * b1) . [f,f] is set
( the ObjectMap of (c1 * b1) . (f,f)) `1 is set
(B2 * B1) . f1 is M2( the carrier of F)
the ObjectMap of (B2 * B1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of F, the carrier of F:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:] is non empty set
the ObjectMap of (B2 * B1) . (f1,f1) is M2([: the carrier of F, the carrier of F:])
the ObjectMap of (B2 * B1) . [f1,f1] is set
( the ObjectMap of (B2 * B1) . (f1,f1)) `1 is set
f is M2( the carrier of G)
f1 is M2( the carrier of G)
<^f,f1^> is set
the Arrows of G is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty total set
the Arrows of G . (f,f1) is set
[f,f1] is V15() set
{f,f1} is set
{f} is set
{{f,f1},{f}} is set
the Arrows of G . [f,f1] is set
c1 is M2( the carrier of A1)
a9 is M2( the carrier of A1)
<^c1,a9^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (c1,a9) is set
[c1,a9] is V15() set
{c1,a9} is set
{c1} is set
{{c1,a9},{c1}} is set
the Arrows of A1 . [c1,a9] is set
Morph-Map ((B2 * B1),c1,a9) is Relation-like Function-like set
the MorphMap of (B2 * B1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (B2 * B1), the Arrows of A1, the Arrows of F
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like non empty total set
the MorphMap of (B2 * B1) . (c1,a9) is Relation-like Function-like set
the MorphMap of (B2 * B1) . [c1,a9] is Relation-like Function-like set
(B2 * B1) . c1 is M2( the carrier of F)
the ObjectMap of (B2 * B1) . (c1,c1) is M2([: the carrier of F, the carrier of F:])
[c1,c1] is V15() set
{c1,c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of (B2 * B1) . [c1,c1] is set
( the ObjectMap of (B2 * B1) . (c1,c1)) `1 is set
B1 . c1 is M2( the carrier of A2)
the ObjectMap of B1 . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [c1,c1] is set
( the ObjectMap of B1 . (c1,c1)) `1 is set
B2 . (B1 . c1) is M2( the carrier of F)
the ObjectMap of B2 . ((B1 . c1),(B1 . c1)) is M2([: the carrier of F, the carrier of F:])
[(B1 . c1),(B1 . c1)] is V15() set
{(B1 . c1),(B1 . c1)} is set
{(B1 . c1)} is set
{{(B1 . c1),(B1 . c1)},{(B1 . c1)}} is set
the ObjectMap of B2 . [(B1 . c1),(B1 . c1)] is set
( the ObjectMap of B2 . ((B1 . c1),(B1 . c1))) `1 is set
(B2 * B1) . a9 is M2( the carrier of F)
the ObjectMap of (B2 * B1) . (a9,a9) is M2([: the carrier of F, the carrier of F:])
[a9,a9] is V15() set
{a9,a9} is set
{a9} is set
{{a9,a9},{a9}} is set
the ObjectMap of (B2 * B1) . [a9,a9] is set
( the ObjectMap of (B2 * B1) . (a9,a9)) `1 is set
B1 . a9 is M2( the carrier of A2)
the ObjectMap of B1 . (a9,a9) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [a9,a9] is set
( the ObjectMap of B1 . (a9,a9)) `1 is set
B2 . (B1 . a9) is M2( the carrier of F)
the ObjectMap of B2 . ((B1 . a9),(B1 . a9)) is M2([: the carrier of F, the carrier of F:])
[(B1 . a9),(B1 . a9)] is V15() set
{(B1 . a9),(B1 . a9)} is set
{(B1 . a9)} is set
{{(B1 . a9),(B1 . a9)},{(B1 . a9)}} is set
the ObjectMap of B2 . [(B1 . a9),(B1 . a9)] is set
( the ObjectMap of B2 . ((B1 . a9),(B1 . a9))) `1 is set
b9 is M2(<^f,f1^>)
(c1 * b1) . b9 is M2(<^((c1 * b1) . f),((c1 * b1) . f1)^>)
(c1 * b1) . f is M2( the carrier of c)
the ObjectMap of (c1 * b1) . (f,f) is M2([: the carrier of c, the carrier of c:])
[f,f] is V15() set
{f,f} is set
{{f,f},{f}} is set
the ObjectMap of (c1 * b1) . [f,f] is set
( the ObjectMap of (c1 * b1) . (f,f)) `1 is set
(c1 * b1) . f1 is M2( the carrier of c)
the ObjectMap of (c1 * b1) . (f1,f1) is M2([: the carrier of c, the carrier of c:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of (c1 * b1) . [f1,f1] is set
( the ObjectMap of (c1 * b1) . (f1,f1)) `1 is set
<^((c1 * b1) . f),((c1 * b1) . f1)^> is set
the Arrows of c is Relation-like [: the carrier of c, the carrier of c:] -defined Function-like non empty total set
the Arrows of c . (((c1 * b1) . f),((c1 * b1) . f1)) is set
[((c1 * b1) . f),((c1 * b1) . f1)] is V15() set
{((c1 * b1) . f),((c1 * b1) . f1)} is set
{((c1 * b1) . f)} is set
{{((c1 * b1) . f),((c1 * b1) . f1)},{((c1 * b1) . f)}} is set
the Arrows of c . [((c1 * b1) . f),((c1 * b1) . f1)] is set
c9 is M2(<^c1,a9^>)
(Morph-Map ((B2 * B1),c1,a9)) . c9 is set
<^((B2 * B1) . c1),((B2 * B1) . a9)^> is set
the Arrows of F . (((B2 * B1) . c1),((B2 * B1) . a9)) is set
[((B2 * B1) . c1),((B2 * B1) . a9)] is V15() set
{((B2 * B1) . c1),((B2 * B1) . a9)} is set
{((B2 * B1) . c1)} is set
{{((B2 * B1) . c1),((B2 * B1) . a9)},{((B2 * B1) . c1)}} is set
the Arrows of F . [((B2 * B1) . c1),((B2 * B1) . a9)] is set
b1 . f is M2( the carrier of b)
the ObjectMap of b1 . (f,f) is M2([: the carrier of b, the carrier of b:])
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
b1 . f1 is M2( the carrier of b)
the ObjectMap of b1 . (f1,f1) is M2([: the carrier of b, the carrier of b:])
the ObjectMap of b1 . [f1,f1] is set
( the ObjectMap of b1 . (f1,f1)) `1 is set
<^(b1 . f),(b1 . f1)^> is set
the Arrows of b is Relation-like [: the carrier of b, the carrier of b:] -defined Function-like non empty total set
the Arrows of b . ((b1 . f),(b1 . f1)) is set
[(b1 . f),(b1 . f1)] is V15() set
{(b1 . f),(b1 . f1)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f1)},{(b1 . f)}} is set
the Arrows of b . [(b1 . f),(b1 . f1)] is set
b1 . b9 is M2(<^(b1 . f),(b1 . f1)^>)
<^(B1 . c1),(B1 . a9)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((B1 . c1),(B1 . a9)) is set
[(B1 . c1),(B1 . a9)] is V15() set
{(B1 . c1),(B1 . a9)} is set
{{(B1 . c1),(B1 . a9)},{(B1 . c1)}} is set
the Arrows of A2 . [(B1 . c1),(B1 . a9)] is set
Morph-Map (B1,c1,a9) is Relation-like <^c1,a9^> -defined <^(B1 . c1),(B1 . a9)^> -valued Function-like quasi_total M2( bool [:<^c1,a9^>,<^(B1 . c1),(B1 . a9)^>:])
[:<^c1,a9^>,<^(B1 . c1),(B1 . a9)^>:] is Relation-like set
bool [:<^c1,a9^>,<^(B1 . c1),(B1 . a9)^>:] is non empty set
the MorphMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A1, the Arrows of A2
the MorphMap of B1 . (c1,a9) is Relation-like Function-like set
the MorphMap of B1 . [c1,a9] is Relation-like Function-like set
(Morph-Map (B1,c1,a9)) . c9 is set
B1 . c9 is M2(<^(B1 . c1),(B1 . a9)^>)
c1 . (b1 . b9) is M2(<^(c1 . (b1 . f)),(c1 . (b1 . f1))^>)
c1 . (b1 . f) is M2( the carrier of c)
the ObjectMap of c1 . ((b1 . f),(b1 . f)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of c1 . [(b1 . f),(b1 . f)] is set
( the ObjectMap of c1 . ((b1 . f),(b1 . f))) `1 is set
c1 . (b1 . f1) is M2( the carrier of c)
the ObjectMap of c1 . ((b1 . f1),(b1 . f1)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f1),(b1 . f1)] is V15() set
{(b1 . f1),(b1 . f1)} is set
{(b1 . f1)} is set
{{(b1 . f1),(b1 . f1)},{(b1 . f1)}} is set
the ObjectMap of c1 . [(b1 . f1),(b1 . f1)] is set
( the ObjectMap of c1 . ((b1 . f1),(b1 . f1))) `1 is set
<^(c1 . (b1 . f)),(c1 . (b1 . f1))^> is set
the Arrows of c . ((c1 . (b1 . f)),(c1 . (b1 . f1))) is set
[(c1 . (b1 . f)),(c1 . (b1 . f1))] is V15() set
{(c1 . (b1 . f)),(c1 . (b1 . f1))} is set
{(c1 . (b1 . f))} is set
{{(c1 . (b1 . f)),(c1 . (b1 . f1))},{(c1 . (b1 . f))}} is set
the Arrows of c . [(c1 . (b1 . f)),(c1 . (b1 . f1))] is set
Morph-Map (B2,(B1 . c1),(B1 . a9)) is Relation-like <^(B1 . c1),(B1 . a9)^> -defined <^(B2 . (B1 . c1)),(B2 . (B1 . a9))^> -valued Function-like quasi_total M2( bool [:<^(B1 . c1),(B1 . a9)^>,<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^>:])
<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^> is set
the Arrows of F . ((B2 . (B1 . c1)),(B2 . (B1 . a9))) is set
[(B2 . (B1 . c1)),(B2 . (B1 . a9))] is V15() set
{(B2 . (B1 . c1)),(B2 . (B1 . a9))} is set
{(B2 . (B1 . c1))} is set
{{(B2 . (B1 . c1)),(B2 . (B1 . a9))},{(B2 . (B1 . c1))}} is set
the Arrows of F . [(B2 . (B1 . c1)),(B2 . (B1 . a9))] is set
[:<^(B1 . c1),(B1 . a9)^>,<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^>:] is Relation-like set
bool [:<^(B1 . c1),(B1 . a9)^>,<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^>:] is non empty set
the MorphMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B2, the Arrows of A2, the Arrows of F
the MorphMap of B2 . ((B1 . c1),(B1 . a9)) is Relation-like Function-like set
the MorphMap of B2 . [(B1 . c1),(B1 . a9)] is Relation-like Function-like set
(Morph-Map (B2,(B1 . c1),(B1 . a9))) . (B1 . c9) is set
B2 . (B1 . c9) is M2(<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^>)
(B2 * B1) . c9 is M2(<^((B2 * B1) . c1),((B2 * B1) . a9)^>)
Morph-Map ((B2 * B1),c1,a9) is Relation-like <^c1,a9^> -defined <^((B2 * B1) . c1),((B2 * B1) . a9)^> -valued Function-like quasi_total M2( bool [:<^c1,a9^>,<^((B2 * B1) . c1),((B2 * B1) . a9)^>:])
[:<^c1,a9^>,<^((B2 * B1) . c1),((B2 * B1) . a9)^>:] is Relation-like set
bool [:<^c1,a9^>,<^((B2 * B1) . c1),((B2 * B1) . a9)^>:] is non empty set
(Morph-Map ((B2 * B1),c1,a9)) . c9 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is non empty transitive V106() with_units reflexive AltCatStr
B1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
B2 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A2,F
B2 * B1 is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A1,F
G is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
b is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A2
c is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of F
the carrier of G is non empty set
the carrier of A1 is non empty set
b1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of G,b
the carrier of b is non empty set
the carrier of A2 is non empty set
c1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of b,c
c1 * b1 is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of G,c
f is M2( the carrier of G)
f1 is M2( the carrier of A1)
b1 . f is M2( the carrier of b)
[: the carrier of b, the carrier of b:] is Relation-like non empty set
the ObjectMap of b1 is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of b, the carrier of b:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:])
[: the carrier of G, the carrier of G:] is Relation-like non empty set
[:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:] is non empty set
the ObjectMap of b1 . (f,f) is M2([: the carrier of b, the carrier of b:])
[f,f] is V15() set
{f,f} is set
{f} is set
{{f,f},{f}} is set
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
c1 . (b1 . f) is M2( the carrier of c)
the carrier of c is non empty set
[: the carrier of c, the carrier of c:] is Relation-like non empty set
the ObjectMap of c1 is Relation-like [: the carrier of b, the carrier of b:] -defined [: the carrier of c, the carrier of c:] -valued Function-like quasi_total M2( bool [:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:])
[:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:] is Relation-like non empty set
bool [:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:] is non empty set
the ObjectMap of c1 . ((b1 . f),(b1 . f)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of c1 . [(b1 . f),(b1 . f)] is set
( the ObjectMap of c1 . ((b1 . f),(b1 . f))) `1 is set
B1 . f1 is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of B1 . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of B1 . [f1,f1] is set
( the ObjectMap of B1 . (f1,f1)) `1 is set
B2 . (B1 . f1) is M2( the carrier of F)
the carrier of F is non empty set
[: the carrier of F, the carrier of F:] is Relation-like non empty set
the ObjectMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of F, the carrier of F:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:] is non empty set
the ObjectMap of B2 . ((B1 . f1),(B1 . f1)) is M2([: the carrier of F, the carrier of F:])
[(B1 . f1),(B1 . f1)] is V15() set
{(B1 . f1),(B1 . f1)} is set
{(B1 . f1)} is set
{{(B1 . f1),(B1 . f1)},{(B1 . f1)}} is set
the ObjectMap of B2 . [(B1 . f1),(B1 . f1)] is set
( the ObjectMap of B2 . ((B1 . f1),(B1 . f1))) `1 is set
(c1 * b1) . f is M2( the carrier of c)
the ObjectMap of (c1 * b1) is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of c, the carrier of c:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:])
[:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:] is non empty set
the ObjectMap of (c1 * b1) . (f,f) is M2([: the carrier of c, the carrier of c:])
the ObjectMap of (c1 * b1) . [f,f] is set
( the ObjectMap of (c1 * b1) . (f,f)) `1 is set
(B2 * B1) . f1 is M2( the carrier of F)
the ObjectMap of (B2 * B1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of F, the carrier of F:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:] is non empty set
the ObjectMap of (B2 * B1) . (f1,f1) is M2([: the carrier of F, the carrier of F:])
the ObjectMap of (B2 * B1) . [f1,f1] is set
( the ObjectMap of (B2 * B1) . (f1,f1)) `1 is set
f is M2( the carrier of G)
f1 is M2( the carrier of G)
<^f,f1^> is set
the Arrows of G is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty total set
the Arrows of G . (f,f1) is set
[f,f1] is V15() set
{f,f1} is set
{f} is set
{{f,f1},{f}} is set
the Arrows of G . [f,f1] is set
c1 is M2( the carrier of A1)
a9 is M2( the carrier of A1)
<^c1,a9^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (c1,a9) is set
[c1,a9] is V15() set
{c1,a9} is set
{c1} is set
{{c1,a9},{c1}} is set
the Arrows of A1 . [c1,a9] is set
Morph-Map ((B2 * B1),c1,a9) is Relation-like Function-like set
the MorphMap of (B2 * B1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (B2 * B1), the Arrows of A1, the Arrows of F
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like non empty total set
the MorphMap of (B2 * B1) . (c1,a9) is Relation-like Function-like set
the MorphMap of (B2 * B1) . [c1,a9] is Relation-like Function-like set
(B2 * B1) . c1 is M2( the carrier of F)
the ObjectMap of (B2 * B1) . (c1,c1) is M2([: the carrier of F, the carrier of F:])
[c1,c1] is V15() set
{c1,c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of (B2 * B1) . [c1,c1] is set
( the ObjectMap of (B2 * B1) . (c1,c1)) `1 is set
B1 . c1 is M2( the carrier of A2)
the ObjectMap of B1 . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [c1,c1] is set
( the ObjectMap of B1 . (c1,c1)) `1 is set
B2 . (B1 . c1) is M2( the carrier of F)
the ObjectMap of B2 . ((B1 . c1),(B1 . c1)) is M2([: the carrier of F, the carrier of F:])
[(B1 . c1),(B1 . c1)] is V15() set
{(B1 . c1),(B1 . c1)} is set
{(B1 . c1)} is set
{{(B1 . c1),(B1 . c1)},{(B1 . c1)}} is set
the ObjectMap of B2 . [(B1 . c1),(B1 . c1)] is set
( the ObjectMap of B2 . ((B1 . c1),(B1 . c1))) `1 is set
(B2 * B1) . a9 is M2( the carrier of F)
the ObjectMap of (B2 * B1) . (a9,a9) is M2([: the carrier of F, the carrier of F:])
[a9,a9] is V15() set
{a9,a9} is set
{a9} is set
{{a9,a9},{a9}} is set
the ObjectMap of (B2 * B1) . [a9,a9] is set
( the ObjectMap of (B2 * B1) . (a9,a9)) `1 is set
B1 . a9 is M2( the carrier of A2)
the ObjectMap of B1 . (a9,a9) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [a9,a9] is set
( the ObjectMap of B1 . (a9,a9)) `1 is set
B2 . (B1 . a9) is M2( the carrier of F)
the ObjectMap of B2 . ((B1 . a9),(B1 . a9)) is M2([: the carrier of F, the carrier of F:])
[(B1 . a9),(B1 . a9)] is V15() set
{(B1 . a9),(B1 . a9)} is set
{(B1 . a9)} is set
{{(B1 . a9),(B1 . a9)},{(B1 . a9)}} is set
the ObjectMap of B2 . [(B1 . a9),(B1 . a9)] is set
( the ObjectMap of B2 . ((B1 . a9),(B1 . a9))) `1 is set
b9 is M2(<^f,f1^>)
(c1 * b1) . b9 is M2(<^((c1 * b1) . f1),((c1 * b1) . f)^>)
(c1 * b1) . f1 is M2( the carrier of c)
the ObjectMap of (c1 * b1) . (f1,f1) is M2([: the carrier of c, the carrier of c:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of (c1 * b1) . [f1,f1] is set
( the ObjectMap of (c1 * b1) . (f1,f1)) `1 is set
(c1 * b1) . f is M2( the carrier of c)
the ObjectMap of (c1 * b1) . (f,f) is M2([: the carrier of c, the carrier of c:])
[f,f] is V15() set
{f,f} is set
{{f,f},{f}} is set
the ObjectMap of (c1 * b1) . [f,f] is set
( the ObjectMap of (c1 * b1) . (f,f)) `1 is set
<^((c1 * b1) . f1),((c1 * b1) . f)^> is set
the Arrows of c is Relation-like [: the carrier of c, the carrier of c:] -defined Function-like non empty total set
the Arrows of c . (((c1 * b1) . f1),((c1 * b1) . f)) is set
[((c1 * b1) . f1),((c1 * b1) . f)] is V15() set
{((c1 * b1) . f1),((c1 * b1) . f)} is set
{((c1 * b1) . f1)} is set
{{((c1 * b1) . f1),((c1 * b1) . f)},{((c1 * b1) . f1)}} is set
the Arrows of c . [((c1 * b1) . f1),((c1 * b1) . f)] is set
c9 is M2(<^c1,a9^>)
(Morph-Map ((B2 * B1),c1,a9)) . c9 is set
<^((B2 * B1) . a9),((B2 * B1) . c1)^> is set
the Arrows of F . (((B2 * B1) . a9),((B2 * B1) . c1)) is set
[((B2 * B1) . a9),((B2 * B1) . c1)] is V15() set
{((B2 * B1) . a9),((B2 * B1) . c1)} is set
{((B2 * B1) . a9)} is set
{{((B2 * B1) . a9),((B2 * B1) . c1)},{((B2 * B1) . a9)}} is set
the Arrows of F . [((B2 * B1) . a9),((B2 * B1) . c1)] is set
b1 . f1 is M2( the carrier of b)
the ObjectMap of b1 . (f1,f1) is M2([: the carrier of b, the carrier of b:])
the ObjectMap of b1 . [f1,f1] is set
( the ObjectMap of b1 . (f1,f1)) `1 is set
b1 . f is M2( the carrier of b)
the ObjectMap of b1 . (f,f) is M2([: the carrier of b, the carrier of b:])
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
<^(b1 . f1),(b1 . f)^> is set
the Arrows of b is Relation-like [: the carrier of b, the carrier of b:] -defined Function-like non empty total set
the Arrows of b . ((b1 . f1),(b1 . f)) is set
[(b1 . f1),(b1 . f)] is V15() set
{(b1 . f1),(b1 . f)} is set
{(b1 . f1)} is set
{{(b1 . f1),(b1 . f)},{(b1 . f1)}} is set
the Arrows of b . [(b1 . f1),(b1 . f)] is set
b1 . b9 is M2(<^(b1 . f1),(b1 . f)^>)
<^(B1 . a9),(B1 . c1)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((B1 . a9),(B1 . c1)) is set
[(B1 . a9),(B1 . c1)] is V15() set
{(B1 . a9),(B1 . c1)} is set
{{(B1 . a9),(B1 . c1)},{(B1 . a9)}} is set
the Arrows of A2 . [(B1 . a9),(B1 . c1)] is set
Morph-Map (B1,c1,a9) is Relation-like <^c1,a9^> -defined <^(B1 . a9),(B1 . c1)^> -valued Function-like quasi_total M2( bool [:<^c1,a9^>,<^(B1 . a9),(B1 . c1)^>:])
[:<^c1,a9^>,<^(B1 . a9),(B1 . c1)^>:] is Relation-like set
bool [:<^c1,a9^>,<^(B1 . a9),(B1 . c1)^>:] is non empty set
the MorphMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A1, the Arrows of A2
the MorphMap of B1 . (c1,a9) is Relation-like Function-like set
the MorphMap of B1 . [c1,a9] is Relation-like Function-like set
(Morph-Map (B1,c1,a9)) . c9 is set
B1 . c9 is M2(<^(B1 . a9),(B1 . c1)^>)
c1 . (b1 . b9) is M2(<^(c1 . (b1 . f1)),(c1 . (b1 . f))^>)
c1 . (b1 . f1) is M2( the carrier of c)
the ObjectMap of c1 . ((b1 . f1),(b1 . f1)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f1),(b1 . f1)] is V15() set
{(b1 . f1),(b1 . f1)} is set
{{(b1 . f1),(b1 . f1)},{(b1 . f1)}} is set
the ObjectMap of c1 . [(b1 . f1),(b1 . f1)] is set
( the ObjectMap of c1 . ((b1 . f1),(b1 . f1))) `1 is set
c1 . (b1 . f) is M2( the carrier of c)
the ObjectMap of c1 . ((b1 . f),(b1 . f)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of c1 . [(b1 . f),(b1 . f)] is set
( the ObjectMap of c1 . ((b1 . f),(b1 . f))) `1 is set
<^(c1 . (b1 . f1)),(c1 . (b1 . f))^> is set
the Arrows of c . ((c1 . (b1 . f1)),(c1 . (b1 . f))) is set
[(c1 . (b1 . f1)),(c1 . (b1 . f))] is V15() set
{(c1 . (b1 . f1)),(c1 . (b1 . f))} is set
{(c1 . (b1 . f1))} is set
{{(c1 . (b1 . f1)),(c1 . (b1 . f))},{(c1 . (b1 . f1))}} is set
the Arrows of c . [(c1 . (b1 . f1)),(c1 . (b1 . f))] is set
Morph-Map (B2,(B1 . a9),(B1 . c1)) is Relation-like <^(B1 . a9),(B1 . c1)^> -defined <^(B2 . (B1 . a9)),(B2 . (B1 . c1))^> -valued Function-like quasi_total M2( bool [:<^(B1 . a9),(B1 . c1)^>,<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^>:])
<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^> is set
the Arrows of F . ((B2 . (B1 . a9)),(B2 . (B1 . c1))) is set
[(B2 . (B1 . a9)),(B2 . (B1 . c1))] is V15() set
{(B2 . (B1 . a9)),(B2 . (B1 . c1))} is set
{(B2 . (B1 . a9))} is set
{{(B2 . (B1 . a9)),(B2 . (B1 . c1))},{(B2 . (B1 . a9))}} is set
the Arrows of F . [(B2 . (B1 . a9)),(B2 . (B1 . c1))] is set
[:<^(B1 . a9),(B1 . c1)^>,<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^>:] is Relation-like set
bool [:<^(B1 . a9),(B1 . c1)^>,<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^>:] is non empty set
the MorphMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B2, the Arrows of A2, the Arrows of F
the MorphMap of B2 . ((B1 . a9),(B1 . c1)) is Relation-like Function-like set
the MorphMap of B2 . [(B1 . a9),(B1 . c1)] is Relation-like Function-like set
(Morph-Map (B2,(B1 . a9),(B1 . c1))) . (B1 . c9) is set
B2 . (B1 . c9) is M2(<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^>)
(B2 * B1) . c9 is M2(<^((B2 * B1) . a9),((B2 * B1) . c1)^>)
Morph-Map ((B2 * B1),c1,a9) is Relation-like <^c1,a9^> -defined <^((B2 * B1) . a9),((B2 * B1) . c1)^> -valued Function-like quasi_total M2( bool [:<^c1,a9^>,<^((B2 * B1) . a9),((B2 * B1) . c1)^>:])
[:<^c1,a9^>,<^((B2 * B1) . a9),((B2 * B1) . c1)^>:] is Relation-like set
bool [:<^c1,a9^>,<^((B2 * B1) . a9),((B2 * B1) . c1)^>:] is non empty set
(Morph-Map ((B2 * B1),c1,a9)) . c9 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is non empty transitive V106() with_units reflexive AltCatStr
B1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
B2 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A2,F
B2 * B1 is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A1,F
G is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
b is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A2
c is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of F
the carrier of G is non empty set
the carrier of A1 is non empty set
b1 is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of G,b
the carrier of b is non empty set
the carrier of A2 is non empty set
c1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of b,c
c1 * b1 is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of G,c
f is M2( the carrier of G)
f1 is M2( the carrier of A1)
b1 . f is M2( the carrier of b)
[: the carrier of b, the carrier of b:] is Relation-like non empty set
the ObjectMap of b1 is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of b, the carrier of b:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:])
[: the carrier of G, the carrier of G:] is Relation-like non empty set
[:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:] is non empty set
the ObjectMap of b1 . (f,f) is M2([: the carrier of b, the carrier of b:])
[f,f] is V15() set
{f,f} is set
{f} is set
{{f,f},{f}} is set
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
c1 . (b1 . f) is M2( the carrier of c)
the carrier of c is non empty set
[: the carrier of c, the carrier of c:] is Relation-like non empty set
the ObjectMap of c1 is Relation-like [: the carrier of b, the carrier of b:] -defined [: the carrier of c, the carrier of c:] -valued Function-like quasi_total M2( bool [:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:])
[:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:] is Relation-like non empty set
bool [:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:] is non empty set
the ObjectMap of c1 . ((b1 . f),(b1 . f)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of c1 . [(b1 . f),(b1 . f)] is set
( the ObjectMap of c1 . ((b1 . f),(b1 . f))) `1 is set
B1 . f1 is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of B1 . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of B1 . [f1,f1] is set
( the ObjectMap of B1 . (f1,f1)) `1 is set
B2 . (B1 . f1) is M2( the carrier of F)
the carrier of F is non empty set
[: the carrier of F, the carrier of F:] is Relation-like non empty set
the ObjectMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of F, the carrier of F:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:] is non empty set
the ObjectMap of B2 . ((B1 . f1),(B1 . f1)) is M2([: the carrier of F, the carrier of F:])
[(B1 . f1),(B1 . f1)] is V15() set
{(B1 . f1),(B1 . f1)} is set
{(B1 . f1)} is set
{{(B1 . f1),(B1 . f1)},{(B1 . f1)}} is set
the ObjectMap of B2 . [(B1 . f1),(B1 . f1)] is set
( the ObjectMap of B2 . ((B1 . f1),(B1 . f1))) `1 is set
(c1 * b1) . f is M2( the carrier of c)
the ObjectMap of (c1 * b1) is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of c, the carrier of c:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:])
[:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:] is non empty set
the ObjectMap of (c1 * b1) . (f,f) is M2([: the carrier of c, the carrier of c:])
the ObjectMap of (c1 * b1) . [f,f] is set
( the ObjectMap of (c1 * b1) . (f,f)) `1 is set
(B2 * B1) . f1 is M2( the carrier of F)
the ObjectMap of (B2 * B1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of F, the carrier of F:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:] is non empty set
the ObjectMap of (B2 * B1) . (f1,f1) is M2([: the carrier of F, the carrier of F:])
the ObjectMap of (B2 * B1) . [f1,f1] is set
( the ObjectMap of (B2 * B1) . (f1,f1)) `1 is set
f is M2( the carrier of G)
f1 is M2( the carrier of G)
<^f,f1^> is set
the Arrows of G is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty total set
the Arrows of G . (f,f1) is set
[f,f1] is V15() set
{f,f1} is set
{f} is set
{{f,f1},{f}} is set
the Arrows of G . [f,f1] is set
c1 is M2( the carrier of A1)
a9 is M2( the carrier of A1)
<^c1,a9^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (c1,a9) is set
[c1,a9] is V15() set
{c1,a9} is set
{c1} is set
{{c1,a9},{c1}} is set
the Arrows of A1 . [c1,a9] is set
Morph-Map ((B2 * B1),c1,a9) is Relation-like Function-like set
the MorphMap of (B2 * B1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (B2 * B1), the Arrows of A1, the Arrows of F
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like non empty total set
the MorphMap of (B2 * B1) . (c1,a9) is Relation-like Function-like set
the MorphMap of (B2 * B1) . [c1,a9] is Relation-like Function-like set
(B2 * B1) . c1 is M2( the carrier of F)
the ObjectMap of (B2 * B1) . (c1,c1) is M2([: the carrier of F, the carrier of F:])
[c1,c1] is V15() set
{c1,c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of (B2 * B1) . [c1,c1] is set
( the ObjectMap of (B2 * B1) . (c1,c1)) `1 is set
B1 . c1 is M2( the carrier of A2)
the ObjectMap of B1 . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [c1,c1] is set
( the ObjectMap of B1 . (c1,c1)) `1 is set
B2 . (B1 . c1) is M2( the carrier of F)
the ObjectMap of B2 . ((B1 . c1),(B1 . c1)) is M2([: the carrier of F, the carrier of F:])
[(B1 . c1),(B1 . c1)] is V15() set
{(B1 . c1),(B1 . c1)} is set
{(B1 . c1)} is set
{{(B1 . c1),(B1 . c1)},{(B1 . c1)}} is set
the ObjectMap of B2 . [(B1 . c1),(B1 . c1)] is set
( the ObjectMap of B2 . ((B1 . c1),(B1 . c1))) `1 is set
(B2 * B1) . a9 is M2( the carrier of F)
the ObjectMap of (B2 * B1) . (a9,a9) is M2([: the carrier of F, the carrier of F:])
[a9,a9] is V15() set
{a9,a9} is set
{a9} is set
{{a9,a9},{a9}} is set
the ObjectMap of (B2 * B1) . [a9,a9] is set
( the ObjectMap of (B2 * B1) . (a9,a9)) `1 is set
B1 . a9 is M2( the carrier of A2)
the ObjectMap of B1 . (a9,a9) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [a9,a9] is set
( the ObjectMap of B1 . (a9,a9)) `1 is set
B2 . (B1 . a9) is M2( the carrier of F)
the ObjectMap of B2 . ((B1 . a9),(B1 . a9)) is M2([: the carrier of F, the carrier of F:])
[(B1 . a9),(B1 . a9)] is V15() set
{(B1 . a9),(B1 . a9)} is set
{(B1 . a9)} is set
{{(B1 . a9),(B1 . a9)},{(B1 . a9)}} is set
the ObjectMap of B2 . [(B1 . a9),(B1 . a9)] is set
( the ObjectMap of B2 . ((B1 . a9),(B1 . a9))) `1 is set
b9 is M2(<^f,f1^>)
(c1 * b1) . b9 is M2(<^((c1 * b1) . f1),((c1 * b1) . f)^>)
(c1 * b1) . f1 is M2( the carrier of c)
the ObjectMap of (c1 * b1) . (f1,f1) is M2([: the carrier of c, the carrier of c:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of (c1 * b1) . [f1,f1] is set
( the ObjectMap of (c1 * b1) . (f1,f1)) `1 is set
(c1 * b1) . f is M2( the carrier of c)
the ObjectMap of (c1 * b1) . (f,f) is M2([: the carrier of c, the carrier of c:])
[f,f] is V15() set
{f,f} is set
{{f,f},{f}} is set
the ObjectMap of (c1 * b1) . [f,f] is set
( the ObjectMap of (c1 * b1) . (f,f)) `1 is set
<^((c1 * b1) . f1),((c1 * b1) . f)^> is set
the Arrows of c is Relation-like [: the carrier of c, the carrier of c:] -defined Function-like non empty total set
the Arrows of c . (((c1 * b1) . f1),((c1 * b1) . f)) is set
[((c1 * b1) . f1),((c1 * b1) . f)] is V15() set
{((c1 * b1) . f1),((c1 * b1) . f)} is set
{((c1 * b1) . f1)} is set
{{((c1 * b1) . f1),((c1 * b1) . f)},{((c1 * b1) . f1)}} is set
the Arrows of c . [((c1 * b1) . f1),((c1 * b1) . f)] is set
c9 is M2(<^c1,a9^>)
(Morph-Map ((B2 * B1),c1,a9)) . c9 is set
<^((B2 * B1) . a9),((B2 * B1) . c1)^> is set
the Arrows of F . (((B2 * B1) . a9),((B2 * B1) . c1)) is set
[((B2 * B1) . a9),((B2 * B1) . c1)] is V15() set
{((B2 * B1) . a9),((B2 * B1) . c1)} is set
{((B2 * B1) . a9)} is set
{{((B2 * B1) . a9),((B2 * B1) . c1)},{((B2 * B1) . a9)}} is set
the Arrows of F . [((B2 * B1) . a9),((B2 * B1) . c1)] is set
b1 . f is M2( the carrier of b)
the ObjectMap of b1 . (f,f) is M2([: the carrier of b, the carrier of b:])
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
b1 . f1 is M2( the carrier of b)
the ObjectMap of b1 . (f1,f1) is M2([: the carrier of b, the carrier of b:])
the ObjectMap of b1 . [f1,f1] is set
( the ObjectMap of b1 . (f1,f1)) `1 is set
<^(b1 . f),(b1 . f1)^> is set
the Arrows of b is Relation-like [: the carrier of b, the carrier of b:] -defined Function-like non empty total set
the Arrows of b . ((b1 . f),(b1 . f1)) is set
[(b1 . f),(b1 . f1)] is V15() set
{(b1 . f),(b1 . f1)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f1)},{(b1 . f)}} is set
the Arrows of b . [(b1 . f),(b1 . f1)] is set
b1 . b9 is M2(<^(b1 . f),(b1 . f1)^>)
<^(B1 . c1),(B1 . a9)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((B1 . c1),(B1 . a9)) is set
[(B1 . c1),(B1 . a9)] is V15() set
{(B1 . c1),(B1 . a9)} is set
{{(B1 . c1),(B1 . a9)},{(B1 . c1)}} is set
the Arrows of A2 . [(B1 . c1),(B1 . a9)] is set
Morph-Map (B1,c1,a9) is Relation-like <^c1,a9^> -defined <^(B1 . c1),(B1 . a9)^> -valued Function-like quasi_total M2( bool [:<^c1,a9^>,<^(B1 . c1),(B1 . a9)^>:])
[:<^c1,a9^>,<^(B1 . c1),(B1 . a9)^>:] is Relation-like set
bool [:<^c1,a9^>,<^(B1 . c1),(B1 . a9)^>:] is non empty set
the MorphMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A1, the Arrows of A2
the MorphMap of B1 . (c1,a9) is Relation-like Function-like set
the MorphMap of B1 . [c1,a9] is Relation-like Function-like set
(Morph-Map (B1,c1,a9)) . c9 is set
B1 . c9 is M2(<^(B1 . c1),(B1 . a9)^>)
c1 . (b1 . b9) is M2(<^(c1 . (b1 . f1)),(c1 . (b1 . f))^>)
c1 . (b1 . f1) is M2( the carrier of c)
the ObjectMap of c1 . ((b1 . f1),(b1 . f1)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f1),(b1 . f1)] is V15() set
{(b1 . f1),(b1 . f1)} is set
{(b1 . f1)} is set
{{(b1 . f1),(b1 . f1)},{(b1 . f1)}} is set
the ObjectMap of c1 . [(b1 . f1),(b1 . f1)] is set
( the ObjectMap of c1 . ((b1 . f1),(b1 . f1))) `1 is set
c1 . (b1 . f) is M2( the carrier of c)
the ObjectMap of c1 . ((b1 . f),(b1 . f)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of c1 . [(b1 . f),(b1 . f)] is set
( the ObjectMap of c1 . ((b1 . f),(b1 . f))) `1 is set
<^(c1 . (b1 . f1)),(c1 . (b1 . f))^> is set
the Arrows of c . ((c1 . (b1 . f1)),(c1 . (b1 . f))) is set
[(c1 . (b1 . f1)),(c1 . (b1 . f))] is V15() set
{(c1 . (b1 . f1)),(c1 . (b1 . f))} is set
{(c1 . (b1 . f1))} is set
{{(c1 . (b1 . f1)),(c1 . (b1 . f))},{(c1 . (b1 . f1))}} is set
the Arrows of c . [(c1 . (b1 . f1)),(c1 . (b1 . f))] is set
Morph-Map (B2,(B1 . c1),(B1 . a9)) is Relation-like <^(B1 . c1),(B1 . a9)^> -defined <^(B2 . (B1 . a9)),(B2 . (B1 . c1))^> -valued Function-like quasi_total M2( bool [:<^(B1 . c1),(B1 . a9)^>,<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^>:])
<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^> is set
the Arrows of F . ((B2 . (B1 . a9)),(B2 . (B1 . c1))) is set
[(B2 . (B1 . a9)),(B2 . (B1 . c1))] is V15() set
{(B2 . (B1 . a9)),(B2 . (B1 . c1))} is set
{(B2 . (B1 . a9))} is set
{{(B2 . (B1 . a9)),(B2 . (B1 . c1))},{(B2 . (B1 . a9))}} is set
the Arrows of F . [(B2 . (B1 . a9)),(B2 . (B1 . c1))] is set
[:<^(B1 . c1),(B1 . a9)^>,<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^>:] is Relation-like set
bool [:<^(B1 . c1),(B1 . a9)^>,<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^>:] is non empty set
the MorphMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B2, the Arrows of A2, the Arrows of F
the MorphMap of B2 . ((B1 . c1),(B1 . a9)) is Relation-like Function-like set
the MorphMap of B2 . [(B1 . c1),(B1 . a9)] is Relation-like Function-like set
(Morph-Map (B2,(B1 . c1),(B1 . a9))) . (B1 . c9) is set
B2 . (B1 . c9) is M2(<^(B2 . (B1 . a9)),(B2 . (B1 . c1))^>)
(B2 * B1) . c9 is M2(<^((B2 * B1) . a9),((B2 * B1) . c1)^>)
Morph-Map ((B2 * B1),c1,a9) is Relation-like <^c1,a9^> -defined <^((B2 * B1) . a9),((B2 * B1) . c1)^> -valued Function-like quasi_total M2( bool [:<^c1,a9^>,<^((B2 * B1) . a9),((B2 * B1) . c1)^>:])
[:<^c1,a9^>,<^((B2 * B1) . a9),((B2 * B1) . c1)^>:] is Relation-like set
bool [:<^c1,a9^>,<^((B2 * B1) . a9),((B2 * B1) . c1)^>:] is non empty set
(Morph-Map ((B2 * B1),c1,a9)) . c9 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
F is non empty transitive V106() with_units reflexive AltCatStr
B1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
B2 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A2,F
B2 * B1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A1,F
G is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
b is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A2
c is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of F
the carrier of G is non empty set
the carrier of A1 is non empty set
b1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of G,b
the carrier of b is non empty set
the carrier of A2 is non empty set
c1 is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of b,c
c1 * b1 is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of G,c
f is M2( the carrier of G)
f1 is M2( the carrier of A1)
b1 . f is M2( the carrier of b)
[: the carrier of b, the carrier of b:] is Relation-like non empty set
the ObjectMap of b1 is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of b, the carrier of b:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:])
[: the carrier of G, the carrier of G:] is Relation-like non empty set
[:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of b, the carrier of b:]:] is non empty set
the ObjectMap of b1 . (f,f) is M2([: the carrier of b, the carrier of b:])
[f,f] is V15() set
{f,f} is set
{f} is set
{{f,f},{f}} is set
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
c1 . (b1 . f) is M2( the carrier of c)
the carrier of c is non empty set
[: the carrier of c, the carrier of c:] is Relation-like non empty set
the ObjectMap of c1 is Relation-like [: the carrier of b, the carrier of b:] -defined [: the carrier of c, the carrier of c:] -valued Function-like quasi_total M2( bool [:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:])
[:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:] is Relation-like non empty set
bool [:[: the carrier of b, the carrier of b:],[: the carrier of c, the carrier of c:]:] is non empty set
the ObjectMap of c1 . ((b1 . f),(b1 . f)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of c1 . [(b1 . f),(b1 . f)] is set
( the ObjectMap of c1 . ((b1 . f),(b1 . f))) `1 is set
B1 . f1 is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of B1 . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of B1 . [f1,f1] is set
( the ObjectMap of B1 . (f1,f1)) `1 is set
B2 . (B1 . f1) is M2( the carrier of F)
the carrier of F is non empty set
[: the carrier of F, the carrier of F:] is Relation-like non empty set
the ObjectMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined [: the carrier of F, the carrier of F:] -valued Function-like quasi_total M2( bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:])
[:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:] is Relation-like non empty set
bool [:[: the carrier of A2, the carrier of A2:],[: the carrier of F, the carrier of F:]:] is non empty set
the ObjectMap of B2 . ((B1 . f1),(B1 . f1)) is M2([: the carrier of F, the carrier of F:])
[(B1 . f1),(B1 . f1)] is V15() set
{(B1 . f1),(B1 . f1)} is set
{(B1 . f1)} is set
{{(B1 . f1),(B1 . f1)},{(B1 . f1)}} is set
the ObjectMap of B2 . [(B1 . f1),(B1 . f1)] is set
( the ObjectMap of B2 . ((B1 . f1),(B1 . f1))) `1 is set
(c1 * b1) . f is M2( the carrier of c)
the ObjectMap of (c1 * b1) is Relation-like [: the carrier of G, the carrier of G:] -defined [: the carrier of c, the carrier of c:] -valued Function-like quasi_total M2( bool [:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:])
[:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:] is Relation-like non empty set
bool [:[: the carrier of G, the carrier of G:],[: the carrier of c, the carrier of c:]:] is non empty set
the ObjectMap of (c1 * b1) . (f,f) is M2([: the carrier of c, the carrier of c:])
the ObjectMap of (c1 * b1) . [f,f] is set
( the ObjectMap of (c1 * b1) . (f,f)) `1 is set
(B2 * B1) . f1 is M2( the carrier of F)
the ObjectMap of (B2 * B1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of F, the carrier of F:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of F, the carrier of F:]:] is non empty set
the ObjectMap of (B2 * B1) . (f1,f1) is M2([: the carrier of F, the carrier of F:])
the ObjectMap of (B2 * B1) . [f1,f1] is set
( the ObjectMap of (B2 * B1) . (f1,f1)) `1 is set
f is M2( the carrier of G)
f1 is M2( the carrier of G)
<^f,f1^> is set
the Arrows of G is Relation-like [: the carrier of G, the carrier of G:] -defined Function-like non empty total set
the Arrows of G . (f,f1) is set
[f,f1] is V15() set
{f,f1} is set
{f} is set
{{f,f1},{f}} is set
the Arrows of G . [f,f1] is set
c1 is M2( the carrier of A1)
a9 is M2( the carrier of A1)
<^c1,a9^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (c1,a9) is set
[c1,a9] is V15() set
{c1,a9} is set
{c1} is set
{{c1,a9},{c1}} is set
the Arrows of A1 . [c1,a9] is set
Morph-Map ((B2 * B1),c1,a9) is Relation-like Function-like set
the MorphMap of (B2 * B1) is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of (B2 * B1), the Arrows of A1, the Arrows of F
the Arrows of F is Relation-like [: the carrier of F, the carrier of F:] -defined Function-like non empty total set
the MorphMap of (B2 * B1) . (c1,a9) is Relation-like Function-like set
the MorphMap of (B2 * B1) . [c1,a9] is Relation-like Function-like set
(B2 * B1) . c1 is M2( the carrier of F)
the ObjectMap of (B2 * B1) . (c1,c1) is M2([: the carrier of F, the carrier of F:])
[c1,c1] is V15() set
{c1,c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of (B2 * B1) . [c1,c1] is set
( the ObjectMap of (B2 * B1) . (c1,c1)) `1 is set
B1 . c1 is M2( the carrier of A2)
the ObjectMap of B1 . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [c1,c1] is set
( the ObjectMap of B1 . (c1,c1)) `1 is set
B2 . (B1 . c1) is M2( the carrier of F)
the ObjectMap of B2 . ((B1 . c1),(B1 . c1)) is M2([: the carrier of F, the carrier of F:])
[(B1 . c1),(B1 . c1)] is V15() set
{(B1 . c1),(B1 . c1)} is set
{(B1 . c1)} is set
{{(B1 . c1),(B1 . c1)},{(B1 . c1)}} is set
the ObjectMap of B2 . [(B1 . c1),(B1 . c1)] is set
( the ObjectMap of B2 . ((B1 . c1),(B1 . c1))) `1 is set
(B2 * B1) . a9 is M2( the carrier of F)
the ObjectMap of (B2 * B1) . (a9,a9) is M2([: the carrier of F, the carrier of F:])
[a9,a9] is V15() set
{a9,a9} is set
{a9} is set
{{a9,a9},{a9}} is set
the ObjectMap of (B2 * B1) . [a9,a9] is set
( the ObjectMap of (B2 * B1) . (a9,a9)) `1 is set
B1 . a9 is M2( the carrier of A2)
the ObjectMap of B1 . (a9,a9) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of B1 . [a9,a9] is set
( the ObjectMap of B1 . (a9,a9)) `1 is set
B2 . (B1 . a9) is M2( the carrier of F)
the ObjectMap of B2 . ((B1 . a9),(B1 . a9)) is M2([: the carrier of F, the carrier of F:])
[(B1 . a9),(B1 . a9)] is V15() set
{(B1 . a9),(B1 . a9)} is set
{(B1 . a9)} is set
{{(B1 . a9),(B1 . a9)},{(B1 . a9)}} is set
the ObjectMap of B2 . [(B1 . a9),(B1 . a9)] is set
( the ObjectMap of B2 . ((B1 . a9),(B1 . a9))) `1 is set
b9 is M2(<^f,f1^>)
(c1 * b1) . b9 is M2(<^((c1 * b1) . f),((c1 * b1) . f1)^>)
(c1 * b1) . f is M2( the carrier of c)
the ObjectMap of (c1 * b1) . (f,f) is M2([: the carrier of c, the carrier of c:])
[f,f] is V15() set
{f,f} is set
{{f,f},{f}} is set
the ObjectMap of (c1 * b1) . [f,f] is set
( the ObjectMap of (c1 * b1) . (f,f)) `1 is set
(c1 * b1) . f1 is M2( the carrier of c)
the ObjectMap of (c1 * b1) . (f1,f1) is M2([: the carrier of c, the carrier of c:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of (c1 * b1) . [f1,f1] is set
( the ObjectMap of (c1 * b1) . (f1,f1)) `1 is set
<^((c1 * b1) . f),((c1 * b1) . f1)^> is set
the Arrows of c is Relation-like [: the carrier of c, the carrier of c:] -defined Function-like non empty total set
the Arrows of c . (((c1 * b1) . f),((c1 * b1) . f1)) is set
[((c1 * b1) . f),((c1 * b1) . f1)] is V15() set
{((c1 * b1) . f),((c1 * b1) . f1)} is set
{((c1 * b1) . f)} is set
{{((c1 * b1) . f),((c1 * b1) . f1)},{((c1 * b1) . f)}} is set
the Arrows of c . [((c1 * b1) . f),((c1 * b1) . f1)] is set
c9 is M2(<^c1,a9^>)
(Morph-Map ((B2 * B1),c1,a9)) . c9 is set
<^((B2 * B1) . c1),((B2 * B1) . a9)^> is set
the Arrows of F . (((B2 * B1) . c1),((B2 * B1) . a9)) is set
[((B2 * B1) . c1),((B2 * B1) . a9)] is V15() set
{((B2 * B1) . c1),((B2 * B1) . a9)} is set
{((B2 * B1) . c1)} is set
{{((B2 * B1) . c1),((B2 * B1) . a9)},{((B2 * B1) . c1)}} is set
the Arrows of F . [((B2 * B1) . c1),((B2 * B1) . a9)] is set
b1 . f1 is M2( the carrier of b)
the ObjectMap of b1 . (f1,f1) is M2([: the carrier of b, the carrier of b:])
the ObjectMap of b1 . [f1,f1] is set
( the ObjectMap of b1 . (f1,f1)) `1 is set
b1 . f is M2( the carrier of b)
the ObjectMap of b1 . (f,f) is M2([: the carrier of b, the carrier of b:])
the ObjectMap of b1 . [f,f] is set
( the ObjectMap of b1 . (f,f)) `1 is set
<^(b1 . f1),(b1 . f)^> is set
the Arrows of b is Relation-like [: the carrier of b, the carrier of b:] -defined Function-like non empty total set
the Arrows of b . ((b1 . f1),(b1 . f)) is set
[(b1 . f1),(b1 . f)] is V15() set
{(b1 . f1),(b1 . f)} is set
{(b1 . f1)} is set
{{(b1 . f1),(b1 . f)},{(b1 . f1)}} is set
the Arrows of b . [(b1 . f1),(b1 . f)] is set
b1 . b9 is M2(<^(b1 . f1),(b1 . f)^>)
<^(B1 . a9),(B1 . c1)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . ((B1 . a9),(B1 . c1)) is set
[(B1 . a9),(B1 . c1)] is V15() set
{(B1 . a9),(B1 . c1)} is set
{{(B1 . a9),(B1 . c1)},{(B1 . a9)}} is set
the Arrows of A2 . [(B1 . a9),(B1 . c1)] is set
Morph-Map (B1,c1,a9) is Relation-like <^c1,a9^> -defined <^(B1 . a9),(B1 . c1)^> -valued Function-like quasi_total M2( bool [:<^c1,a9^>,<^(B1 . a9),(B1 . c1)^>:])
[:<^c1,a9^>,<^(B1 . a9),(B1 . c1)^>:] is Relation-like set
bool [:<^c1,a9^>,<^(B1 . a9),(B1 . c1)^>:] is non empty set
the MorphMap of B1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B1, the Arrows of A1, the Arrows of A2
the MorphMap of B1 . (c1,a9) is Relation-like Function-like set
the MorphMap of B1 . [c1,a9] is Relation-like Function-like set
(Morph-Map (B1,c1,a9)) . c9 is set
B1 . c9 is M2(<^(B1 . a9),(B1 . c1)^>)
c1 . (b1 . b9) is M2(<^(c1 . (b1 . f)),(c1 . (b1 . f1))^>)
c1 . (b1 . f) is M2( the carrier of c)
the ObjectMap of c1 . ((b1 . f),(b1 . f)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f),(b1 . f)] is V15() set
{(b1 . f),(b1 . f)} is set
{(b1 . f)} is set
{{(b1 . f),(b1 . f)},{(b1 . f)}} is set
the ObjectMap of c1 . [(b1 . f),(b1 . f)] is set
( the ObjectMap of c1 . ((b1 . f),(b1 . f))) `1 is set
c1 . (b1 . f1) is M2( the carrier of c)
the ObjectMap of c1 . ((b1 . f1),(b1 . f1)) is M2([: the carrier of c, the carrier of c:])
[(b1 . f1),(b1 . f1)] is V15() set
{(b1 . f1),(b1 . f1)} is set
{{(b1 . f1),(b1 . f1)},{(b1 . f1)}} is set
the ObjectMap of c1 . [(b1 . f1),(b1 . f1)] is set
( the ObjectMap of c1 . ((b1 . f1),(b1 . f1))) `1 is set
<^(c1 . (b1 . f)),(c1 . (b1 . f1))^> is set
the Arrows of c . ((c1 . (b1 . f)),(c1 . (b1 . f1))) is set
[(c1 . (b1 . f)),(c1 . (b1 . f1))] is V15() set
{(c1 . (b1 . f)),(c1 . (b1 . f1))} is set
{(c1 . (b1 . f))} is set
{{(c1 . (b1 . f)),(c1 . (b1 . f1))},{(c1 . (b1 . f))}} is set
the Arrows of c . [(c1 . (b1 . f)),(c1 . (b1 . f1))] is set
Morph-Map (B2,(B1 . a9),(B1 . c1)) is Relation-like <^(B1 . a9),(B1 . c1)^> -defined <^(B2 . (B1 . c1)),(B2 . (B1 . a9))^> -valued Function-like quasi_total M2( bool [:<^(B1 . a9),(B1 . c1)^>,<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^>:])
<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^> is set
the Arrows of F . ((B2 . (B1 . c1)),(B2 . (B1 . a9))) is set
[(B2 . (B1 . c1)),(B2 . (B1 . a9))] is V15() set
{(B2 . (B1 . c1)),(B2 . (B1 . a9))} is set
{(B2 . (B1 . c1))} is set
{{(B2 . (B1 . c1)),(B2 . (B1 . a9))},{(B2 . (B1 . c1))}} is set
the Arrows of F . [(B2 . (B1 . c1)),(B2 . (B1 . a9))] is set
[:<^(B1 . a9),(B1 . c1)^>,<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^>:] is Relation-like set
bool [:<^(B1 . a9),(B1 . c1)^>,<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^>:] is non empty set
the MorphMap of B2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of B2, the Arrows of A2, the Arrows of F
the MorphMap of B2 . ((B1 . a9),(B1 . c1)) is Relation-like Function-like set
the MorphMap of B2 . [(B1 . a9),(B1 . c1)] is Relation-like Function-like set
(Morph-Map (B2,(B1 . a9),(B1 . c1))) . (B1 . c9) is set
B2 . (B1 . c9) is M2(<^(B2 . (B1 . c1)),(B2 . (B1 . a9))^>)
(B2 * B1) . c9 is M2(<^((B2 * B1) . c1),((B2 * B1) . a9)^>)
Morph-Map ((B2 * B1),c1,a9) is Relation-like <^c1,a9^> -defined <^((B2 * B1) . c1),((B2 * B1) . a9)^> -valued Function-like quasi_total M2( bool [:<^c1,a9^>,<^((B2 * B1) . c1),((B2 * B1) . a9)^>:])
[:<^c1,a9^>,<^((B2 * B1) . c1),((B2 * B1) . a9)^>:] is Relation-like set
bool [:<^c1,a9^>,<^((B2 * B1) . c1),((B2 * B1) . a9)^>:] is non empty set
(Morph-Map ((B2 * B1),c1,a9)) . c9 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A1,A2
B1 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
the carrier of B1 is non empty set
B2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A2
the carrier of B2 is non empty set
(A1,A2,B1,F) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B1,A2
incl B1 is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over B1,A1
F * (incl B1) is reflexive feasible strict Covariant id-preserving FunctorStr over B1,A2
the carrier of A2 is non empty set
G is M2( the carrier of B2)
b is M2( the carrier of B2)
<^G,b^> is set
the Arrows of B2 is Relation-like [: the carrier of B2, the carrier of B2:] -defined Function-like non empty total set
[: the carrier of B2, the carrier of B2:] is Relation-like non empty set
the Arrows of B2 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of B2 . [G,b] is set
c1 is M2(<^G,b^>)
c is M2( the carrier of A2)
b1 is M2( the carrier of A2)
<^c,b1^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (c,b1) is set
[c,b1] is V15() set
{c,b1} is set
{c} is set
{{c,b1},{c}} is set
the Arrows of A2 . [c,b1] is set
f is M2(<^c,b1^>)
f1 is M2( the carrier of A1)
c1 is M2( the carrier of A1)
<^f1,c1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{f1} is set
{{f1,c1},{f1}} is set
the Arrows of A1 . [f1,c1] is set
F . f1 is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of F . [f1,f1] is set
( the ObjectMap of F . (f1,f1)) `1 is set
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
a9 is M2(<^f1,c1^>)
F . a9 is M2(<^(F . f1),(F . c1)^>)
<^(F . f1),(F . c1)^> is set
the Arrows of A2 . ((F . f1),(F . c1)) is set
[(F . f1),(F . c1)] is V15() set
{(F . f1),(F . c1)} is set
{(F . f1)} is set
{{(F . f1),(F . c1)},{(F . f1)}} is set
the Arrows of A2 . [(F . f1),(F . c1)] is set
b9 is M2( the carrier of B1)
c9 is M2( the carrier of B1)
<^b9,c9^> is set
the Arrows of B1 is Relation-like [: the carrier of B1, the carrier of B1:] -defined Function-like non empty total set
[: the carrier of B1, the carrier of B1:] is Relation-like non empty set
the Arrows of B1 . (b9,c9) is set
[b9,c9] is V15() set
{b9,c9} is set
{b9} is set
{{b9,c9},{b9}} is set
the Arrows of B1 . [b9,c9] is set
(A1,A2,B1,F) . b9 is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) is Relation-like [: the carrier of B1, the carrier of B1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (A1,A2,B1,F) . (b9,b9) is M2([: the carrier of A2, the carrier of A2:])
[b9,b9] is V15() set
{b9,b9} is set
{{b9,b9},{b9}} is set
the ObjectMap of (A1,A2,B1,F) . [b9,b9] is set
( the ObjectMap of (A1,A2,B1,F) . (b9,b9)) `1 is set
(A1,A2,B1,F) . c9 is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (c9,c9) is M2([: the carrier of A2, the carrier of A2:])
[c9,c9] is V15() set
{c9,c9} is set
{c9} is set
{{c9,c9},{c9}} is set
the ObjectMap of (A1,A2,B1,F) . [c9,c9] is set
( the ObjectMap of (A1,A2,B1,F) . (c9,c9)) `1 is set
f9 is M2(<^b9,c9^>)
(A1,A2,B1,F) . f9 is M2(<^((A1,A2,B1,F) . b9),((A1,A2,B1,F) . c9)^>)
<^((A1,A2,B1,F) . b9),((A1,A2,B1,F) . c9)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . b9),((A1,A2,B1,F) . c9)) is set
[((A1,A2,B1,F) . b9),((A1,A2,B1,F) . c9)] is V15() set
{((A1,A2,B1,F) . b9),((A1,A2,B1,F) . c9)} is set
{((A1,A2,B1,F) . b9)} is set
{{((A1,A2,B1,F) . b9),((A1,A2,B1,F) . c9)},{((A1,A2,B1,F) . b9)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . b9),((A1,A2,B1,F) . c9)] is set
G is M2( the carrier of B1)
(A1,A2,B1,F) . G is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of (A1,A2,B1,F) is Relation-like [: the carrier of B1, the carrier of B1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of B1, the carrier of B1:] is Relation-like non empty set
[:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
b is M2( the carrier of A1)
F . b is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of F . [b,b] is set
( the ObjectMap of F . (b,b)) `1 is set
G is M2( the carrier of B1)
b is M2( the carrier of B1)
<^G,b^> is set
the Arrows of B1 is Relation-like [: the carrier of B1, the carrier of B1:] -defined Function-like non empty total set
the Arrows of B1 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of B1 . [G,b] is set
b1 is M2( the carrier of A1)
c1 is M2( the carrier of A1)
<^b1,c1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (b1,c1) is set
[b1,c1] is V15() set
{b1,c1} is set
{b1} is set
{{b1,c1},{b1}} is set
the Arrows of A1 . [b1,c1] is set
c is M2(<^G,b^>)
(A1,A2,B1,F) . G is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
F . b1 is M2( the carrier of A2)
the ObjectMap of F . (b1,b1) is M2([: the carrier of A2, the carrier of A2:])
[b1,b1] is V15() set
{b1,b1} is set
{{b1,b1},{b1}} is set
the ObjectMap of F . [b1,b1] is set
( the ObjectMap of F . (b1,b1)) `1 is set
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
(A1,A2,B1,F) . c is M2(<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)^>)
<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . (((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)) is set
[((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)] is V15() set
{((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)} is set
{((A1,A2,B1,F) . G)} is set
{{((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)},{((A1,A2,B1,F) . G)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)] is set
f is M2(<^b1,c1^>)
F . f is M2(<^(F . b1),(F . c1)^>)
<^(F . b1),(F . c1)^> is set
the Arrows of A2 . ((F . b1),(F . c1)) is set
[(F . b1),(F . c1)] is V15() set
{(F . b1),(F . c1)} is set
{(F . b1)} is set
{{(F . b1),(F . c1)},{(F . b1)}} is set
the Arrows of A2 . [(F . b1),(F . c1)] is set
f1 is M2( the carrier of B2)
c1 is M2( the carrier of B2)
<^f1,c1^> is set
the Arrows of B2 is Relation-like [: the carrier of B2, the carrier of B2:] -defined Function-like non empty total set
[: the carrier of B2, the carrier of B2:] is Relation-like non empty set
the Arrows of B2 . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{f1} is set
{{f1,c1},{f1}} is set
the Arrows of B2 . [f1,c1] is set
the Arrows of B2 . (H<sub>2</sub>(G),H<sub>2</sub>(b)) is set
the Arrows of B2 . [((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)] is set
G is M2( the carrier of B1)
b is M2( the carrier of B1)
<^G,b^> is set
the Arrows of B1 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of B1 . [G,b] is set
c is M2( the carrier of A1)
b1 is M2( the carrier of A1)
<^c,b1^> is set
the Arrows of A1 . (c,b1) is set
[c,b1] is V15() set
{c,b1} is set
{c} is set
{{c,b1},{c}} is set
the Arrows of A1 . [c,b1] is set
c1 is M2(<^G,b^>)
f is M2(<^G,b^>)
(A1,A2,B1,F) . c1 is M2(<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)^>)
(A1,A2,B1,F) . G is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)) is set
[((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)] is V15() set
{((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)} is set
{((A1,A2,B1,F) . G)} is set
{{((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)},{((A1,A2,B1,F) . G)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)] is set
(A1,A2,B1,F) . f is M2(<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)^>)
f1 is M2(<^c,b1^>)
F . f1 is M2(<^(F . c),(F . b1)^>)
F . c is M2( the carrier of A2)
the ObjectMap of F . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{{c,c},{c}} is set
the ObjectMap of F . [c,c] is set
( the ObjectMap of F . (c,c)) `1 is set
F . b1 is M2( the carrier of A2)
the ObjectMap of F . (b1,b1) is M2([: the carrier of A2, the carrier of A2:])
[b1,b1] is V15() set
{b1,b1} is set
{b1} is set
{{b1,b1},{b1}} is set
the ObjectMap of F . [b1,b1] is set
( the ObjectMap of F . (b1,b1)) `1 is set
<^(F . c),(F . b1)^> is set
the Arrows of A2 . ((F . c),(F . b1)) is set
[(F . c),(F . b1)] is V15() set
{(F . c),(F . b1)} is set
{(F . c)} is set
{{(F . c),(F . b1)},{(F . c)}} is set
the Arrows of A2 . [(F . c),(F . b1)] is set
c1 is M2(<^c,b1^>)
F . c1 is M2(<^(F . c),(F . b1)^>)
G is M2( the carrier of B1)
b is M2( the carrier of B1)
<^G,b^> is set
the Arrows of B1 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of B1 . [G,b] is set
c is M2( the carrier of B1)
<^b,c^> is set
the Arrows of B1 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of B1 . [b,c] is set
a9 is M2( the carrier of B2)
(A1,A2,B1,F) . G is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
b9 is M2( the carrier of B2)
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
c9 is M2( the carrier of B2)
(A1,A2,B1,F) . c is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of (A1,A2,B1,F) . [c,c] is set
( the ObjectMap of (A1,A2,B1,F) . (c,c)) `1 is set
<^a9,b9^> is set
the Arrows of B2 . (a9,b9) is set
[a9,b9] is V15() set
{a9,b9} is set
{a9} is set
{{a9,b9},{a9}} is set
the Arrows of B2 . [a9,b9] is set
<^b9,c9^> is set
the Arrows of B2 . (b9,c9) is set
[b9,c9] is V15() set
{b9,c9} is set
{b9} is set
{{b9,c9},{b9}} is set
the Arrows of B2 . [b9,c9] is set
f9 is M2(<^a9,b9^>)
b1 is M2(<^G,b^>)
(A1,A2,B1,F) . b1 is M2(<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)^>)
<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)) is set
[((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)] is V15() set
{((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)} is set
{((A1,A2,B1,F) . G)} is set
{{((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)},{((A1,A2,B1,F) . G)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . G),((A1,A2,B1,F) . b)] is set
g9 is M2(<^b9,c9^>)
c1 is M2(<^b,c^>)
(A1,A2,B1,F) . c1 is M2(<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)^>)
<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)) is set
[((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)] is V15() set
{((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)} is set
{((A1,A2,B1,F) . b)} is set
{{((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)},{((A1,A2,B1,F) . b)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)] is set
f1 is M2( the carrier of A1)
F . f1 is M2( the carrier of A2)
the ObjectMap of F . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of F . [f1,f1] is set
( the ObjectMap of F . (f1,f1)) `1 is set
c1 is M2( the carrier of A1)
<^f1,c1^> is set
the Arrows of A1 . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{{f1,c1},{f1}} is set
the Arrows of A1 . [f1,c1] is set
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
f is M2( the carrier of A1)
<^f,f1^> is set
the Arrows of A1 . (f,f1) is set
[f,f1] is V15() set
{f,f1} is set
{f} is set
{{f,f1},{f}} is set
the Arrows of A1 . [f,f1] is set
F . f is M2( the carrier of A2)
the ObjectMap of F . (f,f) is M2([: the carrier of A2, the carrier of A2:])
[f,f] is V15() set
{f,f} is set
{{f,f},{f}} is set
the ObjectMap of F . [f,f] is set
( the ObjectMap of F . (f,f)) `1 is set
g1 is M2(<^f1,c1^>)
F . g1 is M2(<^(F . f1),(F . c1)^>)
<^(F . f1),(F . c1)^> is set
the Arrows of A2 . ((F . f1),(F . c1)) is set
[(F . f1),(F . c1)] is V15() set
{(F . f1),(F . c1)} is set
{(F . f1)} is set
{{(F . f1),(F . c1)},{(F . f1)}} is set
the Arrows of A2 . [(F . f1),(F . c1)] is set
f1 is M2(<^f,f1^>)
F . f1 is M2(<^(F . f),(F . f1)^>)
<^(F . f),(F . f1)^> is set
the Arrows of A2 . ((F . f),(F . f1)) is set
[(F . f),(F . f1)] is V15() set
{(F . f),(F . f1)} is set
{(F . f)} is set
{{(F . f),(F . f1)},{(F . f)}} is set
the Arrows of A2 . [(F . f),(F . f1)] is set
<^G,c^> is set
the Arrows of B1 . (G,c) is set
[G,c] is V15() set
{G,c} is set
{{G,c},{G}} is set
the Arrows of B1 . [G,c] is set
c1 * b1 is M2(<^G,c^>)
g1 * f1 is M2(<^f,c1^>)
<^f,c1^> is set
the Arrows of A1 . (f,c1) is set
[f,c1] is V15() set
{f,c1} is set
{{f,c1},{f}} is set
the Arrows of A1 . [f,c1] is set
(A1,A2,B1,F) . (c1 * b1) is M2(<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . c)^>)
<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . c)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . G),((A1,A2,B1,F) . c)) is set
[((A1,A2,B1,F) . G),((A1,A2,B1,F) . c)] is V15() set
{((A1,A2,B1,F) . G),((A1,A2,B1,F) . c)} is set
{{((A1,A2,B1,F) . G),((A1,A2,B1,F) . c)},{((A1,A2,B1,F) . G)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . G),((A1,A2,B1,F) . c)] is set
F . (g1 * f1) is M2(<^(F . f),(F . c1)^>)
<^(F . f),(F . c1)^> is set
the Arrows of A2 . ((F . f),(F . c1)) is set
[(F . f),(F . c1)] is V15() set
{(F . f),(F . c1)} is set
{{(F . f),(F . c1)},{(F . f)}} is set
the Arrows of A2 . [(F . f),(F . c1)] is set
(F . g1) * (F . f1) is M2(<^(F . f),(F . c1)^>)
g9 * f9 is M2(<^a9,c9^>)
<^a9,c9^> is set
the Arrows of B2 . (a9,c9) is set
[a9,c9] is V15() set
{a9,c9} is set
{{a9,c9},{a9}} is set
the Arrows of B2 . [a9,c9] is set
b is M2( the carrier of B2)
G is M2( the carrier of B1)
(A1,A2,B1,F) . G is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
idm G is M2(<^G,G^>)
<^G,G^> is non empty set
the Arrows of B1 . (G,G) is set
the Arrows of B1 . [G,G] is set
(A1,A2,B1,F) . (idm G) is M2(<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)^>)
<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)^> is non empty set
the Arrows of A2 . (((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)) is set
[((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)] is V15() set
{((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)} is set
{((A1,A2,B1,F) . G)} is set
{{((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)},{((A1,A2,B1,F) . G)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)] is set
c is M2( the carrier of A1)
idm c is M2(<^c,c^>)
<^c,c^> is non empty set
the Arrows of A1 . (c,c) is set
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the Arrows of A1 . [c,c] is set
F . (idm c) is M2(<^(F . c),(F . c)^>)
F . c is M2( the carrier of A2)
the ObjectMap of F . (c,c) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [c,c] is set
( the ObjectMap of F . (c,c)) `1 is set
<^(F . c),(F . c)^> is non empty set
the Arrows of A2 . ((F . c),(F . c)) is set
[(F . c),(F . c)] is V15() set
{(F . c),(F . c)} is set
{(F . c)} is set
{{(F . c),(F . c)},{(F . c)}} is set
the Arrows of A2 . [(F . c),(F . c)] is set
idm (F . c) is M2(<^(F . c),(F . c)^>)
idm b is M2(<^b,b^>)
<^b,b^> is non empty set
the Arrows of B2 . (b,b) is set
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the Arrows of B2 . [b,b] is set
G is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of B1,B2
b is M2( the carrier of B1)
c is M2( the carrier of B1)
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
(A1,A2,B1,F) . c is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of (A1,A2,B1,F) . [c,c] is set
( the ObjectMap of (A1,A2,B1,F) . (c,c)) `1 is set
b1 is M2( the carrier of A1)
F . b1 is M2( the carrier of A2)
the ObjectMap of F . (b1,b1) is M2([: the carrier of A2, the carrier of A2:])
[b1,b1] is V15() set
{b1,b1} is set
{b1} is set
{{b1,b1},{b1}} is set
the ObjectMap of F . [b1,b1] is set
( the ObjectMap of F . (b1,b1)) `1 is set
c1 is M2( the carrier of A1)
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
b is M2( the carrier of B1)
c is M2( the carrier of A1)
G . b is M2( the carrier of B2)
the ObjectMap of G is Relation-like [: the carrier of B1, the carrier of B1:] -defined [: the carrier of B2, the carrier of B2:] -valued Function-like quasi_total M2( bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of B2, the carrier of B2:]:])
[:[: the carrier of B1, the carrier of B1:],[: the carrier of B2, the carrier of B2:]:] is Relation-like non empty set
bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of B2, the carrier of B2:]:] is non empty set
the ObjectMap of G . (b,b) is M2([: the carrier of B2, the carrier of B2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of G . [b,b] is set
( the ObjectMap of G . (b,b)) `1 is set
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
F . c is M2( the carrier of A2)
the ObjectMap of F . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of F . [c,c] is set
( the ObjectMap of F . (c,c)) `1 is set
b is M2( the carrier of B1)
c is M2( the carrier of B1)
<^b,c^> is set
the Arrows of B1 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of B1 . [b,c] is set
b1 is M2( the carrier of A1)
c1 is M2( the carrier of A1)
<^b1,c1^> is set
the Arrows of A1 . (b1,c1) is set
[b1,c1] is V15() set
{b1,c1} is set
{b1} is set
{{b1,c1},{b1}} is set
the Arrows of A1 . [b1,c1] is set
Morph-Map (F,b1,c1) is Relation-like Function-like set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the MorphMap of F . (b1,c1) is Relation-like Function-like set
the MorphMap of F . [b1,c1] is Relation-like Function-like set
f is M2(<^b,c^>)
G . f is M2(<^(G . b),(G . c)^>)
G . b is M2( the carrier of B2)
the ObjectMap of G . (b,b) is M2([: the carrier of B2, the carrier of B2:])
[b,b] is V15() set
{b,b} is set
{{b,b},{b}} is set
the ObjectMap of G . [b,b] is set
( the ObjectMap of G . (b,b)) `1 is set
G . c is M2( the carrier of B2)
the ObjectMap of G . (c,c) is M2([: the carrier of B2, the carrier of B2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of G . [c,c] is set
( the ObjectMap of G . (c,c)) `1 is set
<^(G . b),(G . c)^> is set
the Arrows of B2 . ((G . b),(G . c)) is set
[(G . b),(G . c)] is V15() set
{(G . b),(G . c)} is set
{(G . b)} is set
{{(G . b),(G . c)},{(G . b)}} is set
the Arrows of B2 . [(G . b),(G . c)] is set
f1 is M2(<^b1,c1^>)
(Morph-Map (F,b1,c1)) . f1 is set
F . b1 is M2( the carrier of A2)
the ObjectMap of F . (b1,b1) is M2([: the carrier of A2, the carrier of A2:])
[b1,b1] is V15() set
{b1,b1} is set
{{b1,b1},{b1}} is set
the ObjectMap of F . [b1,b1] is set
( the ObjectMap of F . (b1,b1)) `1 is set
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
<^(F . b1),(F . c1)^> is set
the Arrows of A2 . ((F . b1),(F . c1)) is set
[(F . b1),(F . c1)] is V15() set
{(F . b1),(F . c1)} is set
{(F . b1)} is set
{{(F . b1),(F . c1)},{(F . b1)}} is set
the Arrows of A2 . [(F . b1),(F . c1)] is set
(A1,A2,B1,F) . f is M2(<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)^>)
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
(A1,A2,B1,F) . c is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (c,c) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (A1,A2,B1,F) . [c,c] is set
( the ObjectMap of (A1,A2,B1,F) . (c,c)) `1 is set
<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)) is set
[((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)] is V15() set
{((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)} is set
{((A1,A2,B1,F) . b)} is set
{{((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)},{((A1,A2,B1,F) . b)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . b),((A1,A2,B1,F) . c)] is set
F . f1 is M2(<^(F . b1),(F . c1)^>)
Morph-Map (F,b1,c1) is Relation-like <^b1,c1^> -defined <^(F . b1),(F . c1)^> -valued Function-like quasi_total M2( bool [:<^b1,c1^>,<^(F . b1),(F . c1)^>:])
[:<^b1,c1^>,<^(F . b1),(F . c1)^>:] is Relation-like set
bool [:<^b1,c1^>,<^(F . b1),(F . c1)^>:] is non empty set
(Morph-Map (F,b1,c1)) . f1 is set
A1 is non empty transitive V106() with_units reflexive AltCatStr
A2 is non empty transitive V106() with_units reflexive AltCatStr
the carrier of A1 is non empty set
F is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A1,A2
B1 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A1
the carrier of B1 is non empty set
B2 is non empty transitive V106() with_units reflexive id-inheriting SubCatStr of A2
the carrier of B2 is non empty set
(A1,A2,B1,F) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of B1,A2
incl B1 is reflexive feasible strict Covariant id-preserving comp-preserving FunctorStr over B1,A1
F * (incl B1) is reflexive feasible strict Contravariant id-preserving FunctorStr over B1,A2
the carrier of A2 is non empty set
G is M2( the carrier of B2)
b is M2( the carrier of B2)
<^G,b^> is set
the Arrows of B2 is Relation-like [: the carrier of B2, the carrier of B2:] -defined Function-like non empty total set
[: the carrier of B2, the carrier of B2:] is Relation-like non empty set
the Arrows of B2 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of B2 . [G,b] is set
c1 is M2(<^G,b^>)
c is M2( the carrier of A2)
b1 is M2( the carrier of A2)
<^c,b1^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the Arrows of A2 . (c,b1) is set
[c,b1] is V15() set
{c,b1} is set
{c} is set
{{c,b1},{c}} is set
the Arrows of A2 . [c,b1] is set
f is M2(<^c,b1^>)
f1 is M2( the carrier of A1)
c1 is M2( the carrier of A1)
<^f1,c1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
the Arrows of A1 . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{f1} is set
{{f1,c1},{f1}} is set
the Arrows of A1 . [f1,c1] is set
F . f1 is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of F . [f1,f1] is set
( the ObjectMap of F . (f1,f1)) `1 is set
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
a9 is M2(<^f1,c1^>)
F . a9 is M2(<^(F . c1),(F . f1)^>)
<^(F . c1),(F . f1)^> is set
the Arrows of A2 . ((F . c1),(F . f1)) is set
[(F . c1),(F . f1)] is V15() set
{(F . c1),(F . f1)} is set
{(F . c1)} is set
{{(F . c1),(F . f1)},{(F . c1)}} is set
the Arrows of A2 . [(F . c1),(F . f1)] is set
b9 is M2( the carrier of B1)
c9 is M2( the carrier of B1)
<^b9,c9^> is set
the Arrows of B1 is Relation-like [: the carrier of B1, the carrier of B1:] -defined Function-like non empty total set
[: the carrier of B1, the carrier of B1:] is Relation-like non empty set
the Arrows of B1 . (b9,c9) is set
[b9,c9] is V15() set
{b9,c9} is set
{b9} is set
{{b9,c9},{b9}} is set
the Arrows of B1 . [b9,c9] is set
(A1,A2,B1,F) . b9 is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) is Relation-like [: the carrier of B1, the carrier of B1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:])
[:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (A1,A2,B1,F) . (b9,b9) is M2([: the carrier of A2, the carrier of A2:])
[b9,b9] is V15() set
{b9,b9} is set
{{b9,b9},{b9}} is set
the ObjectMap of (A1,A2,B1,F) . [b9,b9] is set
( the ObjectMap of (A1,A2,B1,F) . (b9,b9)) `1 is set
(A1,A2,B1,F) . c9 is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (c9,c9) is M2([: the carrier of A2, the carrier of A2:])
[c9,c9] is V15() set
{c9,c9} is set
{c9} is set
{{c9,c9},{c9}} is set
the ObjectMap of (A1,A2,B1,F) . [c9,c9] is set
( the ObjectMap of (A1,A2,B1,F) . (c9,c9)) `1 is set
f9 is M2(<^b9,c9^>)
(A1,A2,B1,F) . f9 is M2(<^((A1,A2,B1,F) . c9),((A1,A2,B1,F) . b9)^>)
<^((A1,A2,B1,F) . c9),((A1,A2,B1,F) . b9)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . c9),((A1,A2,B1,F) . b9)) is set
[((A1,A2,B1,F) . c9),((A1,A2,B1,F) . b9)] is V15() set
{((A1,A2,B1,F) . c9),((A1,A2,B1,F) . b9)} is set
{((A1,A2,B1,F) . c9)} is set
{{((A1,A2,B1,F) . c9),((A1,A2,B1,F) . b9)},{((A1,A2,B1,F) . c9)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . c9),((A1,A2,B1,F) . b9)] is set
G is M2( the carrier of B1)
(A1,A2,B1,F) . G is M2( the carrier of A2)
[: the carrier of A2, the carrier of A2:] is Relation-like non empty set
the ObjectMap of (A1,A2,B1,F) is Relation-like [: the carrier of B1, the carrier of B1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of B1, the carrier of B1:] is Relation-like non empty set
[:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
b is M2( the carrier of A1)
F . b is M2( the carrier of A2)
the ObjectMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined [: the carrier of A2, the carrier of A2:] -valued Function-like quasi_total M2( bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:])
[: the carrier of A1, the carrier of A1:] is Relation-like non empty set
[:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is Relation-like non empty set
bool [:[: the carrier of A1, the carrier of A1:],[: the carrier of A2, the carrier of A2:]:] is non empty set
the ObjectMap of F . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of F . [b,b] is set
( the ObjectMap of F . (b,b)) `1 is set
G is M2( the carrier of B1)
b is M2( the carrier of B1)
<^G,b^> is set
the Arrows of B1 is Relation-like [: the carrier of B1, the carrier of B1:] -defined Function-like non empty total set
the Arrows of B1 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of B1 . [G,b] is set
b1 is M2( the carrier of A1)
c1 is M2( the carrier of A1)
<^b1,c1^> is set
the Arrows of A1 is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total set
the Arrows of A1 . (b1,c1) is set
[b1,c1] is V15() set
{b1,c1} is set
{b1} is set
{{b1,c1},{b1}} is set
the Arrows of A1 . [b1,c1] is set
c is M2(<^G,b^>)
(A1,A2,B1,F) . G is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
F . b1 is M2( the carrier of A2)
the ObjectMap of F . (b1,b1) is M2([: the carrier of A2, the carrier of A2:])
[b1,b1] is V15() set
{b1,b1} is set
{{b1,b1},{b1}} is set
the ObjectMap of F . [b1,b1] is set
( the ObjectMap of F . (b1,b1)) `1 is set
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
(A1,A2,B1,F) . c is M2(<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)^>)
<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)^> is set
the Arrows of A2 is Relation-like [: the carrier of A2, the carrier of A2:] -defined Function-like non empty total set
the Arrows of A2 . (((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)) is set
[((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)] is V15() set
{((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)} is set
{((A1,A2,B1,F) . b)} is set
{{((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)},{((A1,A2,B1,F) . b)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)] is set
f is M2(<^b1,c1^>)
F . f is M2(<^(F . c1),(F . b1)^>)
<^(F . c1),(F . b1)^> is set
the Arrows of A2 . ((F . c1),(F . b1)) is set
[(F . c1),(F . b1)] is V15() set
{(F . c1),(F . b1)} is set
{(F . c1)} is set
{{(F . c1),(F . b1)},{(F . c1)}} is set
the Arrows of A2 . [(F . c1),(F . b1)] is set
c1 is M2( the carrier of B2)
f1 is M2( the carrier of B2)
<^c1,f1^> is set
the Arrows of B2 is Relation-like [: the carrier of B2, the carrier of B2:] -defined Function-like non empty total set
[: the carrier of B2, the carrier of B2:] is Relation-like non empty set
the Arrows of B2 . (c1,f1) is set
[c1,f1] is V15() set
{c1,f1} is set
{c1} is set
{{c1,f1},{c1}} is set
the Arrows of B2 . [c1,f1] is set
the Arrows of B2 . (H₂(b),H₂(G)) is set
the Arrows of B2 . [((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)] is set
G is M2( the carrier of B1)
b is M2( the carrier of B1)
<^G,b^> is set
the Arrows of B1 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of B1 . [G,b] is set
c is M2( the carrier of A1)
b1 is M2( the carrier of A1)
<^c,b1^> is set
the Arrows of A1 . (c,b1) is set
[c,b1] is V15() set
{c,b1} is set
{c} is set
{{c,b1},{c}} is set
the Arrows of A1 . [c,b1] is set
c1 is M2(<^G,b^>)
f is M2(<^G,b^>)
(A1,A2,B1,F) . c1 is M2(<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)^>)
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
(A1,A2,B1,F) . G is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)) is set
[((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)] is V15() set
{((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)} is set
{((A1,A2,B1,F) . b)} is set
{{((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)},{((A1,A2,B1,F) . b)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)] is set
(A1,A2,B1,F) . f is M2(<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)^>)
f1 is M2(<^c,b1^>)
F . f1 is M2(<^(F . b1),(F . c)^>)
F . b1 is M2( the carrier of A2)
the ObjectMap of F . (b1,b1) is M2([: the carrier of A2, the carrier of A2:])
[b1,b1] is V15() set
{b1,b1} is set
{b1} is set
{{b1,b1},{b1}} is set
the ObjectMap of F . [b1,b1] is set
( the ObjectMap of F . (b1,b1)) `1 is set
F . c is M2( the carrier of A2)
the ObjectMap of F . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{{c,c},{c}} is set
the ObjectMap of F . [c,c] is set
( the ObjectMap of F . (c,c)) `1 is set
<^(F . b1),(F . c)^> is set
the Arrows of A2 . ((F . b1),(F . c)) is set
[(F . b1),(F . c)] is V15() set
{(F . b1),(F . c)} is set
{(F . b1)} is set
{{(F . b1),(F . c)},{(F . b1)}} is set
the Arrows of A2 . [(F . b1),(F . c)] is set
c1 is M2(<^c,b1^>)
F . c1 is M2(<^(F . b1),(F . c)^>)
G is M2( the carrier of B1)
b is M2( the carrier of B1)
<^G,b^> is set
the Arrows of B1 . (G,b) is set
[G,b] is V15() set
{G,b} is set
{G} is set
{{G,b},{G}} is set
the Arrows of B1 . [G,b] is set
c is M2( the carrier of B1)
<^b,c^> is set
the Arrows of B1 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of B1 . [b,c] is set
a9 is M2( the carrier of B2)
(A1,A2,B1,F) . G is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
b9 is M2( the carrier of B2)
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
c9 is M2( the carrier of B2)
(A1,A2,B1,F) . c is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of (A1,A2,B1,F) . [c,c] is set
( the ObjectMap of (A1,A2,B1,F) . (c,c)) `1 is set
<^b9,a9^> is set
the Arrows of B2 . (b9,a9) is set
[b9,a9] is V15() set
{b9,a9} is set
{b9} is set
{{b9,a9},{b9}} is set
the Arrows of B2 . [b9,a9] is set
<^c9,b9^> is set
the Arrows of B2 . (c9,b9) is set
[c9,b9] is V15() set
{c9,b9} is set
{c9} is set
{{c9,b9},{c9}} is set
the Arrows of B2 . [c9,b9] is set
f9 is M2(<^b9,a9^>)
b1 is M2(<^G,b^>)
(A1,A2,B1,F) . b1 is M2(<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)^>)
<^((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)) is set
[((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)] is V15() set
{((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)} is set
{((A1,A2,B1,F) . b)} is set
{{((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)},{((A1,A2,B1,F) . b)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . b),((A1,A2,B1,F) . G)] is set
g9 is M2(<^c9,b9^>)
c1 is M2(<^b,c^>)
(A1,A2,B1,F) . c1 is M2(<^((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)^>)
<^((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)) is set
[((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)] is V15() set
{((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)} is set
{((A1,A2,B1,F) . c)} is set
{{((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)},{((A1,A2,B1,F) . c)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)] is set
f1 is M2( the carrier of A1)
F . f1 is M2( the carrier of A2)
the ObjectMap of F . (f1,f1) is M2([: the carrier of A2, the carrier of A2:])
[f1,f1] is V15() set
{f1,f1} is set
{f1} is set
{{f1,f1},{f1}} is set
the ObjectMap of F . [f1,f1] is set
( the ObjectMap of F . (f1,f1)) `1 is set
c1 is M2( the carrier of A1)
<^f1,c1^> is set
the Arrows of A1 . (f1,c1) is set
[f1,c1] is V15() set
{f1,c1} is set
{{f1,c1},{f1}} is set
the Arrows of A1 . [f1,c1] is set
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
f is M2( the carrier of A1)
<^f,f1^> is set
the Arrows of A1 . (f,f1) is set
[f,f1] is V15() set
{f,f1} is set
{f} is set
{{f,f1},{f}} is set
the Arrows of A1 . [f,f1] is set
F . f is M2( the carrier of A2)
the ObjectMap of F . (f,f) is M2([: the carrier of A2, the carrier of A2:])
[f,f] is V15() set
{f,f} is set
{{f,f},{f}} is set
the ObjectMap of F . [f,f] is set
( the ObjectMap of F . (f,f)) `1 is set
g1 is M2(<^f1,c1^>)
F . g1 is M2(<^(F . c1),(F . f1)^>)
<^(F . c1),(F . f1)^> is set
the Arrows of A2 . ((F . c1),(F . f1)) is set
[(F . c1),(F . f1)] is V15() set
{(F . c1),(F . f1)} is set
{(F . c1)} is set
{{(F . c1),(F . f1)},{(F . c1)}} is set
the Arrows of A2 . [(F . c1),(F . f1)] is set
f1 is M2(<^f,f1^>)
F . f1 is M2(<^(F . f1),(F . f)^>)
<^(F . f1),(F . f)^> is set
the Arrows of A2 . ((F . f1),(F . f)) is set
[(F . f1),(F . f)] is V15() set
{(F . f1),(F . f)} is set
{(F . f1)} is set
{{(F . f1),(F . f)},{(F . f1)}} is set
the Arrows of A2 . [(F . f1),(F . f)] is set
<^G,c^> is set
the Arrows of B1 . (G,c) is set
[G,c] is V15() set
{G,c} is set
{{G,c},{G}} is set
the Arrows of B1 . [G,c] is set
c1 * b1 is M2(<^G,c^>)
g1 * f1 is M2(<^f,c1^>)
<^f,c1^> is set
the Arrows of A1 . (f,c1) is set
[f,c1] is V15() set
{f,c1} is set
{{f,c1},{f}} is set
the Arrows of A1 . [f,c1] is set
(A1,A2,B1,F) . (c1 * b1) is M2(<^((A1,A2,B1,F) . c),((A1,A2,B1,F) . G)^>)
<^((A1,A2,B1,F) . c),((A1,A2,B1,F) . G)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . c),((A1,A2,B1,F) . G)) is set
[((A1,A2,B1,F) . c),((A1,A2,B1,F) . G)] is V15() set
{((A1,A2,B1,F) . c),((A1,A2,B1,F) . G)} is set
{{((A1,A2,B1,F) . c),((A1,A2,B1,F) . G)},{((A1,A2,B1,F) . c)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . c),((A1,A2,B1,F) . G)] is set
F . (g1 * f1) is M2(<^(F . c1),(F . f)^>)
<^(F . c1),(F . f)^> is set
the Arrows of A2 . ((F . c1),(F . f)) is set
[(F . c1),(F . f)] is V15() set
{(F . c1),(F . f)} is set
{{(F . c1),(F . f)},{(F . c1)}} is set
the Arrows of A2 . [(F . c1),(F . f)] is set
(F . f1) * (F . g1) is M2(<^(F . c1),(F . f)^>)
f9 * g9 is M2(<^c9,a9^>)
<^c9,a9^> is set
the Arrows of B2 . (c9,a9) is set
[c9,a9] is V15() set
{c9,a9} is set
{{c9,a9},{c9}} is set
the Arrows of B2 . [c9,a9] is set
b is M2( the carrier of B2)
G is M2( the carrier of B1)
(A1,A2,B1,F) . G is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (G,G) is M2([: the carrier of A2, the carrier of A2:])
[G,G] is V15() set
{G,G} is set
{G} is set
{{G,G},{G}} is set
the ObjectMap of (A1,A2,B1,F) . [G,G] is set
( the ObjectMap of (A1,A2,B1,F) . (G,G)) `1 is set
idm G is M2(<^G,G^>)
<^G,G^> is non empty set
the Arrows of B1 . (G,G) is set
the Arrows of B1 . [G,G] is set
(A1,A2,B1,F) . (idm G) is M2(<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)^>)
<^((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)^> is non empty set
the Arrows of A2 . (((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)) is set
[((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)] is V15() set
{((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)} is set
{((A1,A2,B1,F) . G)} is set
{{((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)},{((A1,A2,B1,F) . G)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . G),((A1,A2,B1,F) . G)] is set
c is M2( the carrier of A1)
idm c is M2(<^c,c^>)
<^c,c^> is non empty set
the Arrows of A1 . (c,c) is set
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the Arrows of A1 . [c,c] is set
F . (idm c) is M2(<^(F . c),(F . c)^>)
F . c is M2( the carrier of A2)
the ObjectMap of F . (c,c) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of F . [c,c] is set
( the ObjectMap of F . (c,c)) `1 is set
<^(F . c),(F . c)^> is non empty set
the Arrows of A2 . ((F . c),(F . c)) is set
[(F . c),(F . c)] is V15() set
{(F . c),(F . c)} is set
{(F . c)} is set
{{(F . c),(F . c)},{(F . c)}} is set
the Arrows of A2 . [(F . c),(F . c)] is set
idm (F . c) is M2(<^(F . c),(F . c)^>)
idm b is M2(<^b,b^>)
<^b,b^> is non empty set
the Arrows of B2 . (b,b) is set
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the Arrows of B2 . [b,b] is set
G is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of B1,B2
b is M2( the carrier of B1)
c is M2( the carrier of B1)
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
(A1,A2,B1,F) . c is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of (A1,A2,B1,F) . [c,c] is set
( the ObjectMap of (A1,A2,B1,F) . (c,c)) `1 is set
b1 is M2( the carrier of A1)
F . b1 is M2( the carrier of A2)
the ObjectMap of F . (b1,b1) is M2([: the carrier of A2, the carrier of A2:])
[b1,b1] is V15() set
{b1,b1} is set
{b1} is set
{{b1,b1},{b1}} is set
the ObjectMap of F . [b1,b1] is set
( the ObjectMap of F . (b1,b1)) `1 is set
c1 is M2( the carrier of A1)
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
b is M2( the carrier of B1)
c is M2( the carrier of A1)
G . b is M2( the carrier of B2)
the ObjectMap of G is Relation-like [: the carrier of B1, the carrier of B1:] -defined [: the carrier of B2, the carrier of B2:] -valued Function-like quasi_total M2( bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of B2, the carrier of B2:]:])
[:[: the carrier of B1, the carrier of B1:],[: the carrier of B2, the carrier of B2:]:] is Relation-like non empty set
bool [:[: the carrier of B1, the carrier of B1:],[: the carrier of B2, the carrier of B2:]:] is non empty set
the ObjectMap of G . (b,b) is M2([: the carrier of B2, the carrier of B2:])
[b,b] is V15() set
{b,b} is set
{b} is set
{{b,b},{b}} is set
the ObjectMap of G . [b,b] is set
( the ObjectMap of G . (b,b)) `1 is set
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
F . c is M2( the carrier of A2)
the ObjectMap of F . (c,c) is M2([: the carrier of A2, the carrier of A2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of F . [c,c] is set
( the ObjectMap of F . (c,c)) `1 is set
b is M2( the carrier of B1)
c is M2( the carrier of B1)
<^b,c^> is set
the Arrows of B1 . (b,c) is set
[b,c] is V15() set
{b,c} is set
{b} is set
{{b,c},{b}} is set
the Arrows of B1 . [b,c] is set
b1 is M2( the carrier of A1)
c1 is M2( the carrier of A1)
<^b1,c1^> is set
the Arrows of A1 . (b1,c1) is set
[b1,c1] is V15() set
{b1,c1} is set
{b1} is set
{{b1,c1},{b1}} is set
the Arrows of A1 . [b1,c1] is set
Morph-Map (F,b1,c1) is Relation-like Function-like set
the MorphMap of F is Relation-like [: the carrier of A1, the carrier of A1:] -defined Function-like non empty total Function-yielding V37() MSUnTrans of the ObjectMap of F, the Arrows of A1, the Arrows of A2
the MorphMap of F . (b1,c1) is Relation-like Function-like set
the MorphMap of F . [b1,c1] is Relation-like Function-like set
f is M2(<^b,c^>)
G . f is M2(<^(G . c),(G . b)^>)
G . c is M2( the carrier of B2)
the ObjectMap of G . (c,c) is M2([: the carrier of B2, the carrier of B2:])
[c,c] is V15() set
{c,c} is set
{c} is set
{{c,c},{c}} is set
the ObjectMap of G . [c,c] is set
( the ObjectMap of G . (c,c)) `1 is set
G . b is M2( the carrier of B2)
the ObjectMap of G . (b,b) is M2([: the carrier of B2, the carrier of B2:])
[b,b] is V15() set
{b,b} is set
{{b,b},{b}} is set
the ObjectMap of G . [b,b] is set
( the ObjectMap of G . (b,b)) `1 is set
<^(G . c),(G . b)^> is set
the Arrows of B2 . ((G . c),(G . b)) is set
[(G . c),(G . b)] is V15() set
{(G . c),(G . b)} is set
{(G . c)} is set
{{(G . c),(G . b)},{(G . c)}} is set
the Arrows of B2 . [(G . c),(G . b)] is set
f1 is M2(<^b1,c1^>)
(Morph-Map (F,b1,c1)) . f1 is set
F . c1 is M2( the carrier of A2)
the ObjectMap of F . (c1,c1) is M2([: the carrier of A2, the carrier of A2:])
[c1,c1] is V15() set
{c1,c1} is set
{c1} is set
{{c1,c1},{c1}} is set
the ObjectMap of F . [c1,c1] is set
( the ObjectMap of F . (c1,c1)) `1 is set
F . b1 is M2( the carrier of A2)
the ObjectMap of F . (b1,b1) is M2([: the carrier of A2, the carrier of A2:])
[b1,b1] is V15() set
{b1,b1} is set
{{b1,b1},{b1}} is set
the ObjectMap of F . [b1,b1] is set
( the ObjectMap of F . (b1,b1)) `1 is set
<^(F . c1),(F . b1)^> is set
the Arrows of A2 . ((F . c1),(F . b1)) is set
[(F . c1),(F . b1)] is V15() set
{(F . c1),(F . b1)} is set
{(F . c1)} is set
{{(F . c1),(F . b1)},{(F . c1)}} is set
the Arrows of A2 . [(F . c1),(F . b1)] is set
(A1,A2,B1,F) . f is M2(<^((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)^>)
(A1,A2,B1,F) . c is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (c,c) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (A1,A2,B1,F) . [c,c] is set
( the ObjectMap of (A1,A2,B1,F) . (c,c)) `1 is set
(A1,A2,B1,F) . b is M2( the carrier of A2)
the ObjectMap of (A1,A2,B1,F) . (b,b) is M2([: the carrier of A2, the carrier of A2:])
the ObjectMap of (A1,A2,B1,F) . [b,b] is set
( the ObjectMap of (A1,A2,B1,F) . (b,b)) `1 is set
<^((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)^> is set
the Arrows of A2 . (((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)) is set
[((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)] is V15() set
{((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)} is set
{((A1,A2,B1,F) . c)} is set
{{((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)},{((A1,A2,B1,F) . c)}} is set
the Arrows of A2 . [((A1,A2,B1,F) . c),((A1,A2,B1,F) . b)] is set
F . f1 is M2(<^(F . c1),(F . b1)^>)
Morph-Map (F,b1,c1) is Relation-like <^b1,c1^> -defined <^(F . c1),(F . b1)^> -valued Function-like quasi_total M2( bool [:<^b1,c1^>,<^(F . c1),(F . b1)^>:])
[:<^b1,c1^>,<^(F . c1),(F . b1)^>:] is Relation-like set
bool [:<^b1,c1^>,<^(F . c1),(F . b1)^>:] is non empty set
(Morph-Map (F,b1,c1)) . f1 is set