:: YELLOW18 semantic presentation

NAT is non empty V15() V16() V17() Element of bool REAL
REAL is set
bool REAL is non empty set
NAT is non empty V15() V16() V17() set
bool NAT is non empty set
bool NAT is non empty set
K145() is Element of bool NAT
[:NAT,K145():] is Relation-like set
bool [:NAT,K145():] is non empty set
{} is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() Function-yielding V63() set
the Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() Function-yielding V63() set is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() Function-yielding V63() set
1 is non empty set
{{},1} is non empty set
F₁() is non empty set
[:F₁(),F₁():] is Relation-like non empty set
A is Relation-like [:F₁(),F₁():] -defined Function-like non empty V14([:F₁(),F₁():]) set
{|A,A|} is Relation-like [:F₁(),F₁(),F₁():] -defined Function-like non empty V14([:F₁(),F₁(),F₁():]) set
[:F₁(),F₁(),F₁():] is non empty set
{|A|} is Relation-like [:F₁(),F₁(),F₁():] -defined Function-like non empty V14([:F₁(),F₁(),F₁():]) set
c₂ is set
FF is set
a is set
b is set
[FF,a,b] is V22() V23() set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
[[FF,a],b] is V22() set
{[FF,a],b} is non empty set
{[FF,a]} is Relation-like Function-like non empty set
{{[FF,a],b},{[FF,a]}} is non empty set
c is Element of F₁()
d is Element of F₁()
f is Element of F₁()
F₂(d,f) is set
F₂(c,d) is set
[:F₂(d,f),F₂(c,d):] is Relation-like set
F₂(c,f) is set
fa is set
fb is set
g is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
F₃(c,d,f,g,fb) is set
g is set
fa is Relation-like Function-like set
proj1 fa is set
proj2 fa is set
A . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
A . [c,d] is set
A . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
A . [d,f] is set
A . (c,f) is set
[c,f] is V22() set
{c,f} is non empty set
{{c,f},{c}} is non empty set
A . [c,f] is set
{|A,A|} . (c,d,f) is set
{|A|} . (c,d,f) is set
[:({|A,A|} . (c,d,f)),({|A|} . (c,d,f)):] is Relation-like set
bool [:({|A,A|} . (c,d,f)),({|A|} . (c,d,f)):] is non empty set
fb is Relation-like {|A,A|} . (c,d,f) -defined {|A|} . (c,d,f) -valued Function-like quasi_total Element of bool [:({|A,A|} . (c,d,f)),({|A|} . (c,d,f)):]
g is Relation-like {|A,A|} . (c,d,f) -defined {|A|} . (c,d,f) -valued Function-like quasi_total Element of bool [:({|A,A|} . (c,d,f)),({|A|} . (c,d,f)):]
[c,d,f] is V22() V23() set
[[c,d],f] is V22() set
{[c,d],f} is non empty set
{[c,d]} is Relation-like Function-like non empty set
{{[c,d],f},{[c,d]}} is non empty set
g is set
c₁₃ is set
[c₁₃,g] is V22() set
{c₁₃,g} is non empty set
{c₁₃} is non empty set
{{c₁₃,g},{c₁₃}} is non empty set
fb . [c₁₃,g] is set
F₃(c,d,f,g,c₁₃) is set
a1 is set
g9 is set
[a1,g9] is V22() set
{a1,g9} is non empty set
{a1} is non empty set
{{a1,g9},{a1}} is non empty set
F₃(c,d,f,g9,a1) is set
c₂ is Relation-like Function-like set
proj1 c₂ is set
a is set
FF is Relation-like [:F₁(),F₁(),F₁():] -defined Function-like non empty V14([:F₁(),F₁(),F₁():]) set
FF . a is set
b is Element of F₁()
c is Element of F₁()
d is Element of F₁()
{|A,A|} . (b,c,d) is set
{|A|} . (b,c,d) is set
[:({|A,A|} . (b,c,d)),({|A|} . (b,c,d)):] is Relation-like set
bool [:({|A,A|} . (b,c,d)),({|A|} . (b,c,d)):] is non empty set
[b,c,d] is V22() V23() set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
[[b,c],d] is V22() set
{[b,c],d} is non empty set
{[b,c]} is Relation-like Function-like non empty set
{{[b,c],d},{[b,c]}} is non empty set
f is Relation-like {|A,A|} . (b,c,d) -defined {|A|} . (b,c,d) -valued Function-like quasi_total Element of bool [:({|A,A|} . (b,c,d)),({|A|} . (b,c,d)):]
F₂(b,c) is set
F₂(c,d) is set
{|A|} . a is set
{|A,A|} . a is set
[:({|A,A|} . a),({|A|} . a):] is Relation-like set
bool [:({|A,A|} . a),({|A|} . a):] is non empty set
a is Relation-like [:F₁(),F₁(),F₁():] -defined Function-like non empty V14([:F₁(),F₁(),F₁():]) Function-yielding V63() ManySortedFunction of {|A,A|},{|A|}
AltCatStr(# F₁(),A,a #) is non empty strict AltCatStr
the carrier of AltCatStr(# F₁(),A,a #) is non empty set
c is Element of the carrier of AltCatStr(# F₁(),A,a #)
d is Element of the carrier of AltCatStr(# F₁(),A,a #)
<^c,d^> is set
the Arrows of AltCatStr(# F₁(),A,a #) is Relation-like [: the carrier of AltCatStr(# F₁(),A,a #), the carrier of AltCatStr(# F₁(),A,a #):] -defined Function-like non empty V14([: the carrier of AltCatStr(# F₁(),A,a #), the carrier of AltCatStr(# F₁(),A,a #):]) set
[: the carrier of AltCatStr(# F₁(),A,a #), the carrier of AltCatStr(# F₁(),A,a #):] is Relation-like non empty set
the Arrows of AltCatStr(# F₁(),A,a #) . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
the Arrows of AltCatStr(# F₁(),A,a #) . [c,d] is set
f is Element of the carrier of AltCatStr(# F₁(),A,a #)
<^d,f^> is set
the Arrows of AltCatStr(# F₁(),A,a #) . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of AltCatStr(# F₁(),A,a #) . [d,f] is set
<^c,f^> is set
the Arrows of AltCatStr(# F₁(),A,a #) . (c,f) is set
[c,f] is V22() set
{c,f} is non empty set
{{c,f},{c}} is non empty set
the Arrows of AltCatStr(# F₁(),A,a #) . [c,f] is set
the Element of <^c,d^> is Element of <^c,d^>
the Element of <^d,f^> is Element of <^d,f^>
fa is Element of F₁()
fb is Element of F₁()
F₂(fa,fb) is set
g is Element of F₁()
F₂(fb,g) is set
F₃(fa,fb,g, the Element of <^c,d^>, the Element of <^d,f^>) is set
F₂(fa,g) is set
c is non empty transitive strict AltCatStr
the carrier of c is non empty set
d is Element of the carrier of c
f is Element of the carrier of c
<^d,f^> is set
the Arrows of c is Relation-like [: the carrier of c, the carrier of c:] -defined Function-like non empty V14([: the carrier of c, the carrier of c:]) set
[: the carrier of c, the carrier of c:] is Relation-like non empty set
the Arrows of c . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of c . [d,f] is set
F₂(d,f) is set
d is Element of the carrier of c
f is Element of the carrier of c
<^d,f^> is set
the Arrows of c is Relation-like [: the carrier of c, the carrier of c:] -defined Function-like non empty V14([: the carrier of c, the carrier of c:]) set
[: the carrier of c, the carrier of c:] is Relation-like non empty set
the Arrows of c . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of c . [d,f] is set
fa is Element of the carrier of c
<^f,fa^> is set
the Arrows of c . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of c . [f,fa] is set
[d,f,fa] is V22() V23() set
[[d,f],fa] is V22() set
{[d,f],fa} is non empty set
{[d,f]} is Relation-like Function-like non empty set
{{[d,f],fa},{[d,f]}} is non empty set
a . [d,f,fa] is Relation-like Function-like set
fb is Element of F₁()
g is Element of F₁()
g is Element of F₁()
{|A,A|} . (fb,g,g) is set
{|A|} . (fb,g,g) is set
[:({|A,A|} . (fb,g,g)),({|A|} . (fb,g,g)):] is Relation-like set
bool [:({|A,A|} . (fb,g,g)),({|A|} . (fb,g,g)):] is non empty set
[fb,g,g] is V22() V23() set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
[[fb,g],g] is V22() set
{[fb,g],g} is non empty set
{[fb,g]} is Relation-like Function-like non empty set
{{[fb,g],g},{[fb,g]}} is non empty set
c₁₃ is Relation-like {|A,A|} . (fb,g,g) -defined {|A|} . (fb,g,g) -valued Function-like quasi_total Element of bool [:({|A,A|} . (fb,g,g)),({|A|} . (fb,g,g)):]
F₂(fb,g) is set
F₂(g,g) is set
g9 is Element of <^d,f^>
a1 is Element of <^f,fa^>
a1 * g9 is Element of <^d,fa^>
<^d,fa^> is set
the Arrows of c . (d,fa) is set
[d,fa] is V22() set
{d,fa} is non empty set
{{d,fa},{d}} is non empty set
the Arrows of c . [d,fa] is set
F₃(d,f,fa,g9,a1) is set
F₂(d,f) is set
F₂(f,fa) is set
[a1,g9] is V22() set
{a1,g9} is non empty set
{a1} is non empty set
{{a1,g9},{a1}} is non empty set
c₁₃ . [a1,g9] is set
the Comp of c is Relation-like [: the carrier of c, the carrier of c, the carrier of c:] -defined Function-like non empty V14([: the carrier of c, the carrier of c, the carrier of c:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c, the Arrows of c|},{| the Arrows of c|}
[: the carrier of c, the carrier of c, the carrier of c:] is non empty set
{| the Arrows of c, the Arrows of c|} is Relation-like [: the carrier of c, the carrier of c, the carrier of c:] -defined Function-like non empty V14([: the carrier of c, the carrier of c, the carrier of c:]) set
{| the Arrows of c|} is Relation-like [: the carrier of c, the carrier of c, the carrier of c:] -defined Function-like non empty V14([: the carrier of c, the carrier of c, the carrier of c:]) set
the Comp of c . (d,f,fa) is Relation-like [:( the Arrows of c . (f,fa)),( the Arrows of c . (d,f)):] -defined the Arrows of c . (d,fa) -valued Function-like quasi_total Element of bool [:[:( the Arrows of c . (f,fa)),( the Arrows of c . (d,f)):],( the Arrows of c . (d,fa)):]
[:( the Arrows of c . (f,fa)),( the Arrows of c . (d,f)):] is Relation-like set
[:[:( the Arrows of c . (f,fa)),( the Arrows of c . (d,f)):],( the Arrows of c . (d,fa)):] is Relation-like set
bool [:[:( the Arrows of c . (f,fa)),( the Arrows of c . (d,f)):],( the Arrows of c . (d,fa)):] is non empty set
( the Comp of c . (d,f,fa)) . (a1,g9) is set
( the Comp of c . (d,f,fa)) . [a1,g9] is set
F₁() is non empty transitive AltCatStr
the carrier of F₁() is non empty set
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
A is Element of the carrier of F₁()
c₂ is Element of the carrier of F₁()
the Arrows of F₁() . (A,c₂) is set
[A,c₂] is V22() set
{A,c₂} is non empty set
{A} is non empty set
{{A,c₂},{A}} is non empty set
the Arrows of F₁() . [A,c₂] is set
FF is Element of the carrier of F₁()
the Arrows of F₁() . (c₂,FF) is set
[c₂,FF] is V22() set
{c₂,FF} is non empty set
{c₂} is non empty set
{{c₂,FF},{c₂}} is non empty set
the Arrows of F₁() . [c₂,FF] is set
a is Element of the carrier of F₁()
the Arrows of F₁() . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of F₁() . [FF,a] is set
the Comp of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) Function-yielding V63() ManySortedFunction of {| the Arrows of F₁(), the Arrows of F₁()|},{| the Arrows of F₁()|}
[: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] is non empty set
{| the Arrows of F₁(), the Arrows of F₁()|} is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) set
{| the Arrows of F₁()|} is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) set
the Comp of F₁() . (A,FF,a) is Relation-like [:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (A,FF)):] -defined the Arrows of F₁() . (A,a) -valued Function-like quasi_total Element of bool [:[:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (A,FF)):],( the Arrows of F₁() . (A,a)):]
the Arrows of F₁() . (A,FF) is set
[A,FF] is V22() set
{A,FF} is non empty set
{{A,FF},{A}} is non empty set
the Arrows of F₁() . [A,FF] is set
[:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (A,FF)):] is Relation-like set
the Arrows of F₁() . (A,a) is set
[A,a] is V22() set
{A,a} is non empty set
{{A,a},{A}} is non empty set
the Arrows of F₁() . [A,a] is set
[:[:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (A,FF)):],( the Arrows of F₁() . (A,a)):] is Relation-like set
bool [:[:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (A,FF)):],( the Arrows of F₁() . (A,a)):] is non empty set
the Comp of F₁() . (A,c₂,FF) is Relation-like [:( the Arrows of F₁() . (c₂,FF)),( the Arrows of F₁() . (A,c₂)):] -defined the Arrows of F₁() . (A,FF) -valued Function-like quasi_total Element of bool [:[:( the Arrows of F₁() . (c₂,FF)),( the Arrows of F₁() . (A,c₂)):],( the Arrows of F₁() . (A,FF)):]
[:( the Arrows of F₁() . (c₂,FF)),( the Arrows of F₁() . (A,c₂)):] is Relation-like set
[:[:( the Arrows of F₁() . (c₂,FF)),( the Arrows of F₁() . (A,c₂)):],( the Arrows of F₁() . (A,FF)):] is Relation-like set
bool [:[:( the Arrows of F₁() . (c₂,FF)),( the Arrows of F₁() . (A,c₂)):],( the Arrows of F₁() . (A,FF)):] is non empty set
the Comp of F₁() . (A,c₂,a) is Relation-like [:( the Arrows of F₁() . (c₂,a)),( the Arrows of F₁() . (A,c₂)):] -defined the Arrows of F₁() . (A,a) -valued Function-like quasi_total Element of bool [:[:( the Arrows of F₁() . (c₂,a)),( the Arrows of F₁() . (A,c₂)):],( the Arrows of F₁() . (A,a)):]
the Arrows of F₁() . (c₂,a) is set
[c₂,a] is V22() set
{c₂,a} is non empty set
{{c₂,a},{c₂}} is non empty set
the Arrows of F₁() . [c₂,a] is set
[:( the Arrows of F₁() . (c₂,a)),( the Arrows of F₁() . (A,c₂)):] is Relation-like set
[:[:( the Arrows of F₁() . (c₂,a)),( the Arrows of F₁() . (A,c₂)):],( the Arrows of F₁() . (A,a)):] is Relation-like set
bool [:[:( the Arrows of F₁() . (c₂,a)),( the Arrows of F₁() . (A,c₂)):],( the Arrows of F₁() . (A,a)):] is non empty set
the Comp of F₁() . (c₂,FF,a) is Relation-like [:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (c₂,FF)):] -defined the Arrows of F₁() . (c₂,a) -valued Function-like quasi_total Element of bool [:[:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (c₂,FF)):],( the Arrows of F₁() . (c₂,a)):]
[:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (c₂,FF)):] is Relation-like set
[:[:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (c₂,FF)):],( the Arrows of F₁() . (c₂,a)):] is Relation-like set
bool [:[:( the Arrows of F₁() . (FF,a)),( the Arrows of F₁() . (c₂,FF)):],( the Arrows of F₁() . (c₂,a)):] is non empty set
g is set
c₁₃ is set
g9 is set
( the Comp of F₁() . (A,c₂,FF)) . (c₁₃,g) is set
[c₁₃,g] is V22() set
{c₁₃,g} is non empty set
{c₁₃} is non empty set
{{c₁₃,g},{c₁₃}} is non empty set
( the Comp of F₁() . (A,c₂,FF)) . [c₁₃,g] is set
( the Comp of F₁() . (A,FF,a)) . (g9,(( the Comp of F₁() . (A,c₂,FF)) . (c₁₃,g))) is set
[g9,(( the Comp of F₁() . (A,c₂,FF)) . (c₁₃,g))] is V22() set
{g9,(( the Comp of F₁() . (A,c₂,FF)) . (c₁₃,g))} is non empty set
{g9} is non empty set
{{g9,(( the Comp of F₁() . (A,c₂,FF)) . (c₁₃,g))},{g9}} is non empty set
( the Comp of F₁() . (A,FF,a)) . [g9,(( the Comp of F₁() . (A,c₂,FF)) . (c₁₃,g))] is set
( the Comp of F₁() . (c₂,FF,a)) . (g9,c₁₃) is set
[g9,c₁₃] is V22() set
{g9,c₁₃} is non empty set
{{g9,c₁₃},{g9}} is non empty set
( the Comp of F₁() . (c₂,FF,a)) . [g9,c₁₃] is set
( the Comp of F₁() . (A,c₂,a)) . ((( the Comp of F₁() . (c₂,FF,a)) . (g9,c₁₃)),g) is set
[(( the Comp of F₁() . (c₂,FF,a)) . (g9,c₁₃)),g] is V22() set
{(( the Comp of F₁() . (c₂,FF,a)) . (g9,c₁₃)),g} is non empty set
{(( the Comp of F₁() . (c₂,FF,a)) . (g9,c₁₃))} is non empty set
{{(( the Comp of F₁() . (c₂,FF,a)) . (g9,c₁₃)),g},{(( the Comp of F₁() . (c₂,FF,a)) . (g9,c₁₃))}} is non empty set
( the Comp of F₁() . (A,c₂,a)) . [(( the Comp of F₁() . (c₂,FF,a)) . (g9,c₁₃)),g] is set
f is Element of the carrier of F₁()
fa is Element of the carrier of F₁()
<^f,fa^> is set
the Arrows of F₁() . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of F₁() . [f,fa] is set
fb is Element of the carrier of F₁()
<^fa,fb^> is set
the Arrows of F₁() . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of F₁() . [fa,fb] is set
g is Element of the carrier of F₁()
<^fb,g^> is set
the Arrows of F₁() . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of F₁() . [fb,g] is set
<^f,fb^> is set
the Arrows of F₁() . (f,fb) is set
[f,fb] is V22() set
{f,fb} is non empty set
{{f,fb},{f}} is non empty set
the Arrows of F₁() . [f,fb] is set
<^fa,g^> is set
the Arrows of F₁() . (fa,g) is set
[fa,g] is V22() set
{fa,g} is non empty set
{{fa,g},{fa}} is non empty set
the Arrows of F₁() . [fa,g] is set
a1 is Element of <^f,fa^>
b1 is Element of <^fa,fb^>
b1 * a1 is Element of <^f,fb^>
( the Comp of F₁() . (A,FF,a)) . (g9,(b1 * a1)) is set
[g9,(b1 * a1)] is V22() set
{g9,(b1 * a1)} is non empty set
{{g9,(b1 * a1)},{g9}} is non empty set
( the Comp of F₁() . (A,FF,a)) . [g9,(b1 * a1)] is set
f1 is Element of <^fb,g^>
f1 * (b1 * a1) is Element of <^f,g^>
<^f,g^> is set
the Arrows of F₁() . (f,g) is set
[f,g] is V22() set
{f,g} is non empty set
{{f,g},{f}} is non empty set
the Arrows of F₁() . [f,g] is set
F₂(A,FF,a,(b1 * a1),f1) is set
F₂(A,c₂,FF,g,c₁₃) is set
F₂(A,FF,a,F₂(A,c₂,FF,g,c₁₃),g9) is set
F₂(fa,fb,g,c₁₃,g9) is set
F₂(f,fa,g,g,F₂(fa,fb,g,c₁₃,g9)) is set
f1 * b1 is Element of <^fa,g^>
F₂(f,fa,g,g,(f1 * b1)) is set
(f1 * b1) * a1 is Element of <^f,g^>
( the Comp of F₁() . (A,c₂,a)) . ((f1 * b1),g) is set
[(f1 * b1),g] is V22() set
{(f1 * b1),g} is non empty set
{(f1 * b1)} is non empty set
{{(f1 * b1),g},{(f1 * b1)}} is non empty set
( the Comp of F₁() . (A,c₂,a)) . [(f1 * b1),g] is set
F₁() is non empty transitive AltCatStr
the carrier of F₁() is non empty set
the Comp of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) Function-yielding V63() ManySortedFunction of {| the Arrows of F₁(), the Arrows of F₁()|},{| the Arrows of F₁()|}
[: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] is non empty set
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
{| the Arrows of F₁(), the Arrows of F₁()|} is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) set
{| the Arrows of F₁()|} is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) set
b is Element of the carrier of F₁()
c is Element of the carrier of F₁()
<^c,c^> is set
the Arrows of F₁() . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of F₁() . [c,c] is set
d is set
f is set
the Arrows of F₁() . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of F₁() . [b,b] is set
fb is set
fa is Element of the carrier of F₁()
the Arrows of F₁() . (fa,b) is set
[fa,b] is V22() set
{fa,b} is non empty set
{fa} is non empty set
{{fa,b},{fa}} is non empty set
the Arrows of F₁() . [fa,b] is set
g is Element of the carrier of F₁()
<^g,c^> is set
the Arrows of F₁() . (g,c) is set
[g,c] is V22() set
{g,c} is non empty set
{g} is non empty set
{{g,c},{g}} is non empty set
the Arrows of F₁() . [g,c] is set
F₂(fa,b,b,fb,f) is set
the Comp of F₁() . (fa,b,b) is Relation-like [:( the Arrows of F₁() . (b,b)),( the Arrows of F₁() . (fa,b)):] -defined the Arrows of F₁() . (fa,b) -valued Function-like quasi_total Element of bool [:[:( the Arrows of F₁() . (b,b)),( the Arrows of F₁() . (fa,b)):],( the Arrows of F₁() . (fa,b)):]
[:( the Arrows of F₁() . (b,b)),( the Arrows of F₁() . (fa,b)):] is Relation-like set
[:[:( the Arrows of F₁() . (b,b)),( the Arrows of F₁() . (fa,b)):],( the Arrows of F₁() . (fa,b)):] is Relation-like set
bool [:[:( the Arrows of F₁() . (b,b)),( the Arrows of F₁() . (fa,b)):],( the Arrows of F₁() . (fa,b)):] is non empty set
( the Comp of F₁() . (fa,b,b)) . (f,fb) is set
[f,fb] is V22() set
{f,fb} is non empty set
{f} is non empty set
{{f,fb},{f}} is non empty set
( the Comp of F₁() . (fa,b,b)) . [f,fb] is set
c₁₃ is Element of <^g,c^>
g is Element of <^c,c^>
g * c₁₃ is Element of <^g,c^>
b is Element of the carrier of F₁()
the Arrows of F₁() . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of F₁() . [b,b] is set
c is Element of the carrier of F₁()
<^c,c^> is set
the Arrows of F₁() . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of F₁() . [c,c] is set
d is set
fa is Element of the carrier of F₁()
the Arrows of F₁() . (b,fa) is set
[b,fa] is V22() set
{b,fa} is non empty set
{{b,fa},{b}} is non empty set
the Arrows of F₁() . [b,fa] is set
the Comp of F₁() . (b,b,fa) is Relation-like [:( the Arrows of F₁() . (b,fa)),( the Arrows of F₁() . (b,b)):] -defined the Arrows of F₁() . (b,fa) -valued Function-like quasi_total Element of bool [:[:( the Arrows of F₁() . (b,fa)),( the Arrows of F₁() . (b,b)):],( the Arrows of F₁() . (b,fa)):]
[:( the Arrows of F₁() . (b,fa)),( the Arrows of F₁() . (b,b)):] is Relation-like set
[:[:( the Arrows of F₁() . (b,fa)),( the Arrows of F₁() . (b,b)):],( the Arrows of F₁() . (b,fa)):] is Relation-like set
bool [:[:( the Arrows of F₁() . (b,fa)),( the Arrows of F₁() . (b,b)):],( the Arrows of F₁() . (b,fa)):] is non empty set
fb is set
( the Comp of F₁() . (b,b,fa)) . (fb,d) is set
[fb,d] is V22() set
{fb,d} is non empty set
{fb} is non empty set
{{fb,d},{fb}} is non empty set
( the Comp of F₁() . (b,b,fa)) . [fb,d] is set
g is Element of the carrier of F₁()
<^c,g^> is set
the Arrows of F₁() . (c,g) is set
[c,g] is V22() set
{c,g} is non empty set
{{c,g},{c}} is non empty set
the Arrows of F₁() . [c,g] is set
F₂(b,b,fa,d,fb) is set
f is Element of <^c,c^>
g is Element of <^c,g^>
g * f is Element of <^c,g^>
F₁() is non empty set
a is set
A is Element of F₁()
c₂ is Element of F₁()
F₂(A,c₂) is set
b is set
FF is Element of F₁()
F₂(c₂,FF) is set
F₃(A,c₂,FF,a,b) is set
F₂(A,FF) is set
A is non empty transitive strict AltCatStr
the carrier of A is non empty set
c₂ is Element of the carrier of A
FF is Element of the carrier of A
<^c₂,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c₂,FF) is set
[c₂,FF] is V22() set
{c₂,FF} is non empty set
{c₂} is non empty set
{{c₂,FF},{c₂}} is non empty set
the Arrows of A . [c₂,FF] is set
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
b is Element of the carrier of A
<^a,b^> is set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
c is set
d is set
f is set
F₃(c₂,FF,a,c,d) is set
F₃(c₂,a,b,H₁(c₂,FF,a,c,d),f) is set
F₃(FF,a,b,d,f) is set
F₃(c₂,FF,b,c,H₁(FF,a,b,d,f)) is set
F₂(c₂,FF) is set
F₂(FF,a) is set
F₂(a,b) is set
c₂ is Element of the carrier of A
<^c₂,c₂^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c₂,c₂) is set
[c₂,c₂] is V22() set
{c₂,c₂} is non empty set
{c₂} is non empty set
{{c₂,c₂},{c₂}} is non empty set
the Arrows of A . [c₂,c₂] is set
F₂(c₂,c₂) is set
FF is set
a is Element of the carrier of A
<^c₂,a^> is set
the Arrows of A . (c₂,a) is set
[c₂,a] is V22() set
{c₂,a} is non empty set
{{c₂,a},{c₂}} is non empty set
the Arrows of A . [c₂,a] is set
F₂(c₂,a) is set
b is set
F₃(c₂,c₂,a,FF,b) is set
c₂ is Element of the carrier of A
<^c₂,c₂^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c₂,c₂) is set
[c₂,c₂] is V22() set
{c₂,c₂} is non empty set
{c₂} is non empty set
{{c₂,c₂},{c₂}} is non empty set
the Arrows of A . [c₂,c₂] is set
F₂(c₂,c₂) is set
FF is set
a is Element of the carrier of A
<^a,c₂^> is set
the Arrows of A . (a,c₂) is set
[a,c₂] is V22() set
{a,c₂} is non empty set
{a} is non empty set
{{a,c₂},{a}} is non empty set
the Arrows of A . [a,c₂] is set
F₂(a,c₂) is set
b is set
F₃(a,c₂,c₂,b,FF) is set
F₁() is non empty set
A is non empty transitive AltCatStr
the carrier of A is non empty set
c₂ is non empty transitive AltCatStr
the carrier of c₂ is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
AltCatStr(# the carrier of A, the Arrows of A, the Comp of A #) is non empty strict AltCatStr
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the Comp of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂, the carrier of c₂:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c₂, the Arrows of c₂|},{| the Arrows of c₂|}
[: the carrier of c₂, the carrier of c₂, the carrier of c₂:] is non empty set
{| the Arrows of c₂, the Arrows of c₂|} is Relation-like [: the carrier of c₂, the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂, the carrier of c₂:]) set
{| the Arrows of c₂|} is Relation-like [: the carrier of c₂, the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂, the carrier of c₂:]) set
AltCatStr(# the carrier of c₂, the Arrows of c₂, the Comp of c₂ #) is non empty strict AltCatStr
FF is set
[:F₁(),F₁():] is Relation-like non empty set
a is set
b is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . FF is set
c is Element of the carrier of A
d is Element of the carrier of A
<^c,d^> is set
the Arrows of A . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
the Arrows of A . [c,d] is set
F₂(c,d) is set
f is Element of the carrier of c₂
fa is Element of the carrier of c₂
<^f,fa^> is set
the Arrows of c₂ . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of c₂ . [f,fa] is set
the Arrows of c₂ . FF is set
FF is set
[:F₁(),F₁(),F₁():] is non empty set
a is set
b is set
c is set
[a,b,c] is V22() V23() set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
[[a,b],c] is V22() set
{[a,b],c} is non empty set
{[a,b]} is Relation-like Function-like non empty set
{{[a,b],c},{[a,b]}} is non empty set
the Comp of A . FF is Relation-like Function-like set
d is Element of the carrier of A
f is Element of the carrier of A
fa is Element of the carrier of A
the Comp of A . (d,f,fa) is Relation-like [:( the Arrows of A . (f,fa)),( the Arrows of A . (d,f)):] -defined the Arrows of A . (d,fa) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (f,fa)),( the Arrows of A . (d,f)):],( the Arrows of A . (d,fa)):]
the Arrows of A . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of A . [f,fa] is set
the Arrows of A . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of A . [d,f] is set
[:( the Arrows of A . (f,fa)),( the Arrows of A . (d,f)):] is Relation-like set
the Arrows of A . (d,fa) is set
[d,fa] is V22() set
{d,fa} is non empty set
{{d,fa},{d}} is non empty set
the Arrows of A . [d,fa] is set
[:[:( the Arrows of A . (f,fa)),( the Arrows of A . (d,f)):],( the Arrows of A . (d,fa)):] is Relation-like set
bool [:[:( the Arrows of A . (f,fa)),( the Arrows of A . (d,f)):],( the Arrows of A . (d,fa)):] is non empty set
the Comp of c₂ . FF is Relation-like Function-like set
fb is Element of the carrier of c₂
g is Element of the carrier of c₂
g is Element of the carrier of c₂
the Comp of c₂ . (fb,g,g) is Relation-like [:( the Arrows of c₂ . (g,g)),( the Arrows of c₂ . (fb,g)):] -defined the Arrows of c₂ . (fb,g) -valued Function-like quasi_total Element of bool [:[:( the Arrows of c₂ . (g,g)),( the Arrows of c₂ . (fb,g)):],( the Arrows of c₂ . (fb,g)):]
the Arrows of c₂ . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of c₂ . [g,g] is set
the Arrows of c₂ . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of c₂ . [fb,g] is set
[:( the Arrows of c₂ . (g,g)),( the Arrows of c₂ . (fb,g)):] is Relation-like set
the Arrows of c₂ . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of c₂ . [fb,g] is set
[:[:( the Arrows of c₂ . (g,g)),( the Arrows of c₂ . (fb,g)):],( the Arrows of c₂ . (fb,g)):] is Relation-like set
bool [:[:( the Arrows of c₂ . (g,g)),( the Arrows of c₂ . (fb,g)):],( the Arrows of c₂ . (fb,g)):] is non empty set
<^f,fa^> is set
<^d,f^> is set
[:<^f,fa^>,<^d,f^>:] is Relation-like set
<^d,fa^> is set
dom ( the Comp of A . (d,f,fa)) is Relation-like the Arrows of A . (f,fa) -defined the Arrows of A . (d,f) -valued Element of bool [:( the Arrows of A . (f,fa)),( the Arrows of A . (d,f)):]
bool [:( the Arrows of A . (f,fa)),( the Arrows of A . (d,f)):] is non empty set
dom ( the Comp of c₂ . (fb,g,g)) is Relation-like the Arrows of c₂ . (g,g) -defined the Arrows of c₂ . (fb,g) -valued Element of bool [:( the Arrows of c₂ . (g,g)),( the Arrows of c₂ . (fb,g)):]
bool [:( the Arrows of c₂ . (g,g)),( the Arrows of c₂ . (fb,g)):] is non empty set
c₁₃ is set
g9 is set
a1 is set
[g9,a1] is V22() set
{g9,a1} is non empty set
{g9} is non empty set
{{g9,a1},{g9}} is non empty set
<^g,g^> is set
b1 is Element of <^f,fa^>
<^fb,g^> is set
f1 is Element of <^d,f^>
( the Comp of A . (d,f,fa)) . c₁₃ is set
( the Comp of A . (d,f,fa)) . (b1,f1) is set
[b1,f1] is V22() set
{b1,f1} is non empty set
{b1} is non empty set
{{b1,f1},{b1}} is non empty set
( the Comp of A . (d,f,fa)) . [b1,f1] is set
b1 * f1 is Element of <^d,fa^>
F₃(d,f,fa,f1,b1) is set
b2 is Element of <^fb,g^>
G1 is Element of <^g,g^>
G1 * b2 is Element of <^fb,g^>
<^fb,g^> is set
( the Comp of c₂ . (fb,g,g)) . (G1,b2) is set
[G1,b2] is V22() set
{G1,b2} is non empty set
{G1} is non empty set
{{G1,b2},{G1}} is non empty set
( the Comp of c₂ . (fb,g,g)) . [G1,b2] is set
( the Comp of c₂ . (fb,g,g)) . c₁₃ is set
F₁() is non empty set
[:F₁(),F₁():] is Relation-like non empty set
A is Relation-like Function-like set
proj1 A is set
c₂ is Element of F₁()
FF is Element of F₁()
[c₂,FF] is V22() set
{c₂,FF} is non empty set
{c₂} is non empty set
{{c₂,FF},{c₂}} is non empty set
[c₂,FF] `1 is set
[c<sub>2</sub>,FF] `2 is set
a is set
A . (c₂,FF) is set
A . [c₂,FF] is set
F₂(c₂,FF) is set
b is set
c₂ is Element of F₁()
FF is Element of F₁()
A . (c₂,FF) is set
[c₂,FF] is V22() set
{c₂,FF} is non empty set
{c₂} is non empty set
{{c₂,FF},{c₂}} is non empty set
A . [c₂,FF] is set
c is set
a is Element of F₁()
A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
A . [FF,a] is set
F₂(c₂,FF) is set
F₂(FF,a) is set
F₃(c₂,FF,a,b,c) is set
F₂(c₂,a) is set
A . (c₂,a) is set
[c₂,a] is V22() set
{c₂,a} is non empty set
{{c₂,a},{c₂}} is non empty set
A . [c₂,a] is set
c is set
c₂ is Element of F₁()
FF is Element of F₁()
A . (c₂,FF) is set
[c₂,FF] is V22() set
{c₂,FF} is non empty set
{c₂} is non empty set
{{c₂,FF},{c₂}} is non empty set
A . [c₂,FF] is set
d is set
a is Element of F₁()
A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
A . [FF,a] is set
f is set
b is Element of F₁()
A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
A . [a,b] is set
F₂(c₂,FF) is set
F₂(FF,a) is set
F₂(a,b) is set
F₃(c₂,FF,a,c,d) is set
F₃(c₂,a,b,H₂(c₂,FF,a,c,d),f) is set
F₃(FF,a,b,d,f) is set
F₃(c₂,FF,b,c,H₂(FF,a,b,d,f)) is set
c₂ is Element of F₁()
F₂(c₂,c₂) is set
FF is set
a is set
A . (c₂,c₂) is set
[c₂,c₂] is V22() set
{c₂,c₂} is non empty set
{c₂} is non empty set
{{c₂,c₂},{c₂}} is non empty set
A . [c₂,c₂] is set
c is set
b is Element of F₁()
A . (c₂,b) is set
[c₂,b] is V22() set
{c₂,b} is non empty set
{{c₂,b},{c₂}} is non empty set
A . [c₂,b] is set
F₂(c₂,b) is set
F₃(c₂,c₂,b,a,c) is set
c₂ is Element of F₁()
F₂(c₂,c₂) is set
FF is set
a is set
A . (c₂,c₂) is set
[c₂,c₂] is V22() set
{c₂,c₂} is non empty set
{c₂} is non empty set
{{c₂,c₂},{c₂}} is non empty set
A . [c₂,c₂] is set
c is set
b is Element of F₁()
A . (b,c₂) is set
[b,c₂] is V22() set
{b,c₂} is non empty set
{b} is non empty set
{{b,c₂},{b}} is non empty set
A . [b,c₂] is set
F₂(b,c₂) is set
F₃(b,c₂,c₂,c,a) is set
c₂ is non empty transitive strict associative with_units reflexive AltCatStr
the carrier of c₂ is non empty set
FF is Element of the carrier of c₂
a is Element of the carrier of c₂
<^FF,a^> is set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the Arrows of c₂ . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c₂ . [FF,a] is set
A . (FF,a) is set
A . [FF,a] is set
b is set
F₂(FF,a) is set
FF is Element of the carrier of c₂
a is Element of the carrier of c₂
<^FF,a^> is set
the Arrows of c₂ . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c₂ . [FF,a] is set
b is Element of the carrier of c₂
<^a,b^> is set
the Arrows of c₂ . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of c₂ . [a,b] is set
c is Element of <^FF,a^>
d is Element of <^a,b^>
d * c is Element of <^FF,b^>
<^FF,b^> is set
the Arrows of c₂ . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of c₂ . [FF,b] is set
F₃(FF,a,b,c,d) is set
A is Relation-like Function-like Function-yielding V63() set
c₂ is set
FF is set
a is set
A . (c₂,FF,a) is set
[c₂,FF,a] is V22() V23() set
[c₂,FF] is V22() set
{c₂,FF} is non empty set
{c₂} is non empty set
{{c₂,FF},{c₂}} is non empty set
[[c₂,FF],a] is V22() set
{[c₂,FF],a} is non empty set
{[c₂,FF]} is Relation-like Function-like non empty set
{{[c₂,FF],a},{[c₂,FF]}} is non empty set
A . [c₂,FF,a] is Relation-like Function-like set
F₁() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F₁() is non empty set
A is set
FF is Element of the carrier of F₁()
c₂ is non empty set
FF is set
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
the Comp of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) Function-yielding V63() ManySortedFunction of {| the Arrows of F₁(), the Arrows of F₁()|},{| the Arrows of F₁()|}
[: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] is non empty set
{| the Arrows of F₁(), the Arrows of F₁()|} is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) set
{| the Arrows of F₁()|} is Relation-like [: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁(), the carrier of F₁():]) set
c is set
FF is Element of c₂
a is Element of c₂
the Arrows of F₁() . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of F₁() . [FF,a] is set
d is set
b is Element of c₂
the Arrows of F₁() . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of F₁() . [a,b] is set
f is Element of the carrier of F₁()
fa is Element of the carrier of F₁()
<^f,fa^> is set
the Arrows of F₁() . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of F₁() . [f,fa] is set
fb is Element of the carrier of F₁()
<^fa,fb^> is set
the Arrows of F₁() . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of F₁() . [fa,fb] is set
the Comp of F₁() . (FF,a,b) is Relation-like Function-like set
( the Comp of F₁() . (FF,a,b)) . (d,c) is set
[d,c] is V22() set
{d,c} is non empty set
{d} is non empty set
{{d,c},{d}} is non empty set
( the Comp of F₁() . (FF,a,b)) . [d,c] is set
g is Element of <^f,fa^>
g is Element of <^fa,fb^>
g * g is Element of <^f,fb^>
<^f,fb^> is set
the Arrows of F₁() . (f,fb) is set
[f,fb] is V22() set
{f,fb} is non empty set
{{f,fb},{f}} is non empty set
the Arrows of F₁() . [f,fb] is set
the Arrows of F₁() . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of F₁() . [FF,b] is set
d is set
FF is Element of c₂
a is Element of c₂
the Arrows of F₁() . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of F₁() . [FF,a] is set
f is set
b is Element of c₂
the Arrows of F₁() . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of F₁() . [a,b] is set
fa is set
c is Element of c₂
the Arrows of F₁() . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of F₁() . [b,c] is set
fb is Element of the carrier of F₁()
g is Element of the carrier of F₁()
<^fb,g^> is set
the Arrows of F₁() . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of F₁() . [fb,g] is set
g is Element of the carrier of F₁()
<^g,g^> is set
the Arrows of F₁() . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of F₁() . [g,g] is set
c₁₃ is Element of the carrier of F₁()
<^g,c₁₃^> is set
the Arrows of F₁() . (g,c₁₃) is set
[g,c₁₃] is V22() set
{g,c₁₃} is non empty set
{g} is non empty set
{{g,c₁₃},{g}} is non empty set
the Arrows of F₁() . [g,c₁₃] is set
<^fb,g^> is set
the Arrows of F₁() . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of F₁() . [fb,g] is set
<^g,c₁₃^> is set
the Arrows of F₁() . (g,c₁₃) is set
[g,c₁₃] is V22() set
{g,c₁₃} is non empty set
{{g,c₁₃},{g}} is non empty set
the Arrows of F₁() . [g,c₁₃] is set
the Comp of F₁() . (FF,a,b) is Relation-like Function-like set
( the Comp of F₁() . (FF,a,b)) . (f,d) is set
[f,d] is V22() set
{f,d} is non empty set
{f} is non empty set
{{f,d},{f}} is non empty set
( the Comp of F₁() . (FF,a,b)) . [f,d] is set
the Comp of F₁() . (FF,b,c) is Relation-like Function-like set
( the Comp of F₁() . (FF,b,c)) . (fa,H₂(FF,a,b,d,f)) is set
[fa,(( the Comp of F₁() . (FF,a,b)) . (f,d))] is V22() set
{fa,(( the Comp of F₁() . (FF,a,b)) . (f,d))} is non empty set
{fa} is non empty set
{{fa,(( the Comp of F₁() . (FF,a,b)) . (f,d))},{fa}} is non empty set
( the Comp of F₁() . (FF,b,c)) . [fa,(( the Comp of F₁() . (FF,a,b)) . (f,d))] is set
g9 is Element of <^fb,g^>
a1 is Element of <^g,g^>
a1 * g9 is Element of <^fb,g^>
the Comp of F₁() . (fb,g,c₁₃) is Relation-like Function-like set
( the Comp of F₁() . (fb,g,c₁₃)) . (fa,(a1 * g9)) is set
[fa,(a1 * g9)] is V22() set
{fa,(a1 * g9)} is non empty set
{{fa,(a1 * g9)},{fa}} is non empty set
( the Comp of F₁() . (fb,g,c₁₃)) . [fa,(a1 * g9)] is set
b1 is Element of <^g,c₁₃^>
b1 * (a1 * g9) is Element of <^fb,c₁₃^>
<^fb,c₁₃^> is set
the Arrows of F₁() . (fb,c₁₃) is set
[fb,c₁₃] is V22() set
{fb,c₁₃} is non empty set
{{fb,c₁₃},{fb}} is non empty set
the Arrows of F₁() . [fb,c₁₃] is set
b1 * a1 is Element of <^g,c₁₃^>
(b1 * a1) * g9 is Element of <^fb,c₁₃^>
the Comp of F₁() . (FF,a,c) is Relation-like Function-like set
( the Comp of F₁() . (FF,a,c)) . ((b1 * a1),d) is set
[(b1 * a1),d] is V22() set
{(b1 * a1),d} is non empty set
{(b1 * a1)} is non empty set
{{(b1 * a1),d},{(b1 * a1)}} is non empty set
( the Comp of F₁() . (FF,a,c)) . [(b1 * a1),d] is set
the Comp of F₁() . (a,b,c) is Relation-like Function-like set
( the Comp of F₁() . (a,b,c)) . (fa,f) is set
[fa,f] is V22() set
{fa,f} is non empty set
{{fa,f},{fa}} is non empty set
( the Comp of F₁() . (a,b,c)) . [fa,f] is set
( the Comp of F₁() . (FF,a,c)) . (H₂(a,b,c,f,fa),d) is set
[(( the Comp of F₁() . (a,b,c)) . (fa,f)),d] is V22() set
{(( the Comp of F₁() . (a,b,c)) . (fa,f)),d} is non empty set
{(( the Comp of F₁() . (a,b,c)) . (fa,f))} is non empty set
{{(( the Comp of F₁() . (a,b,c)) . (fa,f)),d},{(( the Comp of F₁() . (a,b,c)) . (fa,f))}} is non empty set
( the Comp of F₁() . (FF,a,c)) . [(( the Comp of F₁() . (a,b,c)) . (fa,f)),d] is set
FF is Element of c₂
a is Element of the carrier of F₁()
idm a is retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of F₁() . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of F₁() . [a,a] is set
b is set
c is set
the Arrows of F₁() . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of F₁() . [FF,FF] is set
f is set
d is Element of c₂
the Arrows of F₁() . (FF,d) is set
[FF,d] is V22() set
{FF,d} is non empty set
{{FF,d},{FF}} is non empty set
the Arrows of F₁() . [FF,d] is set
fa is Element of the carrier of F₁()
<^a,fa^> is set
the Arrows of F₁() . (a,fa) is set
[a,fa] is V22() set
{a,fa} is non empty set
{{a,fa},{a}} is non empty set
the Arrows of F₁() . [a,fa] is set
the Comp of F₁() . (FF,FF,d) is Relation-like Function-like set
( the Comp of F₁() . (FF,FF,d)) . (f,c) is set
[f,c] is V22() set
{f,c} is non empty set
{f} is non empty set
{{f,c},{f}} is non empty set
( the Comp of F₁() . (FF,FF,d)) . [f,c] is set
fb is Element of <^a,fa^>
fb * (idm a) is Element of <^a,fa^>
FF is Element of c₂
a is Element of the carrier of F₁()
idm a is retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of F₁() . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of F₁() . [a,a] is set
b is set
c is set
the Arrows of F₁() . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of F₁() . [FF,FF] is set
f is set
d is Element of c₂
the Arrows of F₁() . (d,FF) is set
[d,FF] is V22() set
{d,FF} is non empty set
{d} is non empty set
{{d,FF},{d}} is non empty set
the Arrows of F₁() . [d,FF] is set
fa is Element of the carrier of F₁()
<^fa,a^> is set
the Arrows of F₁() . (fa,a) is set
[fa,a] is V22() set
{fa,a} is non empty set
{fa} is non empty set
{{fa,a},{fa}} is non empty set
the Arrows of F₁() . [fa,a] is set
the Comp of F₁() . (d,FF,FF) is Relation-like Function-like set
( the Comp of F₁() . (d,FF,FF)) . (c,f) is set
[c,f] is V22() set
{c,f} is non empty set
{c} is non empty set
{{c,f},{c}} is non empty set
( the Comp of F₁() . (d,FF,FF)) . [c,f] is set
fb is Element of <^fa,a^>
(idm a) * fb is Element of <^fa,a^>
FF is non empty transitive strict associative with_units reflexive AltCatStr
the carrier of FF is non empty set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
[: the carrier of FF, the carrier of FF, the carrier of FF:] is non empty set
the Comp of FF is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) Function-yielding V63() ManySortedFunction of {| the Arrows of FF, the Arrows of FF|},{| the Arrows of FF|}
{| the Arrows of FF, the Arrows of FF|} is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) set
{| the Arrows of FF|} is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) set
a is set
b is set
c is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of FF . a is set
d is Element of the carrier of FF
f is Element of the carrier of FF
<^d,f^> is set
the Arrows of FF . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of FF . [d,f] is set
the Arrows of F₁() . a is set
the Arrows of F₁() . (d,f) is set
the Arrows of F₁() . [d,f] is set
fa is set
a is set
the Comp of FF . a is Relation-like Function-like set
the Comp of F₁() . a is Relation-like Function-like set
b is set
c is set
d is set
[b,c,d] is V22() V23() set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
[[b,c],d] is V22() set
{[b,c],d} is non empty set
{[b,c]} is Relation-like Function-like non empty set
{{[b,c],d},{[b,c]}} is non empty set
f is Element of the carrier of FF
fa is Element of the carrier of FF
fb is Element of the carrier of FF
g9 is set
the Comp of FF . (f,fa,fb) is Relation-like [:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):] -defined the Arrows of FF . (f,fb) -valued Function-like quasi_total Element of bool [:[:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):],( the Arrows of FF . (f,fb)):]
the Arrows of FF . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of FF . [fa,fb] is set
the Arrows of FF . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of FF . [f,fa] is set
[:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):] is Relation-like set
the Arrows of FF . (f,fb) is set
[f,fb] is V22() set
{f,fb} is non empty set
{{f,fb},{f}} is non empty set
the Arrows of FF . [f,fb] is set
[:[:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):],( the Arrows of FF . (f,fb)):] is Relation-like set
bool [:[:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):],( the Arrows of FF . (f,fb)):] is non empty set
a1 is set
b1 is set
[a1,b1] is V22() set
{a1,b1} is non empty set
{a1} is non empty set
{{a1,b1},{a1}} is non empty set
f1 is set
G1 is set
[f1,G1] is V22() set
{f1,G1} is non empty set
{f1} is non empty set
{{f1,G1},{f1}} is non empty set
<^f,fa^> is set
<^fa,fb^> is set
<^f,fb^> is set
g is Element of the carrier of F₁()
g is Element of the carrier of F₁()
c₁₃ is Element of the carrier of F₁()
the Comp of F₁() . (g,g,c₁₃) is Relation-like [:( the Arrows of F₁() . (g,c₁₃)),( the Arrows of F₁() . (g,g)):] -defined the Arrows of F₁() . (g,c₁₃) -valued Function-like quasi_total Element of bool [:[:( the Arrows of F₁() . (g,c₁₃)),( the Arrows of F₁() . (g,g)):],( the Arrows of F₁() . (g,c₁₃)):]
the Arrows of F₁() . (g,c₁₃) is set
[g,c₁₃] is V22() set
{g,c₁₃} is non empty set
{g} is non empty set
{{g,c₁₃},{g}} is non empty set
the Arrows of F₁() . [g,c₁₃] is set
the Arrows of F₁() . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of F₁() . [g,g] is set
[:( the Arrows of F₁() . (g,c₁₃)),( the Arrows of F₁() . (g,g)):] is Relation-like set
the Arrows of F₁() . (g,c₁₃) is set
[g,c₁₃] is V22() set
{g,c₁₃} is non empty set
{{g,c₁₃},{g}} is non empty set
the Arrows of F₁() . [g,c₁₃] is set
[:[:( the Arrows of F₁() . (g,c₁₃)),( the Arrows of F₁() . (g,g)):],( the Arrows of F₁() . (g,c₁₃)):] is Relation-like set
bool [:[:( the Arrows of F₁() . (g,c₁₃)),( the Arrows of F₁() . (g,g)):],( the Arrows of F₁() . (g,c₁₃)):] is non empty set
c2 is Element of <^fa,fb^>
b2 is Element of <^f,fa^>
g2 is Element of <^f,fb^>
( the Comp of FF . (f,fa,fb)) . (c2,b2) is set
[c2,b2] is V22() set
{c2,b2} is non empty set
{c2} is non empty set
{{c2,b2},{c2}} is non empty set
( the Comp of FF . (f,fa,fb)) . [c2,b2] is set
c2 * b2 is Element of <^f,fb^>
( the Comp of F₁() . (g,g,c₁₃)) . (c2,b2) is set
( the Comp of F₁() . (g,g,c₁₃)) . [c2,b2] is set
dom ( the Comp of F₁() . (g,g,c₁₃)) is Relation-like the Arrows of F₁() . (g,c₁₃) -defined the Arrows of F₁() . (g,g) -valued Element of bool [:( the Arrows of F₁() . (g,c₁₃)),( the Arrows of F₁() . (g,g)):]
bool [:( the Arrows of F₁() . (g,c₁₃)),( the Arrows of F₁() . (g,g)):] is non empty set
a is non empty SubCatStr of F₁()
the carrier of a is non empty set
b is Element of the carrier of a
<^b,b^> is set
the Arrows of a is Relation-like [: the carrier of a, the carrier of a:] -defined Function-like non empty V14([: the carrier of a, the carrier of a:]) set
[: the carrier of a, the carrier of a:] is Relation-like non empty set
the Arrows of a . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of a . [b,b] is set
c is Element of the carrier of F₁()
idm c is retraction coretraction iso mono epi Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of F₁() . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of F₁() . [c,c] is set
b is non empty transitive strict associative with_units reflexive id-inheriting SubCatStr of F₁()
the carrier of b is non empty set
c is Element of the carrier of F₁()
d is Element of the carrier of F₁()
c is Element of the carrier of F₁()
d is Element of the carrier of F₁()
<^c,d^> is set
the Arrows of F₁() . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
the Arrows of F₁() . [c,d] is set
f is Element of the carrier of b
fa is Element of the carrier of b
<^f,fa^> is set
the Arrows of b is Relation-like [: the carrier of b, the carrier of b:] -defined Function-like non empty V14([: the carrier of b, the carrier of b:]) set
[: the carrier of b, the carrier of b:] is Relation-like non empty set
the Arrows of b . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of b . [f,fa] is set
fb is Element of <^c,d^>
F₁() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F₁() is non empty set
F₂() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F₂() is non empty set
the Arrows of F₂() is Relation-like [: the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty V14([: the carrier of F₂(), the carrier of F₂():]) set
[: the carrier of F₂(), the carrier of F₂():] is Relation-like non empty set
A is Relation-like Function-like set
proj1 A is set
proj2 A is set
c₂ is set
FF is set
A . FF is set
a is Element of the carrier of F₁()
F₃(a) is set
[: the carrier of F₁(), the carrier of F₂():] is Relation-like non empty set
bool [: the carrier of F₁(), the carrier of F₂():] is non empty set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
[:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:] is Relation-like non empty set
bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:] is non empty set
c₂ is Relation-like the carrier of F₁() -defined the carrier of F₂() -valued Function-like non empty V14( the carrier of F₁()) quasi_total Element of bool [: the carrier of F₁(), the carrier of F₂():]
[:c₂,c₂:] is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) set
FF is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
FF (#) the Arrows of F₂() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) set
a is set
the Arrows of F₁() . a is set
(FF (#) the Arrows of F₂()) . a is set
a `1 is set
a `2 is set
b is set
c is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
fa is set
F₄((a `1),(a `2),fa) is set
d is Element of the carrier of F₁()
f is Element of the carrier of F₁()
<^d,f^> is set
the Arrows of F₁() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F₁() . [d,f] is set
fb is Element of <^d,f^>
F₄(d,f,fb) is set
g is set
F₃(d) is set
F₃(f) is set
the Arrows of F₂() . (F₃(d),F₃(f)) is set
[F₃(d),F₃(f)] is V22() set
{F₃(d),F₃(f)} is non empty set
{F₃(d)} is non empty set
{{F₃(d),F₃(f)},{F₃(d)}} is non empty set
the Arrows of F₂() . [F₃(d),F₃(f)] is set
c₂ . d is Element of the carrier of F₂()
dom FF is Relation-like the carrier of F₁() -defined the carrier of F₁() -valued non empty Element of bool [: the carrier of F₁(), the carrier of F₁():]
bool [: the carrier of F₁(), the carrier of F₁():] is non empty set
FF . (d,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
FF . [d,f] is set
the Arrows of F₂() . (FF . (d,f)) is set
c₂ . f is Element of the carrier of F₂()
the Arrows of F₂() . ((c₂ . d),(c₂ . f)) is set
[(c₂ . d),(c₂ . f)] is V22() set
{(c₂ . d),(c₂ . f)} is non empty set
{(c₂ . d)} is non empty set
{{(c₂ . d),(c₂ . f)},{(c₂ . d)}} is non empty set
the Arrows of F₂() . [(c₂ . d),(c₂ . f)] is set
a is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) Function-yielding V63() ManySortedFunction of the Arrows of F₁(),FF (#) the Arrows of F₂()
b is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) Function-yielding V63() MSUnTrans of FF, the Arrows of F₁(), the Arrows of F₂()
FunctorStr(# FF,b #) is strict FunctorStr over F₁(),F₂()
the ObjectMap of FunctorStr(# FF,b #) is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
c is reflexive Covariant FunctorStr over F₁(),F₂()
d is Element of the carrier of F₁()
c . d is Element of the carrier of F₂()
the ObjectMap of c is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of c . (d,d) is Element of [: the carrier of F₂(), the carrier of F₂():]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
c<sub>2</sub> . d is Element of the carrier of F<sub>2</sub>()
[(c<sub>2</sub> . d),(c<sub>2</sub> . d)] is V22() set
{(c<sub>2</sub> . d),(c<sub>2</sub> . d)} is non empty set
{(c<sub>2</sub> . d)} is non empty set
{{(c<sub>2</sub> . d),(c<sub>2</sub> . d)},{(c<sub>2</sub> . d)}} is non empty set
[(c<sub>2</sub> . d),(c<sub>2</sub> . d)] `1 is set
F₃(d) is set
d is Element of the carrier of F₁()
f is Element of the carrier of F₁()
<^d,f^> is set
the Arrows of F₁() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F₁() . [d,f] is set
(FF (#) the Arrows of F₂()) . [d,f] is set
[:( the Arrows of F₁() . [d,f]),((FF (#) the Arrows of F₂()) . [d,f]):] is Relation-like set
bool [:( the Arrows of F₁() . [d,f]),((FF (#) the Arrows of F₂()) . [d,f]):] is non empty set
b . [d,f] is Relation-like Function-like set
[d,f] `1 is set
[d,f] `2 is set
fb is Relation-like the Arrows of F₁() . [d,f] -defined (FF (#) the Arrows of F₂()) . [d,f] -valued Function-like quasi_total Element of bool [:( the Arrows of F₁() . [d,f]),((FF (#) the Arrows of F₂()) . [d,f]):]
fa is Element of <^d,f^>
fb . fa is set
F₄(([d,f] `1),([d,f] `2),fa) is set
F₄(d,([d,f] `2),fa) is set
F<sub>4</sub>(d,f,fa) is set
Morph-Map (c,d,f) is Relation-like <^d,f^> -defined <^(c . d),(c . f)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(c . d),(c . f)^>:]
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
c . f is Element of the carrier of F₂()
the ObjectMap of c . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of c . [f,f] is set
( the ObjectMap of c . (f,f)) `1 is set
<^(c . d),(c . f)^> is set
the Arrows of F<sub>2</sub>() . ((c . d),(c . f)) is set
[(c . d),(c . f)] is V22() set
{(c . d),(c . f)} is non empty set
{(c . d)} is non empty set
{{(c . d),(c . f)},{(c . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c . d),(c . f)] is set
[:<^d,f^>,<^(c . d),(c . f)^>:] is Relation-like set
bool [:<^d,f^>,<^(c . d),(c . f)^>:] is non empty set
the MorphMap of c is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) Function-yielding V63() MSUnTrans of the ObjectMap of c, the Arrows of F<sub>1</sub>(), the Arrows of F<sub>2</sub>()
the MorphMap of c . (d,f) is set
the MorphMap of c . [d,f] is Relation-like Function-like set
(Morph-Map (c,d,f)) . fa is set
d is Element of the carrier of F<sub>1</sub>()
f is Element of the carrier of F<sub>1</sub>()
<^d,f^> is set
the Arrows of F<sub>1</sub>() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F<sub>1</sub>() . [d,f] is set
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
c . f is Element of the carrier of F₂()
the ObjectMap of c . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of c . [f,f] is set
( the ObjectMap of c . (f,f)) `1 is set
<^(c . d),(c . f)^> is set
the Arrows of F<sub>2</sub>() . ((c . d),(c . f)) is set
[(c . d),(c . f)] is V22() set
{(c . d),(c . f)} is non empty set
{(c . d)} is non empty set
{{(c . d),(c . f)},{(c . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c . d),(c . f)] is set
the Element of <^d,f^> is Element of <^d,f^>
Morph-Map (c,d,f) is Relation-like <^d,f^> -defined <^(c . d),(c . f)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(c . d),(c . f)^>:]
[:<^d,f^>,<^(c . d),(c . f)^>:] is Relation-like set
bool [:<^d,f^>,<^(c . d),(c . f)^>:] is non empty set
the MorphMap of c . (d,f) is set
the MorphMap of c . [d,f] is Relation-like Function-like set
(Morph-Map (c,d,f)) . the Element of <^d,f^> is set
F<sub>4</sub>(d,f, the Element of <^d,f^>) is set
F<sub>3</sub>(d) is set
F<sub>3</sub>(f) is set
the Arrows of F<sub>2</sub>() . (F<sub>3</sub>(d),F<sub>3</sub>(f)) is set
[F<sub>3</sub>(d),F<sub>3</sub>(f)] is V22() set
{F<sub>3</sub>(d),F<sub>3</sub>(f)} is non empty set
{F<sub>3</sub>(d)} is non empty set
{{F<sub>3</sub>(d),F<sub>3</sub>(f)},{F<sub>3</sub>(d)}} is non empty set
the Arrows of F<sub>2</sub>() . [F<sub>3</sub>(d),F<sub>3</sub>(f)] is set
the Arrows of F<sub>2</sub>() . ((c . d),F<sub>3</sub>(f)) is set
[(c . d),F<sub>3</sub>(f)] is V22() set
{(c . d),F<sub>3</sub>(f)} is non empty set
{{(c . d),F<sub>3</sub>(f)},{(c . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c . d),F<sub>3</sub>(f)] is set
d is Element of the carrier of F<sub>1</sub>()
f is Element of the carrier of F<sub>1</sub>()
<^d,f^> is set
the Arrows of F<sub>1</sub>() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F<sub>1</sub>() . [d,f] is set
Morph-Map (c,d,f) is Relation-like <^d,f^> -defined <^(c . d),(c . f)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(c . d),(c . f)^>:]
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
c . f is Element of the carrier of F₂()
the ObjectMap of c . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of c . [f,f] is set
( the ObjectMap of c . (f,f)) `1 is set
<^(c . d),(c . f)^> is set
the Arrows of F<sub>2</sub>() . ((c . d),(c . f)) is set
[(c . d),(c . f)] is V22() set
{(c . d),(c . f)} is non empty set
{(c . d)} is non empty set
{{(c . d),(c . f)},{(c . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c . d),(c . f)] is set
[:<^d,f^>,<^(c . d),(c . f)^>:] is Relation-like set
bool [:<^d,f^>,<^(c . d),(c . f)^>:] is non empty set
the MorphMap of c . (d,f) is set
the MorphMap of c . [d,f] is Relation-like Function-like set
fa is Element of <^d,f^>
(Morph-Map (c,d,f)) . fa is set
F<sub>4</sub>(d,f,fa) is set
c . fa is Element of <^(c . d),(c . f)^>
d is Element of the carrier of F<sub>1</sub>()
f is Element of the carrier of F<sub>1</sub>()
<^d,f^> is set
the Arrows of F<sub>1</sub>() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F<sub>1</sub>() . [d,f] is set
fa is Element of the carrier of F<sub>1</sub>()
<^f,fa^> is set
the Arrows of F<sub>1</sub>() . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of F<sub>1</sub>() . [f,fa] is set
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
c . f is Element of the carrier of F₂()
the ObjectMap of c . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of c . [f,f] is set
( the ObjectMap of c . (f,f)) `1 is set
<^(c . d),(c . f)^> is set
the Arrows of F<sub>2</sub>() . ((c . d),(c . f)) is set
[(c . d),(c . f)] is V22() set
{(c . d),(c . f)} is non empty set
{(c . d)} is non empty set
{{(c . d),(c . f)},{(c . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c . d),(c . f)] is set
c . fa is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (fa,fa) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[fa,fa] is V22() set
{fa,fa} is non empty set
{fa} is non empty set
{{fa,fa},{fa}} is non empty set
the ObjectMap of c . [fa,fa] is set
( the ObjectMap of c . (fa,fa)) `1 is set
<^(c . f),(c . fa)^> is set
the Arrows of F₂() . ((c . f),(c . fa)) is set
[(c . f),(c . fa)] is V22() set
{(c . f),(c . fa)} is non empty set
{(c . f)} is non empty set
{{(c . f),(c . fa)},{(c . f)}} is non empty set
the Arrows of F₂() . [(c . f),(c . fa)] is set
Morph-Map (c,d,f) is Relation-like Function-like set
the MorphMap of c . (d,f) is set
the MorphMap of c . [d,f] is Relation-like Function-like set
Morph-Map (c,f,fa) is Relation-like Function-like set
the MorphMap of c . (f,fa) is set
the MorphMap of c . [f,fa] is Relation-like Function-like set
Morph-Map (c,d,fa) is Relation-like Function-like set
the MorphMap of c . (d,fa) is set
[d,fa] is V22() set
{d,fa} is non empty set
{{d,fa},{d}} is non empty set
the MorphMap of c . [d,fa] is Relation-like Function-like set
fb is Element of <^d,f^>
(Morph-Map (c,d,f)) . fb is set
g is Element of <^f,fa^>
(Morph-Map (c,f,fa)) . g is set
g * fb is Element of <^d,fa^>
<^d,fa^> is set
the Arrows of F₁() . (d,fa) is set
the Arrows of F₁() . [d,fa] is set
(Morph-Map (c,d,fa)) . (g * fb) is set
c₂ . d is Element of the carrier of F₂()
c₂ . f is Element of the carrier of F₂()
c₂ . fa is Element of the carrier of F₂()
F₃(d) is set
F₃(f) is set
F₃(fa) is set
<^(c₂ . d),(c₂ . f)^> is set
the Arrows of F₂() . ((c₂ . d),(c₂ . f)) is set
[(c₂ . d),(c₂ . f)] is V22() set
{(c₂ . d),(c₂ . f)} is non empty set
{(c₂ . d)} is non empty set
{{(c₂ . d),(c₂ . f)},{(c₂ . d)}} is non empty set
the Arrows of F₂() . [(c₂ . d),(c₂ . f)] is set
F₄(d,f,fb) is set
<^(c₂ . f),(c₂ . fa)^> is set
the Arrows of F₂() . ((c₂ . f),(c₂ . fa)) is set
[(c₂ . f),(c₂ . fa)] is V22() set
{(c₂ . f),(c₂ . fa)} is non empty set
{(c₂ . f)} is non empty set
{{(c₂ . f),(c₂ . fa)},{(c₂ . f)}} is non empty set
the Arrows of F₂() . [(c₂ . f),(c₂ . fa)] is set
F₄(f,fa,g) is set
a1 is Element of <^(c₂ . d),(c₂ . f)^>
b1 is Element of <^(c₂ . f),(c₂ . fa)^>
f1 is Element of <^(c . d),(c . f)^>
G1 is Element of <^(c . f),(c . fa)^>
G1 * f1 is Element of <^(c . d),(c . fa)^>
<^(c . d),(c . fa)^> is set
the Arrows of F₂() . ((c . d),(c . fa)) is set
[(c . d),(c . fa)] is V22() set
{(c . d),(c . fa)} is non empty set
{{(c . d),(c . fa)},{(c . d)}} is non empty set
the Arrows of F₂() . [(c . d),(c . fa)] is set
F₄(d,fa,(g * fb)) is set
Morph-Map (c,d,f) is Relation-like <^d,f^> -defined <^(c . d),(c . f)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(c . d),(c . f)^>:]
[:<^d,f^>,<^(c . d),(c . f)^>:] is Relation-like set
bool [:<^d,f^>,<^(c . d),(c . f)^>:] is non empty set
(Morph-Map (c,d,f)) . fb is set
Morph-Map (c,f,fa) is Relation-like <^f,fa^> -defined <^(c . f),(c . fa)^> -valued Function-like quasi_total Element of bool [:<^f,fa^>,<^(c . f),(c . fa)^>:]
[:<^f,fa^>,<^(c . f),(c . fa)^>:] is Relation-like set
bool [:<^f,fa^>,<^(c . f),(c . fa)^>:] is non empty set
(Morph-Map (c,f,fa)) . g is set
Morph-Map (c,d,fa) is Relation-like <^d,fa^> -defined <^(c . d),(c . fa)^> -valued Function-like quasi_total Element of bool [:<^d,fa^>,<^(c . d),(c . fa)^>:]
[:<^d,fa^>,<^(c . d),(c . fa)^>:] is Relation-like set
bool [:<^d,fa^>,<^(c . d),(c . fa)^>:] is non empty set
(Morph-Map (c,d,fa)) . (g * fb) is set
d is Element of the carrier of F₁()
c . d is Element of the carrier of F₂()
the ObjectMap of c . (d,d) is Element of [: the carrier of F₂(), the carrier of F₂():]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
F<sub>3</sub>(d) is set
<^d,d^> is non empty set
the Arrows of F<sub>1</sub>() . (d,d) is set
the Arrows of F<sub>1</sub>() . [d,d] is set
<^(c . d),(c . d)^> is non empty set
the Arrows of F<sub>2</sub>() . ((c . d),(c . d)) is set
[(c . d),(c . d)] is V22() set
{(c . d),(c . d)} is non empty set
{(c . d)} is non empty set
{{(c . d),(c . d)},{(c . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c . d),(c . d)] is set
Morph-Map (c,d,d) is Relation-like <^d,d^> -defined <^(c . d),(c . d)^> -valued Function-like non empty V14(<^d,d^>) quasi_total Element of bool [:<^d,d^>,<^(c . d),(c . d)^>:]
[:<^d,d^>,<^(c . d),(c . d)^>:] is Relation-like non empty set
bool [:<^d,d^>,<^(c . d),(c . d)^>:] is non empty set
the MorphMap of c . (d,d) is set
the MorphMap of c . [d,d] is Relation-like Function-like set
idm d is retraction coretraction iso mono epi Element of <^d,d^>
(Morph-Map (c,d,d)) . (idm d) is Element of <^(c . d),(c . d)^>
F<sub>4</sub>(d,d,(idm d)) is set
idm (c . d) is retraction coretraction iso mono epi Element of <^(c . d),(c . d)^>
d is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
fa is Element of the carrier of F<sub>1</sub>()
fb is Element of the carrier of F<sub>1</sub>()
<^fa,fb^> is set
the Arrows of F<sub>1</sub>() . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of F<sub>1</sub>() . [fa,fb] is set
f is Element of the carrier of F<sub>1</sub>()
d . f is Element of the carrier of F<sub>2</sub>()
the ObjectMap of d is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
the ObjectMap of d . (f,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of d . [f,f] is set
( the ObjectMap of d . (f,f)) `1 is set
F₃(f) is set
g is Element of <^fa,fb^>
d . g is Element of <^(d . fa),(d . fb)^>
d . fa is Element of the carrier of F₂()
the ObjectMap of d . (fa,fa) is Element of [: the carrier of F₂(), the carrier of F₂():]
[fa,fa] is V22() set
{fa,fa} is non empty set
{{fa,fa},{fa}} is non empty set
the ObjectMap of d . [fa,fa] is set
( the ObjectMap of d . (fa,fa)) `1 is set
d . fb is Element of the carrier of F<sub>2</sub>()
the ObjectMap of d . (fb,fb) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[fb,fb] is V22() set
{fb,fb} is non empty set
{fb} is non empty set
{{fb,fb},{fb}} is non empty set
the ObjectMap of d . [fb,fb] is set
( the ObjectMap of d . (fb,fb)) `1 is set
<^(d . fa),(d . fb)^> is set
the Arrows of F₂() . ((d . fa),(d . fb)) is set
[(d . fa),(d . fb)] is V22() set
{(d . fa),(d . fb)} is non empty set
{(d . fa)} is non empty set
{{(d . fa),(d . fb)},{(d . fa)}} is non empty set
the Arrows of F₂() . [(d . fa),(d . fb)] is set
F₄(fa,fb,g) is set
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
FF is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,c₂
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,c₂
the ObjectMap of FF is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c₂, the carrier of c₂:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the carrier of c₂ is non empty set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:] is non empty set
the MorphMap of FF is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of FF, the Arrows of A, the Arrows of c₂
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
FunctorStr(# the ObjectMap of FF, the MorphMap of FF #) is strict FunctorStr over A,c₂
the ObjectMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c₂, the carrier of c₂:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:]
the MorphMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of a, the Arrows of A, the Arrows of c₂
FunctorStr(# the ObjectMap of a, the MorphMap of a #) is strict FunctorStr over A,c₂
[: the carrier of A, the carrier of c₂:] is Relation-like non empty set
bool [: the carrier of A, the carrier of c₂:] is non empty set
b is Relation-like the carrier of A -defined the carrier of c₂ -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of c₂:]
[:b,b:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c₂, the carrier of c₂:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:]
c is Relation-like the carrier of A -defined the carrier of c₂ -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of c₂:]
[:c,c:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c₂, the carrier of c₂:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:]
d is Element of the carrier of A
f is Element of the carrier of A
dom b is non empty Element of bool the carrier of A
bool the carrier of A is non empty set
dom c is non empty Element of bool the carrier of A
fa is Element of the carrier of A
the ObjectMap of FF . (fa,fa) is Element of [: the carrier of c₂, the carrier of c₂:]
[fa,fa] is V22() set
{fa,fa} is non empty set
{fa} is non empty set
{{fa,fa},{fa}} is non empty set
the ObjectMap of FF . [fa,fa] is set
b . fa is Element of the carrier of c₂
[(b . fa),(b . fa)] is V22() set
{(b . fa),(b . fa)} is non empty set
{(b . fa)} is non empty set
{{(b . fa),(b . fa)},{(b . fa)}} is non empty set
fb is Element of the carrier of A
the ObjectMap of FF . (fb,fb) is Element of [: the carrier of c₂, the carrier of c₂:]
[fb,fb] is V22() set
{fb,fb} is non empty set
{fb} is non empty set
{{fb,fb},{fb}} is non empty set
the ObjectMap of FF . [fb,fb] is set
b . fb is Element of the carrier of c₂
[(b . fb),(b . fb)] is V22() set
{(b . fb),(b . fb)} is non empty set
{(b . fb)} is non empty set
{{(b . fb),(b . fb)},{(b . fb)}} is non empty set
the ObjectMap of a . (fa,fa) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of a . [fa,fa] is set
c . fa is Element of the carrier of c₂
[(c . fa),(c . fa)] is V22() set
{(c . fa),(c . fa)} is non empty set
{(c . fa)} is non empty set
{{(c . fa),(c . fa)},{(c . fa)}} is non empty set
the ObjectMap of a . (fb,fb) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of a . [fb,fb] is set
c . fb is Element of the carrier of c₂
[(c . fb),(c . fb)] is V22() set
{(c . fb),(c . fb)} is non empty set
{(c . fb)} is non empty set
{{(c . fb),(c . fb)},{(c . fb)}} is non empty set
FF . fa is Element of the carrier of c₂
( the ObjectMap of FF . (fa,fa)) `1 is set
FF . fb is Element of the carrier of c<sub>2</sub>
( the ObjectMap of FF . (fb,fb)) `1 is set
a . fa is Element of the carrier of c₂
( the ObjectMap of a . (fa,fa)) `1 is set
a . fb is Element of the carrier of c<sub>2</sub>
( the ObjectMap of a . (fb,fb)) `1 is set
the ObjectMap of FF . (d,f) is Element of [: the carrier of c₂, the carrier of c₂:]
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the ObjectMap of FF . [d,f] is set
b . d is Element of the carrier of c₂
b . f is Element of the carrier of c₂
[(b . d),(b . f)] is V22() set
{(b . d),(b . f)} is non empty set
{(b . d)} is non empty set
{{(b . d),(b . f)},{(b . d)}} is non empty set
the ObjectMap of a . (d,f) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of a . [d,f] is set
d is set
f is set
fa is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
fb is Element of the carrier of A
g is Element of the carrier of A
<^fb,g^> is set
the Arrows of A . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of A . [fb,g] is set
FF . fb is Element of the carrier of c₂
the ObjectMap of FF . (fb,fb) is Element of [: the carrier of c₂, the carrier of c₂:]
[fb,fb] is V22() set
{fb,fb} is non empty set
{{fb,fb},{fb}} is non empty set
the ObjectMap of FF . [fb,fb] is set
( the ObjectMap of FF . (fb,fb)) `1 is set
FF . g is Element of the carrier of c<sub>2</sub>
the ObjectMap of FF . (g,g) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of FF . [g,g] is set
( the ObjectMap of FF . (g,g)) `1 is set
<^(FF . fb),(FF . g)^> is set
the Arrows of c₂ . ((FF . fb),(FF . g)) is set
[(FF . fb),(FF . g)] is V22() set
{(FF . fb),(FF . g)} is non empty set
{(FF . fb)} is non empty set
{{(FF . fb),(FF . g)},{(FF . fb)}} is non empty set
the Arrows of c₂ . [(FF . fb),(FF . g)] is set
a . fb is Element of the carrier of c₂
the ObjectMap of a . (fb,fb) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of a . [fb,fb] is set
( the ObjectMap of a . (fb,fb)) `1 is set
a . g is Element of the carrier of c<sub>2</sub>
the ObjectMap of a . (g,g) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of a . [g,g] is set
( the ObjectMap of a . (g,g)) `1 is set
<^(a . fb),(a . g)^> is set
the Arrows of c₂ . ((a . fb),(a . g)) is set
[(a . fb),(a . g)] is V22() set
{(a . fb),(a . g)} is non empty set
{(a . fb)} is non empty set
{{(a . fb),(a . g)},{(a . fb)}} is non empty set
the Arrows of c₂ . [(a . fb),(a . g)] is set
Morph-Map (FF,fb,g) is Relation-like <^fb,g^> -defined <^(FF . fb),(FF . g)^> -valued Function-like quasi_total Element of bool [:<^fb,g^>,<^(FF . fb),(FF . g)^>:]
[:<^fb,g^>,<^(FF . fb),(FF . g)^>:] is Relation-like set
bool [:<^fb,g^>,<^(FF . fb),(FF . g)^>:] is non empty set
the MorphMap of FF . (fb,g) is set
the MorphMap of FF . [fb,g] is Relation-like Function-like set
dom (Morph-Map (FF,fb,g)) is Element of bool <^fb,g^>
bool <^fb,g^> is non empty set
Morph-Map (a,fb,g) is Relation-like <^fb,g^> -defined <^(a . fb),(a . g)^> -valued Function-like quasi_total Element of bool [:<^fb,g^>,<^(a . fb),(a . g)^>:]
[:<^fb,g^>,<^(a . fb),(a . g)^>:] is Relation-like set
bool [:<^fb,g^>,<^(a . fb),(a . g)^>:] is non empty set
the MorphMap of a . (fb,g) is set
the MorphMap of a . [fb,g] is Relation-like Function-like set
dom (Morph-Map (a,fb,g)) is Element of bool <^fb,g^>
g is set
(Morph-Map (FF,fb,g)) . g is set
c₁₃ is Element of <^fb,g^>
FF . c₁₃ is Element of <^(FF . fb),(FF . g)^>
a . c₁₃ is Element of <^(a . fb),(a . g)^>
(Morph-Map (a,fb,g)) . g is set
the MorphMap of FF . d is Relation-like Function-like set
the MorphMap of a . d is Relation-like Function-like set
F₁() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F₁() is non empty set
F₂() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F₂() is non empty set
the Arrows of F₂() is Relation-like [: the carrier of F₂(), the carrier of F₂():] -defined Function-like non empty V14([: the carrier of F₂(), the carrier of F₂():]) set
[: the carrier of F₂(), the carrier of F₂():] is Relation-like non empty set
A is Relation-like Function-like set
proj1 A is set
proj2 A is set
c₂ is set
FF is set
A . FF is set
a is Element of the carrier of F₁()
F₃(a) is set
[: the carrier of F₁(), the carrier of F₂():] is Relation-like non empty set
bool [: the carrier of F₁(), the carrier of F₂():] is non empty set
[: the carrier of F₁(), the carrier of F₁():] is Relation-like non empty set
[:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:] is Relation-like non empty set
bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:] is non empty set
c₂ is Relation-like the carrier of F₁() -defined the carrier of F₂() -valued Function-like non empty V14( the carrier of F₁()) quasi_total Element of bool [: the carrier of F₁(), the carrier of F₂():]
[:c₂,c₂:] is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
~ [:c₂,c₂:] is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
dom [:c₂,c₂:] is Relation-like the carrier of F₁() -defined the carrier of F₁() -valued non empty Element of bool [: the carrier of F₁(), the carrier of F₁():]
bool [: the carrier of F₁(), the carrier of F₁():] is non empty set
FF is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
dom FF is Relation-like the carrier of F₁() -defined the carrier of F₁() -valued non empty Element of bool [: the carrier of F₁(), the carrier of F₁():]
the Arrows of F₁() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) set
FF (#) the Arrows of F₂() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) set
a is set
the Arrows of F₁() . a is set
(FF (#) the Arrows of F₂()) . a is set
a `1 is set
a `2 is set
b is set
c is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
fa is set
F₄((a `1),(a `2),fa) is set
d is Element of the carrier of F₁()
f is Element of the carrier of F₁()
<^d,f^> is set
the Arrows of F₁() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F₁() . [d,f] is set
fb is Element of <^d,f^>
F₄(d,f,fb) is set
g is set
F₃(f) is set
F₃(d) is set
the Arrows of F₂() . (F₃(f),F₃(d)) is set
[F₃(f),F₃(d)] is V22() set
{F₃(f),F₃(d)} is non empty set
{F₃(f)} is non empty set
{{F₃(f),F₃(d)},{F₃(f)}} is non empty set
the Arrows of F₂() . [F₃(f),F₃(d)] is set
c₂ . d is Element of the carrier of F₂()
FF . (d,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
FF . [d,f] is set
the Arrows of F₂() . (FF . (d,f)) is set
[:c₂,c₂:] . (f,d) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,d] is V22() set
{f,d} is non empty set
{f} is non empty set
{{f,d},{f}} is non empty set
[:c₂,c₂:] . [f,d] is set
the Arrows of F₂() . ([:c₂,c₂:] . (f,d)) is set
c₂ . f is Element of the carrier of F₂()
the Arrows of F₂() . ((c₂ . f),(c₂ . d)) is set
[(c₂ . f),(c₂ . d)] is V22() set
{(c₂ . f),(c₂ . d)} is non empty set
{(c₂ . f)} is non empty set
{{(c₂ . f),(c₂ . d)},{(c₂ . f)}} is non empty set
the Arrows of F₂() . [(c₂ . f),(c₂ . d)] is set
a is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) Function-yielding V63() ManySortedFunction of the Arrows of F₁(),FF (#) the Arrows of F₂()
b is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) Function-yielding V63() MSUnTrans of FF, the Arrows of F₁(), the Arrows of F₂()
FunctorStr(# FF,b #) is strict FunctorStr over F₁(),F₂()
the ObjectMap of FunctorStr(# FF,b #) is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
d is Element of the carrier of F₁()
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
c is reflexive Contravariant FunctorStr over F₁(),F₂()
c . d is Element of the carrier of F₂()
the ObjectMap of c is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of c . (d,d) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
[:c<sub>2</sub>,c<sub>2</sub>:] . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[:c<sub>2</sub>,c<sub>2</sub>:] . [d,d] is set
([:c<sub>2</sub>,c<sub>2</sub>:] . (d,d)) `1 is set
c₂ . d is Element of the carrier of F₂()
[(c₂ . d),(c₂ . d)] is V22() set
{(c₂ . d),(c₂ . d)} is non empty set
{(c₂ . d)} is non empty set
{{(c₂ . d),(c₂ . d)},{(c₂ . d)}} is non empty set
[(c₂ . d),(c₂ . d)] `1 is set
F<sub>3</sub>(d) is set
d is Element of the carrier of F<sub>1</sub>()
f is Element of the carrier of F<sub>1</sub>()
<^d,f^> is set
the Arrows of F<sub>1</sub>() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F<sub>1</sub>() . [d,f] is set
(FF (#) the Arrows of F<sub>2</sub>()) . [d,f] is set
[:( the Arrows of F<sub>1</sub>() . [d,f]),((FF (#) the Arrows of F<sub>2</sub>()) . [d,f]):] is Relation-like set
bool [:( the Arrows of F<sub>1</sub>() . [d,f]),((FF (#) the Arrows of F<sub>2</sub>()) . [d,f]):] is non empty set
b . [d,f] is Relation-like Function-like set
[d,f] `1 is set
[d,f] `2 is set
fb is Relation-like the Arrows of F<sub>1</sub>() . [d,f] -defined (FF (#) the Arrows of F<sub>2</sub>()) . [d,f] -valued Function-like quasi_total Element of bool [:( the Arrows of F<sub>1</sub>() . [d,f]),((FF (#) the Arrows of F<sub>2</sub>()) . [d,f]):]
fa is Element of <^d,f^>
fb . fa is set
F<sub>4</sub>(([d,f] `1),([d,f] `2),fa) is set
F<sub>4</sub>(d,([d,f] `2),fa) is set
F₄(d,f,fa) is set
Morph-Map (c,d,f) is Relation-like <^d,f^> -defined <^(c . f),(c . d)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(c . f),(c . d)^>:]
c . f is Element of the carrier of F₂()
the ObjectMap of c . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of c . [f,f] is set
( the ObjectMap of c . (f,f)) `1 is set
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
<^(c . f),(c . d)^> is set
the Arrows of F₂() . ((c . f),(c . d)) is set
[(c . f),(c . d)] is V22() set
{(c . f),(c . d)} is non empty set
{(c . f)} is non empty set
{{(c . f),(c . d)},{(c . f)}} is non empty set
the Arrows of F₂() . [(c . f),(c . d)] is set
[:<^d,f^>,<^(c . f),(c . d)^>:] is Relation-like set
bool [:<^d,f^>,<^(c . f),(c . d)^>:] is non empty set
the MorphMap of c is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) Function-yielding V63() MSUnTrans of the ObjectMap of c, the Arrows of F₁(), the Arrows of F₂()
the MorphMap of c . (d,f) is set
the MorphMap of c . [d,f] is Relation-like Function-like set
(Morph-Map (c,d,f)) . fa is set
d is Element of the carrier of F₁()
f is Element of the carrier of F₁()
<^d,f^> is set
the Arrows of F₁() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F₁() . [d,f] is set
c . f is Element of the carrier of F₂()
the ObjectMap of c . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of c . [f,f] is set
( the ObjectMap of c . (f,f)) `1 is set
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
<^(c . f),(c . d)^> is set
the Arrows of F₂() . ((c . f),(c . d)) is set
[(c . f),(c . d)] is V22() set
{(c . f),(c . d)} is non empty set
{(c . f)} is non empty set
{{(c . f),(c . d)},{(c . f)}} is non empty set
the Arrows of F₂() . [(c . f),(c . d)] is set
the Element of <^d,f^> is Element of <^d,f^>
Morph-Map (c,d,f) is Relation-like <^d,f^> -defined <^(c . f),(c . d)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(c . f),(c . d)^>:]
[:<^d,f^>,<^(c . f),(c . d)^>:] is Relation-like set
bool [:<^d,f^>,<^(c . f),(c . d)^>:] is non empty set
the MorphMap of c . (d,f) is set
the MorphMap of c . [d,f] is Relation-like Function-like set
(Morph-Map (c,d,f)) . the Element of <^d,f^> is set
F₄(d,f, the Element of <^d,f^>) is set
F₃(f) is set
F₃(d) is set
the Arrows of F₂() . (F₃(f),F₃(d)) is set
[F₃(f),F₃(d)] is V22() set
{F₃(f),F₃(d)} is non empty set
{F₃(f)} is non empty set
{{F₃(f),F₃(d)},{F₃(f)}} is non empty set
the Arrows of F₂() . [F₃(f),F₃(d)] is set
the Arrows of F₂() . ((c . f),F₃(d)) is set
[(c . f),F₃(d)] is V22() set
{(c . f),F₃(d)} is non empty set
{{(c . f),F₃(d)},{(c . f)}} is non empty set
the Arrows of F₂() . [(c . f),F₃(d)] is set
d is Element of the carrier of F₁()
f is Element of the carrier of F₁()
<^d,f^> is set
the Arrows of F₁() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F₁() . [d,f] is set
Morph-Map (c,d,f) is Relation-like <^d,f^> -defined <^(c . f),(c . d)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(c . f),(c . d)^>:]
c . f is Element of the carrier of F₂()
the ObjectMap of c . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of c . [f,f] is set
( the ObjectMap of c . (f,f)) `1 is set
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
<^(c . f),(c . d)^> is set
the Arrows of F₂() . ((c . f),(c . d)) is set
[(c . f),(c . d)] is V22() set
{(c . f),(c . d)} is non empty set
{(c . f)} is non empty set
{{(c . f),(c . d)},{(c . f)}} is non empty set
the Arrows of F₂() . [(c . f),(c . d)] is set
[:<^d,f^>,<^(c . f),(c . d)^>:] is Relation-like set
bool [:<^d,f^>,<^(c . f),(c . d)^>:] is non empty set
the MorphMap of c . (d,f) is set
the MorphMap of c . [d,f] is Relation-like Function-like set
fa is Element of <^d,f^>
(Morph-Map (c,d,f)) . fa is set
F₄(d,f,fa) is set
c . fa is Element of <^(c . f),(c . d)^>
d is Element of the carrier of F₁()
f is Element of the carrier of F₁()
<^d,f^> is set
the Arrows of F₁() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F₁() . [d,f] is set
fa is Element of the carrier of F₁()
<^f,fa^> is set
the Arrows of F₁() . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of F₁() . [f,fa] is set
c . f is Element of the carrier of F₂()
the ObjectMap of c . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of c . [f,f] is set
( the ObjectMap of c . (f,f)) `1 is set
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
<^(c . f),(c . d)^> is set
the Arrows of F₂() . ((c . f),(c . d)) is set
[(c . f),(c . d)] is V22() set
{(c . f),(c . d)} is non empty set
{(c . f)} is non empty set
{{(c . f),(c . d)},{(c . f)}} is non empty set
the Arrows of F₂() . [(c . f),(c . d)] is set
c . fa is Element of the carrier of F₂()
the ObjectMap of c . (fa,fa) is Element of [: the carrier of F₂(), the carrier of F₂():]
[fa,fa] is V22() set
{fa,fa} is non empty set
{fa} is non empty set
{{fa,fa},{fa}} is non empty set
the ObjectMap of c . [fa,fa] is set
( the ObjectMap of c . (fa,fa)) `1 is set
<^(c . fa),(c . f)^> is set
the Arrows of F<sub>2</sub>() . ((c . fa),(c . f)) is set
[(c . fa),(c . f)] is V22() set
{(c . fa),(c . f)} is non empty set
{(c . fa)} is non empty set
{{(c . fa),(c . f)},{(c . fa)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c . fa),(c . f)] is set
Morph-Map (c,d,f) is Relation-like Function-like set
the MorphMap of c . (d,f) is set
the MorphMap of c . [d,f] is Relation-like Function-like set
Morph-Map (c,f,fa) is Relation-like Function-like set
the MorphMap of c . (f,fa) is set
the MorphMap of c . [f,fa] is Relation-like Function-like set
Morph-Map (c,d,fa) is Relation-like Function-like set
the MorphMap of c . (d,fa) is set
[d,fa] is V22() set
{d,fa} is non empty set
{{d,fa},{d}} is non empty set
the MorphMap of c . [d,fa] is Relation-like Function-like set
fb is Element of <^d,f^>
(Morph-Map (c,d,f)) . fb is set
g is Element of <^f,fa^>
(Morph-Map (c,f,fa)) . g is set
g * fb is Element of <^d,fa^>
<^d,fa^> is set
the Arrows of F<sub>1</sub>() . (d,fa) is set
the Arrows of F<sub>1</sub>() . [d,fa] is set
(Morph-Map (c,d,fa)) . (g * fb) is set
c<sub>2</sub> . d is Element of the carrier of F<sub>2</sub>()
c<sub>2</sub> . f is Element of the carrier of F<sub>2</sub>()
c<sub>2</sub> . fa is Element of the carrier of F<sub>2</sub>()
F<sub>3</sub>(d) is set
F<sub>3</sub>(f) is set
F<sub>3</sub>(fa) is set
<^(c<sub>2</sub> . f),(c<sub>2</sub> . d)^> is set
the Arrows of F<sub>2</sub>() . ((c<sub>2</sub> . f),(c<sub>2</sub> . d)) is set
[(c<sub>2</sub> . f),(c<sub>2</sub> . d)] is V22() set
{(c<sub>2</sub> . f),(c<sub>2</sub> . d)} is non empty set
{(c<sub>2</sub> . f)} is non empty set
{{(c<sub>2</sub> . f),(c<sub>2</sub> . d)},{(c<sub>2</sub> . f)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c<sub>2</sub> . f),(c<sub>2</sub> . d)] is set
F<sub>4</sub>(d,f,fb) is set
<^(c<sub>2</sub> . fa),(c<sub>2</sub> . f)^> is set
the Arrows of F<sub>2</sub>() . ((c<sub>2</sub> . fa),(c<sub>2</sub> . f)) is set
[(c<sub>2</sub> . fa),(c<sub>2</sub> . f)] is V22() set
{(c<sub>2</sub> . fa),(c<sub>2</sub> . f)} is non empty set
{(c<sub>2</sub> . fa)} is non empty set
{{(c<sub>2</sub> . fa),(c<sub>2</sub> . f)},{(c<sub>2</sub> . fa)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c<sub>2</sub> . fa),(c<sub>2</sub> . f)] is set
F<sub>4</sub>(f,fa,g) is set
a1 is Element of <^(c<sub>2</sub> . f),(c<sub>2</sub> . d)^>
b1 is Element of <^(c<sub>2</sub> . fa),(c<sub>2</sub> . f)^>
f1 is Element of <^(c . f),(c . d)^>
G1 is Element of <^(c . fa),(c . f)^>
f1 * G1 is Element of <^(c . fa),(c . d)^>
<^(c . fa),(c . d)^> is set
the Arrows of F<sub>2</sub>() . ((c . fa),(c . d)) is set
[(c . fa),(c . d)] is V22() set
{(c . fa),(c . d)} is non empty set
{{(c . fa),(c . d)},{(c . fa)}} is non empty set
the Arrows of F<sub>2</sub>() . [(c . fa),(c . d)] is set
F<sub>4</sub>(d,fa,(g * fb)) is set
Morph-Map (c,d,f) is Relation-like <^d,f^> -defined <^(c . f),(c . d)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(c . f),(c . d)^>:]
[:<^d,f^>,<^(c . f),(c . d)^>:] is Relation-like set
bool [:<^d,f^>,<^(c . f),(c . d)^>:] is non empty set
(Morph-Map (c,d,f)) . fb is set
Morph-Map (c,f,fa) is Relation-like <^f,fa^> -defined <^(c . fa),(c . f)^> -valued Function-like quasi_total Element of bool [:<^f,fa^>,<^(c . fa),(c . f)^>:]
[:<^f,fa^>,<^(c . fa),(c . f)^>:] is Relation-like set
bool [:<^f,fa^>,<^(c . fa),(c . f)^>:] is non empty set
(Morph-Map (c,f,fa)) . g is set
Morph-Map (c,d,fa) is Relation-like <^d,fa^> -defined <^(c . fa),(c . d)^> -valued Function-like quasi_total Element of bool [:<^d,fa^>,<^(c . fa),(c . d)^>:]
[:<^d,fa^>,<^(c . fa),(c . d)^>:] is Relation-like set
bool [:<^d,fa^>,<^(c . fa),(c . d)^>:] is non empty set
(Morph-Map (c,d,fa)) . (g * fb) is set
d is Element of the carrier of F<sub>1</sub>()
c . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of c . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of c . [d,d] is set
( the ObjectMap of c . (d,d)) `1 is set
F₃(d) is set
<^d,d^> is non empty set
the Arrows of F₁() . (d,d) is set
the Arrows of F₁() . [d,d] is set
<^(c . d),(c . d)^> is non empty set
the Arrows of F₂() . ((c . d),(c . d)) is set
[(c . d),(c . d)] is V22() set
{(c . d),(c . d)} is non empty set
{(c . d)} is non empty set
{{(c . d),(c . d)},{(c . d)}} is non empty set
the Arrows of F₂() . [(c . d),(c . d)] is set
Morph-Map (c,d,d) is Relation-like <^d,d^> -defined <^(c . d),(c . d)^> -valued Function-like non empty V14(<^d,d^>) quasi_total Element of bool [:<^d,d^>,<^(c . d),(c . d)^>:]
[:<^d,d^>,<^(c . d),(c . d)^>:] is Relation-like non empty set
bool [:<^d,d^>,<^(c . d),(c . d)^>:] is non empty set
the MorphMap of c . (d,d) is set
the MorphMap of c . [d,d] is Relation-like Function-like set
idm d is retraction coretraction iso mono epi Element of <^d,d^>
(Morph-Map (c,d,d)) . (idm d) is Element of <^(c . d),(c . d)^>
F₄(d,d,(idm d)) is set
idm (c . d) is retraction coretraction iso mono epi Element of <^(c . d),(c . d)^>
d is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of F₁(),F₂()
fa is Element of the carrier of F₁()
fb is Element of the carrier of F₁()
<^fa,fb^> is set
the Arrows of F₁() . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of F₁() . [fa,fb] is set
f is Element of the carrier of F₁()
d . f is Element of the carrier of F₂()
the ObjectMap of d is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of d . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of d . [f,f] is set
( the ObjectMap of d . (f,f)) `1 is set
F<sub>3</sub>(f) is set
g is Element of <^fa,fb^>
d . g is Element of <^(d . fb),(d . fa)^>
d . fb is Element of the carrier of F<sub>2</sub>()
the ObjectMap of d . (fb,fb) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[fb,fb] is V22() set
{fb,fb} is non empty set
{fb} is non empty set
{{fb,fb},{fb}} is non empty set
the ObjectMap of d . [fb,fb] is set
( the ObjectMap of d . (fb,fb)) `1 is set
d . fa is Element of the carrier of F₂()
the ObjectMap of d . (fa,fa) is Element of [: the carrier of F₂(), the carrier of F₂():]
[fa,fa] is V22() set
{fa,fa} is non empty set
{{fa,fa},{fa}} is non empty set
the ObjectMap of d . [fa,fa] is set
( the ObjectMap of d . (fa,fa)) `1 is set
<^(d . fb),(d . fa)^> is set
the Arrows of F<sub>2</sub>() . ((d . fb),(d . fa)) is set
[(d . fb),(d . fa)] is V22() set
{(d . fb),(d . fa)} is non empty set
{(d . fb)} is non empty set
{{(d . fb),(d . fa)},{(d . fb)}} is non empty set
the Arrows of F<sub>2</sub>() . [(d . fb),(d . fa)] is set
F<sub>4</sub>(fa,fb,g) is set
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
FF is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
a is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
the ObjectMap of FF is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the carrier of c<sub>2</sub> is non empty set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the MorphMap of FF is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of FF, the Arrows of A, the Arrows of c<sub>2</sub>
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
FunctorStr(# the ObjectMap of FF, the MorphMap of FF #) is strict FunctorStr over A,c<sub>2</sub>
the ObjectMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
the MorphMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of a, the Arrows of A, the Arrows of c<sub>2</sub>
FunctorStr(# the ObjectMap of a, the MorphMap of a #) is strict FunctorStr over A,c<sub>2</sub>
[: the carrier of A, the carrier of c<sub>2</sub>:] is Relation-like non empty set
bool [: the carrier of A, the carrier of c<sub>2</sub>:] is non empty set
b is Relation-like the carrier of A -defined the carrier of c<sub>2</sub> -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of c<sub>2</sub>:]
[:b,b:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
~ [:b,b:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
c is Relation-like the carrier of A -defined the carrier of c<sub>2</sub> -valued Function-like non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of c<sub>2</sub>:]
[:c,c:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
~ [:c,c:] is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
d is Element of the carrier of A
f is Element of the carrier of A
dom b is non empty Element of bool the carrier of A
bool the carrier of A is non empty set
dom c is non empty Element of bool the carrier of A
dom [:b,b:] is Relation-like the carrier of A -defined the carrier of A -valued non empty Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
[f,d] is V22() set
{f,d} is non empty set
{f} is non empty set
{{f,d},{f}} is non empty set
dom [:c,c:] is Relation-like the carrier of A -defined the carrier of A -valued non empty Element of bool [: the carrier of A, the carrier of A:]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
[f,f] is V22() set
{f,f} is non empty set
{{f,f},{f}} is non empty set
fa is Element of the carrier of A
the ObjectMap of FF . (fa,fa) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[fa,fa] is V22() set
{fa,fa} is non empty set
{fa} is non empty set
{{fa,fa},{fa}} is non empty set
the ObjectMap of FF . [fa,fa] is set
[:b,b:] . (fa,fa) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[:b,b:] . [fa,fa] is set
fb is Element of the carrier of A
the ObjectMap of FF . (fb,fb) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[fb,fb] is V22() set
{fb,fb} is non empty set
{fb} is non empty set
{{fb,fb},{fb}} is non empty set
the ObjectMap of FF . [fb,fb] is set
[:b,b:] . (fb,fb) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[:b,b:] . [fb,fb] is set
the ObjectMap of a . (fa,fa) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of a . [fa,fa] is set
[:c,c:] . (fa,fa) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[:c,c:] . [fa,fa] is set
the ObjectMap of a . (fb,fb) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of a . [fb,fb] is set
[:c,c:] . (fb,fb) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[:c,c:] . [fb,fb] is set
b . fa is Element of the carrier of c<sub>2</sub>
[(b . fa),(b . fa)] is V22() set
{(b . fa),(b . fa)} is non empty set
{(b . fa)} is non empty set
{{(b . fa),(b . fa)},{(b . fa)}} is non empty set
b . fb is Element of the carrier of c<sub>2</sub>
[(b . fb),(b . fb)] is V22() set
{(b . fb),(b . fb)} is non empty set
{(b . fb)} is non empty set
{{(b . fb),(b . fb)},{(b . fb)}} is non empty set
c . fa is Element of the carrier of c<sub>2</sub>
[(c . fa),(c . fa)] is V22() set
{(c . fa),(c . fa)} is non empty set
{(c . fa)} is non empty set
{{(c . fa),(c . fa)},{(c . fa)}} is non empty set
c . fb is Element of the carrier of c<sub>2</sub>
[(c . fb),(c . fb)] is V22() set
{(c . fb),(c . fb)} is non empty set
{(c . fb)} is non empty set
{{(c . fb),(c . fb)},{(c . fb)}} is non empty set
FF . fa is Element of the carrier of c<sub>2</sub>
( the ObjectMap of FF . (fa,fa)) `1 is set
FF . fb is Element of the carrier of c₂
( the ObjectMap of FF . (fb,fb)) `1 is set
a . fa is Element of the carrier of c<sub>2</sub>
( the ObjectMap of a . (fa,fa)) `1 is set
a . fb is Element of the carrier of c₂
( the ObjectMap of a . (fb,fb)) `1 is set
the ObjectMap of FF . (d,f) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[d,f] is V22() set
{d,f} is non empty set
{{d,f},{d}} is non empty set
the ObjectMap of FF . [d,f] is set
[:b,b:] . (f,d) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[:b,b:] . [f,d] is set
b . f is Element of the carrier of c<sub>2</sub>
b . d is Element of the carrier of c<sub>2</sub>
[(b . f),(b . d)] is V22() set
{(b . f),(b . d)} is non empty set
{(b . f)} is non empty set
{{(b . f),(b . d)},{(b . f)}} is non empty set
[:c,c:] . (f,d) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[:c,c:] . [f,d] is set
the ObjectMap of a . (d,f) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of a . [d,f] is set
d is set
f is set
fa is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
fb is Element of the carrier of A
g is Element of the carrier of A
<^fb,g^> is set
the Arrows of A . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of A . [fb,g] is set
FF . g is Element of the carrier of c<sub>2</sub>
the ObjectMap of FF . (g,g) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of FF . [g,g] is set
( the ObjectMap of FF . (g,g)) `1 is set
FF . fb is Element of the carrier of c₂
the ObjectMap of FF . (fb,fb) is Element of [: the carrier of c₂, the carrier of c₂:]
[fb,fb] is V22() set
{fb,fb} is non empty set
{{fb,fb},{fb}} is non empty set
the ObjectMap of FF . [fb,fb] is set
( the ObjectMap of FF . (fb,fb)) `1 is set
<^(FF . g),(FF . fb)^> is set
the Arrows of c<sub>2</sub> . ((FF . g),(FF . fb)) is set
[(FF . g),(FF . fb)] is V22() set
{(FF . g),(FF . fb)} is non empty set
{(FF . g)} is non empty set
{{(FF . g),(FF . fb)},{(FF . g)}} is non empty set
the Arrows of c<sub>2</sub> . [(FF . g),(FF . fb)] is set
a . g is Element of the carrier of c<sub>2</sub>
the ObjectMap of a . (g,g) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of a . [g,g] is set
( the ObjectMap of a . (g,g)) `1 is set
a . fb is Element of the carrier of c₂
the ObjectMap of a . (fb,fb) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of a . [fb,fb] is set
( the ObjectMap of a . (fb,fb)) `1 is set
<^(a . g),(a . fb)^> is set
the Arrows of c<sub>2</sub> . ((a . g),(a . fb)) is set
[(a . g),(a . fb)] is V22() set
{(a . g),(a . fb)} is non empty set
{(a . g)} is non empty set
{{(a . g),(a . fb)},{(a . g)}} is non empty set
the Arrows of c<sub>2</sub> . [(a . g),(a . fb)] is set
Morph-Map (FF,fb,g) is Relation-like <^fb,g^> -defined <^(FF . g),(FF . fb)^> -valued Function-like quasi_total Element of bool [:<^fb,g^>,<^(FF . g),(FF . fb)^>:]
[:<^fb,g^>,<^(FF . g),(FF . fb)^>:] is Relation-like set
bool [:<^fb,g^>,<^(FF . g),(FF . fb)^>:] is non empty set
the MorphMap of FF . (fb,g) is set
the MorphMap of FF . [fb,g] is Relation-like Function-like set
dom (Morph-Map (FF,fb,g)) is Element of bool <^fb,g^>
bool <^fb,g^> is non empty set
Morph-Map (a,fb,g) is Relation-like <^fb,g^> -defined <^(a . g),(a . fb)^> -valued Function-like quasi_total Element of bool [:<^fb,g^>,<^(a . g),(a . fb)^>:]
[:<^fb,g^>,<^(a . g),(a . fb)^>:] is Relation-like set
bool [:<^fb,g^>,<^(a . g),(a . fb)^>:] is non empty set
the MorphMap of a . (fb,g) is set
the MorphMap of a . [fb,g] is Relation-like Function-like set
dom (Morph-Map (a,fb,g)) is Element of bool <^fb,g^>
g is set
(Morph-Map (FF,fb,g)) . g is set
c<sub>13</sub> is Element of <^fb,g^>
FF . c<sub>13</sub> is Element of <^(FF . g),(FF . fb)^>
a . c<sub>13</sub> is Element of <^(a . g),(a . fb)^>
(Morph-Map (a,fb,g)) . g is set
the MorphMap of FF . d is Relation-like Function-like set
the MorphMap of a . d is Relation-like Function-like set
A is non empty set
c<sub>2</sub> is non empty set
[:A,c<sub>2</sub>:] is Relation-like non empty set
FF is non empty set
[:[:A,c<sub>2</sub>:],FF:] is Relation-like non empty set
bool [:[:A,c<sub>2</sub>:],FF:] is non empty set
a is Relation-like [:A,c<sub>2</sub>:] -defined FF -valued Function-like non empty V14([:A,c<sub>2</sub>:]) quasi_total Element of bool [:[:A,c<sub>2</sub>:],FF:]
dom a is Relation-like A -defined c<sub>2</sub> -valued non empty Element of bool [:A,c<sub>2</sub>:]
bool [:A,c<sub>2</sub>:] is non empty set
b is Element of A
c is Element of A
d is Element of c<sub>2</sub>
a . (b,d) is Element of FF
[b,d] is V22() set
{b,d} is non empty set
{b} is non empty set
{{b,d},{b}} is non empty set
a . [b,d] is set
f is Element of c<sub>2</sub>
a . (c,f) is Element of FF
[c,f] is V22() set
{c,f} is non empty set
{c} is non empty set
{{c,f},{c}} is non empty set
a . [c,f] is set
b is set
proj1 a is Relation-like non empty set
c is set
a . b is set
a . c is set
d is set
f is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
fa is set
fb is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
g is Element of A
c<sub>13</sub> is Element of c<sub>2</sub>
a . (g,c<sub>13</sub>) is Element of FF
[g,c<sub>13</sub>] is V22() set
{g,c<sub>13</sub>} is non empty set
{g} is non empty set
{{g,c<sub>13</sub>},{g}} is non empty set
a . [g,c<sub>13</sub>] is set
g is Element of A
g9 is Element of c<sub>2</sub>
a . (g,g9) is Element of FF
[g,g9] is V22() set
{g,g9} is non empty set
{g} is non empty set
{{g,g9},{g}} is non empty set
a . [g,g9] is set
F<sub>1</sub>() is non empty transitive associative with_units reflexive AltCatStr
F<sub>2</sub>() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F<sub>1</sub>() is non empty set
F<sub>3</sub>() is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
the ObjectMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
a is Element of the carrier of F<sub>1</sub>()
the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,a) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c<sub>2</sub>,a] is V22() set
{c<sub>2</sub>,a} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,a},{c<sub>2</sub>}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c<sub>2</sub>,a] is set
FF is Element of the carrier of F<sub>1</sub>()
b is Element of the carrier of F<sub>1</sub>()
the ObjectMap of F<sub>3</sub>() . (FF,b) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[FF,b] is V22() set
{FF,b} is non empty set
{FF} is non empty set
{{FF,b},{FF}} is non empty set
the ObjectMap of F<sub>3</sub>() . [FF,b] is set
c is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>() . c is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (c,c) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c,c] is set
( the ObjectMap of F<sub>3</sub>() . (c,c)) `1 is set
f is Element of the carrier of F₁()
F₃() . f is Element of the carrier of F₂()
the ObjectMap of F₃() . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of F₃() . [f,f] is set
( the ObjectMap of F₃() . (f,f)) `1 is set
[(F<sub>3</sub>() . c),(F<sub>3</sub>() . f)] is V22() set
{(F<sub>3</sub>() . c),(F<sub>3</sub>() . f)} is non empty set
{(F<sub>3</sub>() . c)} is non empty set
{{(F<sub>3</sub>() . c),(F<sub>3</sub>() . f)},{(F<sub>3</sub>() . c)}} is non empty set
d is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>() . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of F<sub>3</sub>() . [d,d] is set
( the ObjectMap of F<sub>3</sub>() . (d,d)) `1 is set
fa is Element of the carrier of F₁()
F₃() . fa is Element of the carrier of F₂()
the ObjectMap of F₃() . (fa,fa) is Element of [: the carrier of F₂(), the carrier of F₂():]
[fa,fa] is V22() set
{fa,fa} is non empty set
{fa} is non empty set
{{fa,fa},{fa}} is non empty set
the ObjectMap of F₃() . [fa,fa] is set
( the ObjectMap of F₃() . (fa,fa)) `1 is set
[(F<sub>3</sub>() . d),(F<sub>3</sub>() . fa)] is V22() set
{(F<sub>3</sub>() . d),(F<sub>3</sub>() . fa)} is non empty set
{(F<sub>3</sub>() . d)} is non empty set
{{(F<sub>3</sub>() . d),(F<sub>3</sub>() . fa)},{(F<sub>3</sub>() . d)}} is non empty set
F<sub>4</sub>(c) is set
F<sub>4</sub>(f) is set
F<sub>4</sub>(d) is set
F<sub>4</sub>(fa) is set
c<sub>2</sub> is set
FF is set
a is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
b is Element of the carrier of F<sub>1</sub>()
c is Element of the carrier of F<sub>1</sub>()
<^b,c^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
the Arrows of F<sub>1</sub>() . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of F<sub>1</sub>() . [b,c] is set
F<sub>3</sub>() . b is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (b,b) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[b,b] is V22() set
{b,b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of F<sub>3</sub>() . [b,b] is set
( the ObjectMap of F<sub>3</sub>() . (b,b)) `1 is set
F₃() . c is Element of the carrier of F₂()
the ObjectMap of F₃() . (c,c) is Element of [: the carrier of F₂(), the carrier of F₂():]
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of F₃() . [c,c] is set
( the ObjectMap of F₃() . (c,c)) `1 is set
<^(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . b),(F<sub>3</sub>() . c)) is set
[(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)] is V22() set
{(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)} is non empty set
{(F<sub>3</sub>() . b)} is non empty set
{{(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)},{(F<sub>3</sub>() . b)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)] is set
Morph-Map (F<sub>3</sub>(),b,c) is Relation-like <^b,c^> -defined <^(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)^> -valued Function-like quasi_total Element of bool [:<^b,c^>,<^(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)^>:]
[:<^b,c^>,<^(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)^>:] is Relation-like set
bool [:<^b,c^>,<^(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)^>:] is non empty set
the MorphMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) Function-yielding V63() MSUnTrans of the ObjectMap of F<sub>3</sub>(), the Arrows of F<sub>1</sub>(), the Arrows of F<sub>2</sub>()
the MorphMap of F<sub>3</sub>() . (b,c) is set
the MorphMap of F<sub>3</sub>() . [b,c] is Relation-like Function-like set
d is set
proj1 (Morph-Map (F<sub>3</sub>(),b,c)) is set
f is set
(Morph-Map (F<sub>3</sub>(),b,c)) . d is set
(Morph-Map (F<sub>3</sub>(),b,c)) . f is set
dom (Morph-Map (F<sub>3</sub>(),b,c)) is Element of bool <^b,c^>
bool <^b,c^> is non empty set
fa is Element of <^b,c^>
F<sub>3</sub>() . fa is Element of <^(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)^>
fb is Element of <^b,c^>
F<sub>3</sub>() . fb is Element of <^(F<sub>3</sub>() . b),(F<sub>3</sub>() . c)^>
F<sub>5</sub>(b,c,fa) is set
F<sub>5</sub>(b,c,fb) is set
the MorphMap of F<sub>3</sub>() . c<sub>2</sub> is Relation-like Function-like set
the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
c<sub>2</sub> is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) Function-yielding V63() ManySortedFunction of the Arrows of F<sub>1</sub>(), the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()
FF is set
c<sub>2</sub> . FF is Relation-like Function-like set
proj2 (c<sub>2</sub> . FF) is set
( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . FF is set
a is Element of [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
c<sub>2</sub> . a is Relation-like the Arrows of F<sub>1</sub>() . a -defined ( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a -valued Function-like quasi_total Element of bool [:( the Arrows of F<sub>1</sub>() . a),(( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a):]
the Arrows of F<sub>1</sub>() . a is set
( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a is set
[:( the Arrows of F<sub>1</sub>() . a),(( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a):] is Relation-like set
bool [:( the Arrows of F<sub>1</sub>() . a),(( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a):] is non empty set
b is set
c is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the ObjectMap of F<sub>3</sub>() . a is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
d is Element of the carrier of F<sub>1</sub>()
f is Element of the carrier of F<sub>1</sub>()
the ObjectMap of F<sub>3</sub>() . (d,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the ObjectMap of F<sub>3</sub>() . [d,f] is set
F<sub>3</sub>() . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of F<sub>3</sub>() . [d,d] is set
( the ObjectMap of F<sub>3</sub>() . (d,d)) `1 is set
F₃() . f is Element of the carrier of F₂()
the ObjectMap of F₃() . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of F₃() . [f,f] is set
( the ObjectMap of F₃() . (f,f)) `1 is set
[(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)] is V22() set
{(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)} is non empty set
{(F<sub>3</sub>() . d)} is non empty set
{{(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)},{(F<sub>3</sub>() . d)}} is non empty set
<^(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . d),(F<sub>3</sub>() . f)) is set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)] is set
fa is set
fb is Element of <^(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)^>
g is Element of the carrier of F<sub>1</sub>()
g is Element of the carrier of F<sub>1</sub>()
<^g,g^> is set
the Arrows of F<sub>1</sub>() . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of F<sub>1</sub>() . [g,g] is set
F<sub>4</sub>(g) is set
F<sub>4</sub>(g) is set
c<sub>13</sub> is Element of <^g,g^>
F<sub>5</sub>(g,g,c<sub>13</sub>) is set
F<sub>4</sub>(d) is set
F<sub>4</sub>(f) is set
F<sub>3</sub>() . c<sub>13</sub> is Element of <^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^>
F<sub>3</sub>() . g is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (g,g) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[g,g] is V22() set
{g,g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of F<sub>3</sub>() . [g,g] is set
( the ObjectMap of F<sub>3</sub>() . (g,g)) `1 is set
F₃() . g is Element of the carrier of F₂()
the ObjectMap of F₃() . (g,g) is Element of [: the carrier of F₂(), the carrier of F₂():]
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of F₃() . [g,g] is set
( the ObjectMap of F₃() . (g,g)) `1 is set
<^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . g),(F<sub>3</sub>() . g)) is set
[(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)] is V22() set
{(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)} is non empty set
{(F<sub>3</sub>() . g)} is non empty set
{{(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)},{(F<sub>3</sub>() . g)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)] is set
Morph-Map (F<sub>3</sub>(),g,g) is Relation-like <^g,g^> -defined <^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^> -valued Function-like quasi_total Element of bool [:<^g,g^>,<^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^>:]
[:<^g,g^>,<^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^>:] is Relation-like set
bool [:<^g,g^>,<^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^>:] is non empty set
the MorphMap of F<sub>3</sub>() . (g,g) is set
the MorphMap of F<sub>3</sub>() . [g,g] is Relation-like Function-like set
(Morph-Map (F<sub>3</sub>(),g,g)) . c<sub>13</sub> is set
<^d,f^> is set
the Arrows of F<sub>1</sub>() . (d,f) is set
the Arrows of F<sub>1</sub>() . [d,f] is set
Morph-Map (F<sub>3</sub>(),d,f) is Relation-like <^d,f^> -defined <^(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)^>:]
[:<^d,f^>,<^(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)^>:] is Relation-like set
bool [:<^d,f^>,<^(F<sub>3</sub>() . d),(F<sub>3</sub>() . f)^>:] is non empty set
the MorphMap of F<sub>3</sub>() . (d,f) is set
the MorphMap of F<sub>3</sub>() . [d,f] is Relation-like Function-like set
dom (Morph-Map (F<sub>3</sub>(),d,f)) is Element of bool <^d,f^>
bool <^d,f^> is non empty set
rng the ObjectMap of F<sub>3</sub>() is Relation-like the carrier of F<sub>2</sub>() -defined the carrier of F<sub>2</sub>() -valued non empty Element of bool [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
bool [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is non empty set
rng the ObjectMap of F<sub>3</sub>() is Relation-like the carrier of F<sub>2</sub>() -defined the carrier of F<sub>2</sub>() -valued non empty Element of bool [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
FF is set
a is set
b is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
c is Element of the carrier of F<sub>2</sub>()
idm c is retraction coretraction iso mono epi Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of F<sub>2</sub>() . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of F<sub>2</sub>() . [c,c] is set
f is Element of the carrier of F<sub>1</sub>()
fa is Element of the carrier of F<sub>1</sub>()
<^f,fa^> is set
the Arrows of F<sub>1</sub>() . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of F<sub>1</sub>() . [f,fa] is set
F<sub>4</sub>(f) is set
F<sub>4</sub>(fa) is set
fb is Element of <^f,fa^>
F<sub>5</sub>(f,fa,fb) is set
d is Element of the carrier of F<sub>2</sub>()
idm d is retraction coretraction iso mono epi Element of <^d,d^>
<^d,d^> is non empty set
the Arrows of F<sub>2</sub>() . (d,d) is set
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the Arrows of F<sub>2</sub>() . [d,d] is set
g is Element of the carrier of F<sub>1</sub>()
g is Element of the carrier of F<sub>1</sub>()
<^g,g^> is set
the Arrows of F<sub>1</sub>() . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of F<sub>1</sub>() . [g,g] is set
F<sub>4</sub>(g) is set
F<sub>4</sub>(g) is set
c<sub>13</sub> is Element of <^g,g^>
F<sub>5</sub>(g,g,c<sub>13</sub>) is set
[f,g] is V22() set
{f,g} is non empty set
{{f,g},{f}} is non empty set
dom the ObjectMap of F<sub>3</sub>() is Relation-like the carrier of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() -valued non empty Element of bool [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
bool [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is non empty set
the ObjectMap of F<sub>3</sub>() . [f,g] is set
the ObjectMap of F<sub>3</sub>() . (f,g) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
F<sub>3</sub>() . f is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (f,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[f,f] is V22() set
{f,f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of F<sub>3</sub>() . [f,f] is set
( the ObjectMap of F<sub>3</sub>() . (f,f)) `1 is set
F₃() . g is Element of the carrier of F₂()
the ObjectMap of F₃() . (g,g) is Element of [: the carrier of F₂(), the carrier of F₂():]
[g,g] is V22() set
{g,g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of F₃() . [g,g] is set
( the ObjectMap of F₃() . (g,g)) `1 is set
[(F<sub>3</sub>() . f),(F<sub>3</sub>() . g)] is V22() set
{(F<sub>3</sub>() . f),(F<sub>3</sub>() . g)} is non empty set
{(F<sub>3</sub>() . f)} is non empty set
{{(F<sub>3</sub>() . f),(F<sub>3</sub>() . g)},{(F<sub>3</sub>() . f)}} is non empty set
[c,(F<sub>3</sub>() . g)] is V22() set
{c,(F<sub>3</sub>() . g)} is non empty set
{{c,(F<sub>3</sub>() . g)},{c}} is non empty set
F<sub>1</sub>() is non empty transitive associative with_units reflexive AltCatStr
F<sub>2</sub>() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F<sub>1</sub>() is non empty set
the carrier of F<sub>2</sub>() is non empty set
A is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>(A) is set
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>(c<sub>2</sub>) is set
A is Element of the carrier of F<sub>1</sub>()
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
<^A,c<sub>2</sub>^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
the Arrows of F<sub>1</sub>() . (A,c<sub>2</sub>) is set
[A,c<sub>2</sub>] is V22() set
{A,c<sub>2</sub>} is non empty set
{A} is non empty set
{{A,c<sub>2</sub>},{A}} is non empty set
the Arrows of F<sub>1</sub>() . [A,c<sub>2</sub>] is set
FF is Element of <^A,c<sub>2</sub>^>
F<sub>4</sub>(A,c<sub>2</sub>,FF) is set
a is Element of <^A,c<sub>2</sub>^>
F<sub>4</sub>(A,c<sub>2</sub>,a) is set
A is Element of the carrier of F<sub>2</sub>()
c<sub>2</sub> is Element of the carrier of F<sub>2</sub>()
<^A,c<sub>2</sub>^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the Arrows of F<sub>2</sub>() . (A,c<sub>2</sub>) is set
[A,c<sub>2</sub>] is V22() set
{A,c<sub>2</sub>} is non empty set
{A} is non empty set
{{A,c<sub>2</sub>},{A}} is non empty set
the Arrows of F<sub>2</sub>() . [A,c<sub>2</sub>] is set
FF is Element of <^A,c<sub>2</sub>^>
A is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
A is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
F<sub>1</sub>() is non empty transitive associative with_units reflexive AltCatStr
F<sub>2</sub>() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F<sub>1</sub>() is non empty set
F<sub>3</sub>() is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
the ObjectMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
a is Element of the carrier of F<sub>1</sub>()
the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,a) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c<sub>2</sub>,a] is V22() set
{c<sub>2</sub>,a} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,a},{c<sub>2</sub>}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c<sub>2</sub>,a] is set
FF is Element of the carrier of F<sub>1</sub>()
b is Element of the carrier of F<sub>1</sub>()
the ObjectMap of F<sub>3</sub>() . (FF,b) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[FF,b] is V22() set
{FF,b} is non empty set
{FF} is non empty set
{{FF,b},{FF}} is non empty set
the ObjectMap of F<sub>3</sub>() . [FF,b] is set
f is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>() . f is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (f,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of F<sub>3</sub>() . [f,f] is set
( the ObjectMap of F<sub>3</sub>() . (f,f)) `1 is set
c is Element of the carrier of F₁()
F₃() . c is Element of the carrier of F₂()
the ObjectMap of F₃() . (c,c) is Element of [: the carrier of F₂(), the carrier of F₂():]
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of F₃() . [c,c] is set
( the ObjectMap of F₃() . (c,c)) `1 is set
[(F<sub>3</sub>() . f),(F<sub>3</sub>() . c)] is V22() set
{(F<sub>3</sub>() . f),(F<sub>3</sub>() . c)} is non empty set
{(F<sub>3</sub>() . f)} is non empty set
{{(F<sub>3</sub>() . f),(F<sub>3</sub>() . c)},{(F<sub>3</sub>() . f)}} is non empty set
fa is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>() . fa is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (fa,fa) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[fa,fa] is V22() set
{fa,fa} is non empty set
{fa} is non empty set
{{fa,fa},{fa}} is non empty set
the ObjectMap of F<sub>3</sub>() . [fa,fa] is set
( the ObjectMap of F<sub>3</sub>() . (fa,fa)) `1 is set
d is Element of the carrier of F₁()
F₃() . d is Element of the carrier of F₂()
the ObjectMap of F₃() . (d,d) is Element of [: the carrier of F₂(), the carrier of F₂():]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of F₃() . [d,d] is set
( the ObjectMap of F₃() . (d,d)) `1 is set
[(F<sub>3</sub>() . fa),(F<sub>3</sub>() . d)] is V22() set
{(F<sub>3</sub>() . fa),(F<sub>3</sub>() . d)} is non empty set
{(F<sub>3</sub>() . fa)} is non empty set
{{(F<sub>3</sub>() . fa),(F<sub>3</sub>() . d)},{(F<sub>3</sub>() . fa)}} is non empty set
F<sub>4</sub>(c) is set
F<sub>4</sub>(f) is set
F<sub>4</sub>(d) is set
F<sub>4</sub>(fa) is set
c<sub>2</sub> is set
FF is set
a is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
b is Element of the carrier of F<sub>1</sub>()
c is Element of the carrier of F<sub>1</sub>()
<^b,c^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
the Arrows of F<sub>1</sub>() . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of F<sub>1</sub>() . [b,c] is set
F<sub>3</sub>() . c is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (c,c) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c,c] is set
( the ObjectMap of F<sub>3</sub>() . (c,c)) `1 is set
F₃() . b is Element of the carrier of F₂()
the ObjectMap of F₃() . (b,b) is Element of [: the carrier of F₂(), the carrier of F₂():]
[b,b] is V22() set
{b,b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of F₃() . [b,b] is set
( the ObjectMap of F₃() . (b,b)) `1 is set
<^(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . c),(F<sub>3</sub>() . b)) is set
[(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)] is V22() set
{(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)} is non empty set
{(F<sub>3</sub>() . c)} is non empty set
{{(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)},{(F<sub>3</sub>() . c)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)] is set
Morph-Map (F<sub>3</sub>(),b,c) is Relation-like <^b,c^> -defined <^(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)^> -valued Function-like quasi_total Element of bool [:<^b,c^>,<^(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)^>:]
[:<^b,c^>,<^(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)^>:] is Relation-like set
bool [:<^b,c^>,<^(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)^>:] is non empty set
the MorphMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) Function-yielding V63() MSUnTrans of the ObjectMap of F<sub>3</sub>(), the Arrows of F<sub>1</sub>(), the Arrows of F<sub>2</sub>()
the MorphMap of F<sub>3</sub>() . (b,c) is set
the MorphMap of F<sub>3</sub>() . [b,c] is Relation-like Function-like set
d is set
proj1 (Morph-Map (F<sub>3</sub>(),b,c)) is set
f is set
(Morph-Map (F<sub>3</sub>(),b,c)) . d is set
(Morph-Map (F<sub>3</sub>(),b,c)) . f is set
dom (Morph-Map (F<sub>3</sub>(),b,c)) is Element of bool <^b,c^>
bool <^b,c^> is non empty set
fa is Element of <^b,c^>
F<sub>3</sub>() . fa is Element of <^(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)^>
fb is Element of <^b,c^>
F<sub>3</sub>() . fb is Element of <^(F<sub>3</sub>() . c),(F<sub>3</sub>() . b)^>
F<sub>5</sub>(b,c,fa) is set
F<sub>5</sub>(b,c,fb) is set
the MorphMap of F<sub>3</sub>() . c<sub>2</sub> is Relation-like Function-like set
the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
c<sub>2</sub> is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) Function-yielding V63() ManySortedFunction of the Arrows of F<sub>1</sub>(), the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()
FF is set
c<sub>2</sub> . FF is Relation-like Function-like set
proj2 (c<sub>2</sub> . FF) is set
( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . FF is set
a is Element of [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
c<sub>2</sub> . a is Relation-like the Arrows of F<sub>1</sub>() . a -defined ( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a -valued Function-like quasi_total Element of bool [:( the Arrows of F<sub>1</sub>() . a),(( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a):]
the Arrows of F<sub>1</sub>() . a is set
( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a is set
[:( the Arrows of F<sub>1</sub>() . a),(( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a):] is Relation-like set
bool [:( the Arrows of F<sub>1</sub>() . a),(( the ObjectMap of F<sub>3</sub>() (#) the Arrows of F<sub>2</sub>()) . a):] is non empty set
b is set
c is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the ObjectMap of F<sub>3</sub>() . a is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
d is Element of the carrier of F<sub>1</sub>()
f is Element of the carrier of F<sub>1</sub>()
the ObjectMap of F<sub>3</sub>() . (d,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the ObjectMap of F<sub>3</sub>() . [d,f] is set
F<sub>3</sub>() . f is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (f,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of F<sub>3</sub>() . [f,f] is set
( the ObjectMap of F<sub>3</sub>() . (f,f)) `1 is set
F₃() . d is Element of the carrier of F₂()
the ObjectMap of F₃() . (d,d) is Element of [: the carrier of F₂(), the carrier of F₂():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of F₃() . [d,d] is set
( the ObjectMap of F₃() . (d,d)) `1 is set
[(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)] is V22() set
{(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)} is non empty set
{(F<sub>3</sub>() . f)} is non empty set
{{(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)},{(F<sub>3</sub>() . f)}} is non empty set
<^(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . f),(F<sub>3</sub>() . d)) is set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)] is set
fa is set
fb is Element of <^(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)^>
g is Element of the carrier of F<sub>1</sub>()
g is Element of the carrier of F<sub>1</sub>()
<^g,g^> is set
the Arrows of F<sub>1</sub>() . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of F<sub>1</sub>() . [g,g] is set
F<sub>4</sub>(g) is set
F<sub>4</sub>(g) is set
c<sub>13</sub> is Element of <^g,g^>
F<sub>5</sub>(g,g,c<sub>13</sub>) is set
F<sub>4</sub>(d) is set
F<sub>4</sub>(f) is set
F<sub>3</sub>() . c<sub>13</sub> is Element of <^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^>
F<sub>3</sub>() . g is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (g,g) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of F<sub>3</sub>() . [g,g] is set
( the ObjectMap of F<sub>3</sub>() . (g,g)) `1 is set
F₃() . g is Element of the carrier of F₂()
the ObjectMap of F₃() . (g,g) is Element of [: the carrier of F₂(), the carrier of F₂():]
[g,g] is V22() set
{g,g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of F₃() . [g,g] is set
( the ObjectMap of F₃() . (g,g)) `1 is set
<^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . g),(F<sub>3</sub>() . g)) is set
[(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)] is V22() set
{(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)} is non empty set
{(F<sub>3</sub>() . g)} is non empty set
{{(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)},{(F<sub>3</sub>() . g)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)] is set
Morph-Map (F<sub>3</sub>(),g,g) is Relation-like <^g,g^> -defined <^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^> -valued Function-like quasi_total Element of bool [:<^g,g^>,<^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^>:]
[:<^g,g^>,<^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^>:] is Relation-like set
bool [:<^g,g^>,<^(F<sub>3</sub>() . g),(F<sub>3</sub>() . g)^>:] is non empty set
the MorphMap of F<sub>3</sub>() . (g,g) is set
the MorphMap of F<sub>3</sub>() . [g,g] is Relation-like Function-like set
(Morph-Map (F<sub>3</sub>(),g,g)) . c<sub>13</sub> is set
<^d,f^> is set
the Arrows of F<sub>1</sub>() . (d,f) is set
the Arrows of F<sub>1</sub>() . [d,f] is set
Morph-Map (F<sub>3</sub>(),d,f) is Relation-like <^d,f^> -defined <^(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)^> -valued Function-like quasi_total Element of bool [:<^d,f^>,<^(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)^>:]
[:<^d,f^>,<^(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)^>:] is Relation-like set
bool [:<^d,f^>,<^(F<sub>3</sub>() . f),(F<sub>3</sub>() . d)^>:] is non empty set
the MorphMap of F<sub>3</sub>() . (d,f) is set
the MorphMap of F<sub>3</sub>() . [d,f] is Relation-like Function-like set
dom (Morph-Map (F<sub>3</sub>(),d,f)) is Element of bool <^d,f^>
bool <^d,f^> is non empty set
rng the ObjectMap of F<sub>3</sub>() is Relation-like the carrier of F<sub>2</sub>() -defined the carrier of F<sub>2</sub>() -valued non empty Element of bool [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
bool [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is non empty set
rng the ObjectMap of F<sub>3</sub>() is Relation-like the carrier of F<sub>2</sub>() -defined the carrier of F<sub>2</sub>() -valued non empty Element of bool [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
FF is set
a is set
b is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
c is Element of the carrier of F<sub>2</sub>()
idm c is retraction coretraction iso mono epi Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of F<sub>2</sub>() . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of F<sub>2</sub>() . [c,c] is set
f is Element of the carrier of F<sub>1</sub>()
fa is Element of the carrier of F<sub>1</sub>()
<^f,fa^> is set
the Arrows of F<sub>1</sub>() . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of F<sub>1</sub>() . [f,fa] is set
F<sub>4</sub>(f) is set
F<sub>4</sub>(fa) is set
fb is Element of <^f,fa^>
F<sub>5</sub>(f,fa,fb) is set
d is Element of the carrier of F<sub>2</sub>()
idm d is retraction coretraction iso mono epi Element of <^d,d^>
<^d,d^> is non empty set
the Arrows of F<sub>2</sub>() . (d,d) is set
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the Arrows of F<sub>2</sub>() . [d,d] is set
g is Element of the carrier of F<sub>1</sub>()
g is Element of the carrier of F<sub>1</sub>()
<^g,g^> is set
the Arrows of F<sub>1</sub>() . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of F<sub>1</sub>() . [g,g] is set
F<sub>4</sub>(g) is set
F<sub>4</sub>(g) is set
c<sub>13</sub> is Element of <^g,g^>
F<sub>5</sub>(g,g,c<sub>13</sub>) is set
[g,f] is V22() set
{g,f} is non empty set
{{g,f},{g}} is non empty set
dom the ObjectMap of F<sub>3</sub>() is Relation-like the carrier of F<sub>1</sub>() -defined the carrier of F<sub>1</sub>() -valued non empty Element of bool [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
bool [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is non empty set
the ObjectMap of F<sub>3</sub>() . [g,f] is set
the ObjectMap of F<sub>3</sub>() . (g,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
F<sub>3</sub>() . f is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (f,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[f,f] is V22() set
{f,f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of F<sub>3</sub>() . [f,f] is set
( the ObjectMap of F<sub>3</sub>() . (f,f)) `1 is set
F₃() . g is Element of the carrier of F₂()
the ObjectMap of F₃() . (g,g) is Element of [: the carrier of F₂(), the carrier of F₂():]
[g,g] is V22() set
{g,g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of F₃() . [g,g] is set
( the ObjectMap of F₃() . (g,g)) `1 is set
[(F<sub>3</sub>() . f),(F<sub>3</sub>() . g)] is V22() set
{(F<sub>3</sub>() . f),(F<sub>3</sub>() . g)} is non empty set
{(F<sub>3</sub>() . f)} is non empty set
{{(F<sub>3</sub>() . f),(F<sub>3</sub>() . g)},{(F<sub>3</sub>() . f)}} is non empty set
[c,(F<sub>3</sub>() . g)] is V22() set
{c,(F<sub>3</sub>() . g)} is non empty set
{{c,(F<sub>3</sub>() . g)},{c}} is non empty set
F<sub>1</sub>() is non empty transitive associative with_units reflexive AltCatStr
F<sub>2</sub>() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F<sub>1</sub>() is non empty set
the carrier of F<sub>2</sub>() is non empty set
A is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
A is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>(c<sub>2</sub>) is set
FF is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>(FF) is set
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
FF is Element of the carrier of F<sub>1</sub>()
<^c<sub>2</sub>,FF^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
the Arrows of F<sub>1</sub>() . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of F<sub>1</sub>() . [c<sub>2</sub>,FF] is set
a is Element of <^c<sub>2</sub>,FF^>
F<sub>4</sub>(c<sub>2</sub>,FF,a) is set
b is Element of <^c<sub>2</sub>,FF^>
F<sub>4</sub>(c<sub>2</sub>,FF,b) is set
c<sub>2</sub> is Element of the carrier of F<sub>2</sub>()
FF is Element of the carrier of F<sub>2</sub>()
<^c<sub>2</sub>,FF^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the Arrows of F<sub>2</sub>() . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of F<sub>2</sub>() . [c<sub>2</sub>,FF] is set
a is Element of <^c<sub>2</sub>,FF^>
FF is non empty transitive associative with_units reflexive AltCatStr
id FF is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of FF,FF
(id FF) * (id FF) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,FF
FF is non empty transitive associative with_units reflexive AltCatStr
a is non empty transitive associative with_units reflexive AltCatStr
b is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of FF,a
c is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of a,FF
c * b is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,FF
id FF is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of FF,FF
b * c is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
id a is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of a,a
A is non empty reflexive AltGraph
c<sub>2</sub> is non empty reflexive AltGraph
FF is non empty reflexive AltGraph
a is feasible FunctorStr over A,c<sub>2</sub>
the ObjectMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the carrier of c<sub>2</sub> is non empty set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the MorphMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of a, the Arrows of A, the Arrows of c<sub>2</sub>
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
FunctorStr(# the ObjectMap of a, the MorphMap of a #) is strict FunctorStr over A,c<sub>2</sub>
b is feasible FunctorStr over A,c<sub>2</sub>
the ObjectMap of b is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
the MorphMap of b is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of b, the Arrows of A, the Arrows of c<sub>2</sub>
FunctorStr(# the ObjectMap of b, the MorphMap of b #) is strict FunctorStr over A,c<sub>2</sub>
c is FunctorStr over c<sub>2</sub>,FF
the ObjectMap of c is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined [: the carrier of FF, the carrier of FF:] -valued Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) quasi_total Element of bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:]
the carrier of FF is non empty set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
[:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:] is Relation-like non empty set
bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:] is non empty set
the MorphMap of c is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() MSUnTrans of the ObjectMap of c, the Arrows of c<sub>2</sub>, the Arrows of FF
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
FunctorStr(# the ObjectMap of c, the MorphMap of c #) is strict FunctorStr over c<sub>2</sub>,FF
d is FunctorStr over c<sub>2</sub>,FF
the ObjectMap of d is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined [: the carrier of FF, the carrier of FF:] -valued Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) quasi_total Element of bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:]
the MorphMap of d is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() MSUnTrans of the ObjectMap of d, the Arrows of c<sub>2</sub>, the Arrows of FF
FunctorStr(# the ObjectMap of d, the MorphMap of d #) is strict FunctorStr over c<sub>2</sub>,FF
c * a is strict FunctorStr over A,FF
d * b is strict FunctorStr over A,FF
the ObjectMap of (c * a) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of FF, the carrier of FF:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of FF, the carrier of FF:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of FF, the carrier of FF:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of FF, the carrier of FF:]:] is non empty set
the ObjectMap of c * the ObjectMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of FF, the carrier of FF:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of FF, the carrier of FF:]:]
the MorphMap of (c * a) is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of (c * a), the Arrows of A, the Arrows of FF
the ObjectMap of a (#) the MorphMap of c is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() set
( the ObjectMap of a (#) the MorphMap of c) ** the MorphMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() set
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
id A is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A,A
id c<sub>2</sub> is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of c<sub>2</sub>,c<sub>2</sub>
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,c<sub>2</sub>
b is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,A
b * a is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,A
a * b is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
id FF is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of FF,FF
c is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,FF
d is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of FF,c<sub>2</sub>
d * c is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
c * d is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,FF
c * a is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,FF
f is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,FF
b * d is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,A
fa is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,A
fa * f is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,A
f * fa is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,FF
the ObjectMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the carrier of c<sub>2</sub> is non empty set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the MorphMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of a, the Arrows of A, the Arrows of c<sub>2</sub>
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
FunctorStr(# the ObjectMap of a, the MorphMap of a #) is strict FunctorStr over A,c<sub>2</sub>
the ObjectMap of b is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) quasi_total Element of bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of A, the carrier of A:]:] is non empty set
the MorphMap of b is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() MSUnTrans of the ObjectMap of b, the Arrows of c<sub>2</sub>, the Arrows of A
FunctorStr(# the ObjectMap of b, the MorphMap of b #) is strict FunctorStr over c<sub>2</sub>,A
FunctorStr(# the ObjectMap of b, the MorphMap of b #) * a is strict FunctorStr over A,A
the ObjectMap of d is Relation-like [: the carrier of FF, the carrier of FF:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of FF, the carrier of FF:]) quasi_total Element of bool [:[: the carrier of FF, the carrier of FF:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
the carrier of FF is non empty set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
[:[: the carrier of FF, the carrier of FF:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of FF, the carrier of FF:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the MorphMap of d is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) Function-yielding V63() MSUnTrans of the ObjectMap of d, the Arrows of FF, the Arrows of c<sub>2</sub>
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
FunctorStr(# the ObjectMap of d, the MorphMap of d #) is strict FunctorStr over FF,c<sub>2</sub>
the ObjectMap of c is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined [: the carrier of FF, the carrier of FF:] -valued Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) quasi_total Element of bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:]
[:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:] is Relation-like non empty set
bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:] is non empty set
the MorphMap of c is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() MSUnTrans of the ObjectMap of c, the Arrows of c<sub>2</sub>, the Arrows of FF
FunctorStr(# the ObjectMap of c, the MorphMap of c #) is strict FunctorStr over c<sub>2</sub>,FF
FunctorStr(# the ObjectMap of c, the MorphMap of c #) * d is strict FunctorStr over FF,FF
b * (id c<sub>2</sub>) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,A
c * (id c<sub>2</sub>) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,FF
fa * c is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,A
b * (d * c) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,A
f * b is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,FF
c * (a * b) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,FF
(fa * c) * a is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,A
(f * b) * d is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,FF
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
FF is feasible id-preserving Functor of A,c<sub>2</sub>
a is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,c<sub>2</sub>
a " is strict FunctorStr over c<sub>2</sub>,A
b is feasible id-preserving Functor of c<sub>2</sub>,A
id A is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A,A
id c<sub>2</sub> is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of c<sub>2</sub>,c<sub>2</sub>
c is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,A
c * a is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,A
a * c is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
F<sub>1</sub>() is non empty transitive associative with_units reflexive AltCatStr
F<sub>2</sub>() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F<sub>1</sub>() is non empty set
F<sub>3</sub>() is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
F<sub>4</sub>() is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
A is Relation-like the carrier of F<sub>1</sub>() -defined Function-like non empty V14( the carrier of F<sub>1</sub>()) set
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>() . c<sub>2</sub> is Element of the carrier of F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c<sub>2</sub>,c<sub>2</sub>] is set
( the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>)) `1 is set
F₄() . c₂ is Element of the carrier of F₂()
the ObjectMap of F₄() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of F₄() . (c₂,c₂) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [c₂,c₂] is set
( the ObjectMap of F₄() . (c₂,c₂)) `1 is set
<^(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)) is set
[(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)} is non empty set
{(F<sub>3</sub>() . c<sub>2</sub>)} is non empty set
{{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)},{(F<sub>3</sub>() . c<sub>2</sub>)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is set
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
A . c<sub>2</sub> is set
F<sub>5</sub>(c<sub>2</sub>) is set
F<sub>3</sub>() . c<sub>2</sub> is Element of the carrier of F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c<sub>2</sub>,c<sub>2</sub>] is set
( the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>)) `1 is set
F₄() . c₂ is Element of the carrier of F₂()
the ObjectMap of F₄() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of F₄() . (c₂,c₂) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [c₂,c₂] is set
( the ObjectMap of F₄() . (c₂,c₂)) `1 is set
<^(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)) is set
[(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)} is non empty set
{(F<sub>3</sub>() . c<sub>2</sub>)} is non empty set
{{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)},{(F<sub>3</sub>() . c<sub>2</sub>)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is set
c<sub>2</sub> is Relation-like the carrier of F<sub>1</sub>() -defined Function-like non empty V14( the carrier of F<sub>1</sub>()) transformation of F<sub>3</sub>(),F<sub>4</sub>()
FF is Element of the carrier of F<sub>1</sub>()
c<sub>2</sub> . FF is set
F<sub>5</sub>(FF) is set
c<sub>2</sub> ! FF is Element of <^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)^>
F<sub>3</sub>() . FF is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (FF,FF) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the ObjectMap of F<sub>3</sub>() . [FF,FF] is set
( the ObjectMap of F<sub>3</sub>() . (FF,FF)) `1 is set
F₄() . FF is Element of the carrier of F₂()
the ObjectMap of F₄() . (FF,FF) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [FF,FF] is set
( the ObjectMap of F₄() . (FF,FF)) `1 is set
<^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)) is set
[(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)] is V22() set
{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)} is non empty set
{(F<sub>3</sub>() . FF)} is non empty set
{{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)},{(F<sub>3</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)] is set
FF is Element of the carrier of F<sub>1</sub>()
a is Element of the carrier of F<sub>1</sub>()
<^FF,a^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
the Arrows of F<sub>1</sub>() . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of F<sub>1</sub>() . [FF,a] is set
F<sub>3</sub>() . FF is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (FF,FF) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the ObjectMap of F<sub>3</sub>() . [FF,FF] is set
( the ObjectMap of F<sub>3</sub>() . (FF,FF)) `1 is set
F₃() . a is Element of the carrier of F₂()
the ObjectMap of F₃() . (a,a) is Element of [: the carrier of F₂(), the carrier of F₂():]
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the ObjectMap of F₃() . [a,a] is set
( the ObjectMap of F₃() . (a,a)) `1 is set
F<sub>4</sub>() . a is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>4</sub>() . (a,a) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
the ObjectMap of F<sub>4</sub>() . [a,a] is set
( the ObjectMap of F<sub>4</sub>() . (a,a)) `1 is set
c₂ ! a is Element of <^(F₃() . a),(F₄() . a)^>
<^(F₃() . a),(F₄() . a)^> is set
the Arrows of F₂() . ((F₃() . a),(F₄() . a)) is set
[(F₃() . a),(F₄() . a)] is V22() set
{(F₃() . a),(F₄() . a)} is non empty set
{(F₃() . a)} is non empty set
{{(F₃() . a),(F₄() . a)},{(F₃() . a)}} is non empty set
the Arrows of F₂() . [(F₃() . a),(F₄() . a)] is set
F₄() . FF is Element of the carrier of F₂()
the ObjectMap of F₄() . (FF,FF) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [FF,FF] is set
( the ObjectMap of F₄() . (FF,FF)) `1 is set
c<sub>2</sub> ! FF is Element of <^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)^>
<^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)) is set
[(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)] is V22() set
{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)} is non empty set
{(F<sub>3</sub>() . FF)} is non empty set
{{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)},{(F<sub>3</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)] is set
F<sub>5</sub>(FF) is set
F<sub>5</sub>(a) is set
b is Element of <^FF,a^>
F<sub>3</sub>() . b is Element of <^(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)^>
<^(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)) is set
[(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)] is V22() set
{(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)} is non empty set
{{(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)},{(F<sub>3</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)] is set
(c<sub>2</sub> ! a) * (F<sub>3</sub>() . b) is Element of <^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)^>
<^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)) is set
[(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)] is V22() set
{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)} is non empty set
{{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)},{(F<sub>3</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)] is set
F<sub>4</sub>() . b is Element of <^(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)^>
<^(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)) is set
[(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)] is V22() set
{(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)} is non empty set
{(F<sub>4</sub>() . FF)} is non empty set
{{(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)},{(F<sub>4</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)] is set
(F<sub>4</sub>() . b) * (c<sub>2</sub> ! FF) is Element of <^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)^>
FF is Element of the carrier of F<sub>1</sub>()
c<sub>2</sub> ! FF is Element of <^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)^>
F<sub>3</sub>() . FF is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (FF,FF) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the ObjectMap of F<sub>3</sub>() . [FF,FF] is set
( the ObjectMap of F<sub>3</sub>() . (FF,FF)) `1 is set
F₄() . FF is Element of the carrier of F₂()
the ObjectMap of F₄() . (FF,FF) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [FF,FF] is set
( the ObjectMap of F₄() . (FF,FF)) `1 is set
<^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)) is set
[(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)] is V22() set
{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)} is non empty set
{(F<sub>3</sub>() . FF)} is non empty set
{{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)},{(F<sub>3</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . FF),(F<sub>4</sub>() . FF)] is set
F<sub>5</sub>(FF) is set
a is Element of the carrier of F<sub>1</sub>()
c<sub>2</sub> ! a is Element of <^(F<sub>3</sub>() . a),(F<sub>4</sub>() . a)^>
F<sub>3</sub>() . a is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (a,a) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the ObjectMap of F<sub>3</sub>() . [a,a] is set
( the ObjectMap of F<sub>3</sub>() . (a,a)) `1 is set
F₄() . a is Element of the carrier of F₂()
the ObjectMap of F₄() . (a,a) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [a,a] is set
( the ObjectMap of F₄() . (a,a)) `1 is set
<^(F<sub>3</sub>() . a),(F<sub>4</sub>() . a)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . a),(F<sub>4</sub>() . a)) is set
[(F<sub>3</sub>() . a),(F<sub>4</sub>() . a)] is V22() set
{(F<sub>3</sub>() . a),(F<sub>4</sub>() . a)} is non empty set
{(F<sub>3</sub>() . a)} is non empty set
{{(F<sub>3</sub>() . a),(F<sub>4</sub>() . a)},{(F<sub>3</sub>() . a)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . a),(F<sub>4</sub>() . a)] is set
F<sub>5</sub>(a) is set
<^FF,a^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
the Arrows of F<sub>1</sub>() . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of F<sub>1</sub>() . [FF,a] is set
b is Element of <^FF,a^>
F<sub>3</sub>() . b is Element of <^(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)^>
<^(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)) is set
[(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)] is V22() set
{(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)} is non empty set
{{(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)},{(F<sub>3</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . FF),(F<sub>3</sub>() . a)] is set
(c<sub>2</sub> ! a) * (F<sub>3</sub>() . b) is Element of <^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)^>
<^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)) is set
[(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)] is V22() set
{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)} is non empty set
{{(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)},{(F<sub>3</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)] is set
F<sub>4</sub>() . b is Element of <^(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)^>
<^(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)) is set
[(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)] is V22() set
{(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)} is non empty set
{(F<sub>4</sub>() . FF)} is non empty set
{{(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)},{(F<sub>4</sub>() . FF)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>4</sub>() . FF),(F<sub>4</sub>() . a)] is set
(F<sub>4</sub>() . b) * (c<sub>2</sub> ! FF) is Element of <^(F<sub>3</sub>() . FF),(F<sub>4</sub>() . a)^>
F<sub>1</sub>() is non empty transitive associative with_units reflexive AltCatStr
F<sub>2</sub>() is non empty transitive associative with_units reflexive AltCatStr
the carrier of F<sub>1</sub>() is non empty set
F<sub>3</sub>() is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
F<sub>4</sub>() is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
A is Element of the carrier of F<sub>1</sub>()
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
<^A,c<sub>2</sub>^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
the Arrows of F<sub>1</sub>() . (A,c<sub>2</sub>) is set
[A,c<sub>2</sub>] is V22() set
{A,c<sub>2</sub>} is non empty set
{A} is non empty set
{{A,c<sub>2</sub>},{A}} is non empty set
the Arrows of F<sub>1</sub>() . [A,c<sub>2</sub>] is set
F<sub>3</sub>() . A is Element of the carrier of F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of F<sub>3</sub>() . (A,A) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[A,A] is V22() set
{A,A} is non empty set
{{A,A},{A}} is non empty set
the ObjectMap of F<sub>3</sub>() . [A,A] is set
( the ObjectMap of F<sub>3</sub>() . (A,A)) `1 is set
F₄() . A is Element of the carrier of F₂()
the ObjectMap of F₄() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of F₄() . (A,A) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [A,A] is set
( the ObjectMap of F₄() . (A,A)) `1 is set
<^(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . A),(F<sub>4</sub>() . A)) is set
[(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)] is V22() set
{(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)} is non empty set
{(F<sub>3</sub>() . A)} is non empty set
{{(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)},{(F<sub>3</sub>() . A)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)] is set
F<sub>3</sub>() . c<sub>2</sub> is Element of the carrier of F<sub>2</sub>()
the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c<sub>2</sub>,c<sub>2</sub>] is set
( the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>)) `1 is set
F₄() . c₂ is Element of the carrier of F₂()
the ObjectMap of F₄() . (c₂,c₂) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [c₂,c₂] is set
( the ObjectMap of F₄() . (c₂,c₂)) `1 is set
<^(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)) is set
[(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)} is non empty set
{(F<sub>3</sub>() . c<sub>2</sub>)} is non empty set
{{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)},{(F<sub>3</sub>() . c<sub>2</sub>)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is set
a is Element of <^(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)^>
F<sub>5</sub>(A) is set
b is Element of <^(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)^>
F<sub>5</sub>(c<sub>2</sub>) is set
FF is Element of <^A,c<sub>2</sub>^>
F<sub>3</sub>() . FF is Element of <^(F<sub>3</sub>() . A),(F<sub>3</sub>() . c<sub>2</sub>)^>
<^(F<sub>3</sub>() . A),(F<sub>3</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . A),(F<sub>3</sub>() . c<sub>2</sub>)) is set
[(F<sub>3</sub>() . A),(F<sub>3</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>3</sub>() . A),(F<sub>3</sub>() . c<sub>2</sub>)} is non empty set
{{(F<sub>3</sub>() . A),(F<sub>3</sub>() . c<sub>2</sub>)},{(F<sub>3</sub>() . A)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . A),(F<sub>3</sub>() . c<sub>2</sub>)] is set
b * (F<sub>3</sub>() . FF) is Element of <^(F<sub>3</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)^>
<^(F<sub>3</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)) is set
[(F<sub>3</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>3</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)} is non empty set
{{(F<sub>3</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)},{(F<sub>3</sub>() . A)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)] is set
F<sub>4</sub>() . FF is Element of <^(F<sub>4</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)^>
<^(F<sub>4</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() . ((F<sub>4</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)) is set
[(F<sub>4</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>4</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)} is non empty set
{(F<sub>4</sub>() . A)} is non empty set
{{(F<sub>4</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)},{(F<sub>4</sub>() . A)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>4</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)] is set
(F<sub>4</sub>() . FF) * a is Element of <^(F<sub>3</sub>() . A),(F<sub>4</sub>() . c<sub>2</sub>)^>
A is Element of the carrier of F<sub>1</sub>()
F<sub>5</sub>(A) is set
F<sub>3</sub>() . A is Element of the carrier of F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of F<sub>3</sub>() . (A,A) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[A,A] is V22() set
{A,A} is non empty set
{A} is non empty set
{{A,A},{A}} is non empty set
the ObjectMap of F<sub>3</sub>() . [A,A] is set
( the ObjectMap of F<sub>3</sub>() . (A,A)) `1 is set
F₄() . A is Element of the carrier of F₂()
the ObjectMap of F₄() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of F₄() . (A,A) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [A,A] is set
( the ObjectMap of F₄() . (A,A)) `1 is set
<^(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . A),(F<sub>4</sub>() . A)) is set
[(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)] is V22() set
{(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)} is non empty set
{(F<sub>3</sub>() . A)} is non empty set
{{(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)},{(F<sub>3</sub>() . A)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . A),(F<sub>4</sub>() . A)] is set
A is Relation-like the carrier of F<sub>1</sub>() -defined Function-like non empty V14( the carrier of F<sub>1</sub>()) natural_transformation of F<sub>3</sub>(),F<sub>4</sub>()
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
F<sub>4</sub>() . c<sub>2</sub> is Element of the carrier of F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of F<sub>4</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of F<sub>4</sub>() . (c<sub>2</sub>,c<sub>2</sub>) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the ObjectMap of F<sub>4</sub>() . [c<sub>2</sub>,c<sub>2</sub>] is set
( the ObjectMap of F<sub>4</sub>() . (c<sub>2</sub>,c<sub>2</sub>)) `1 is set
F₃() . c₂ is Element of the carrier of F₂()
the ObjectMap of F₃() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of F₃() . (c₂,c₂) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₃() . [c₂,c₂] is set
( the ObjectMap of F₃() . (c₂,c₂)) `1 is set
<^(F<sub>4</sub>() . c<sub>2</sub>),(F<sub>3</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>4</sub>() . c<sub>2</sub>),(F<sub>3</sub>() . c<sub>2</sub>)) is set
[(F<sub>4</sub>() . c<sub>2</sub>),(F<sub>3</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>4</sub>() . c<sub>2</sub>),(F<sub>3</sub>() . c<sub>2</sub>)} is non empty set
{(F<sub>4</sub>() . c<sub>2</sub>)} is non empty set
{{(F<sub>4</sub>() . c<sub>2</sub>),(F<sub>3</sub>() . c<sub>2</sub>)},{(F<sub>4</sub>() . c<sub>2</sub>)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>4</sub>() . c<sub>2</sub>),(F<sub>3</sub>() . c<sub>2</sub>)] is set
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
F<sub>3</sub>() . c<sub>2</sub> is Element of the carrier of F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c<sub>2</sub>,c<sub>2</sub>] is set
( the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>)) `1 is set
F₄() . c₂ is Element of the carrier of F₂()
the ObjectMap of F₄() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of F₄() . (c₂,c₂) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [c₂,c₂] is set
( the ObjectMap of F₄() . (c₂,c₂)) `1 is set
A ! c<sub>2</sub> is Element of <^(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)^>
<^(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)) is set
[(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)} is non empty set
{(F<sub>3</sub>() . c<sub>2</sub>)} is non empty set
{{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)},{(F<sub>3</sub>() . c<sub>2</sub>)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is set
F<sub>5</sub>(c<sub>2</sub>) is set
c<sub>2</sub> is Element of the carrier of F<sub>1</sub>()
A ! c<sub>2</sub> is Element of <^(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)^>
F<sub>3</sub>() . c<sub>2</sub> is Element of the carrier of F<sub>2</sub>()
the carrier of F<sub>2</sub>() is non empty set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of F<sub>3</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the ObjectMap of F<sub>3</sub>() . [c<sub>2</sub>,c<sub>2</sub>] is set
( the ObjectMap of F<sub>3</sub>() . (c<sub>2</sub>,c<sub>2</sub>)) `1 is set
F₄() . c₂ is Element of the carrier of F₂()
the ObjectMap of F₄() is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of F₄() . (c₂,c₂) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of F₄() . [c₂,c₂] is set
( the ObjectMap of F₄() . (c₂,c₂)) `1 is set
<^(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)) is set
[(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is V22() set
{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)} is non empty set
{(F<sub>3</sub>() . c<sub>2</sub>)} is non empty set
{{(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)},{(F<sub>3</sub>() . c<sub>2</sub>)}} is non empty set
the Arrows of F<sub>2</sub>() . [(F<sub>3</sub>() . c<sub>2</sub>),(F<sub>4</sub>() . c<sub>2</sub>)] is set
F<sub>5</sub>(c<sub>2</sub>) is set
a is non empty AltCatStr
the carrier of a is non empty set
FF is non empty AltCatStr
the carrier of FF is non empty set
the Arrows of a is Relation-like [: the carrier of a, the carrier of a:] -defined Function-like non empty V14([: the carrier of a, the carrier of a:]) set
[: the carrier of a, the carrier of a:] is Relation-like non empty set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
~ the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
the Comp of a is Relation-like [: the carrier of a, the carrier of a, the carrier of a:] -defined Function-like non empty V14([: the carrier of a, the carrier of a, the carrier of a:]) Function-yielding V63() ManySortedFunction of {| the Arrows of a, the Arrows of a|},{| the Arrows of a|}
[: the carrier of a, the carrier of a, the carrier of a:] is non empty set
{| the Arrows of a, the Arrows of a|} is Relation-like [: the carrier of a, the carrier of a, the carrier of a:] -defined Function-like non empty V14([: the carrier of a, the carrier of a, the carrier of a:]) set
{| the Arrows of a|} is Relation-like [: the carrier of a, the carrier of a, the carrier of a:] -defined Function-like non empty V14([: the carrier of a, the carrier of a, the carrier of a:]) set
the Comp of FF is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) Function-yielding V63() ManySortedFunction of {| the Arrows of FF, the Arrows of FF|},{| the Arrows of FF|}
[: the carrier of FF, the carrier of FF, the carrier of FF:] is non empty set
{| the Arrows of FF, the Arrows of FF|} is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) set
{| the Arrows of FF|} is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) set
~ the Arrows of a is Relation-like [: the carrier of a, the carrier of a:] -defined Function-like non empty V14([: the carrier of a, the carrier of a:]) set
dom the Arrows of FF is Relation-like the carrier of FF -defined the carrier of FF -valued non empty Element of bool [: the carrier of FF, the carrier of FF:]
bool [: the carrier of FF, the carrier of FF:] is non empty set
b is Element of the carrier of a
c is Element of the carrier of a
d is Element of the carrier of a
the Arrows of a . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of a . [c,b] is set
the Arrows of a . (d,c) is set
[d,c] is V22() set
{d,c} is non empty set
{d} is non empty set
{{d,c},{d}} is non empty set
the Arrows of a . [d,c] is set
the Arrows of a . (d,b) is set
[d,b] is V22() set
{d,b} is non empty set
{{d,b},{d}} is non empty set
the Arrows of a . [d,b] is set
the Comp of a . (d,c,b) is Relation-like [:( the Arrows of a . (c,b)),( the Arrows of a . (d,c)):] -defined the Arrows of a . (d,b) -valued Function-like quasi_total Element of bool [:[:( the Arrows of a . (c,b)),( the Arrows of a . (d,c)):],( the Arrows of a . (d,b)):]
[:( the Arrows of a . (c,b)),( the Arrows of a . (d,c)):] is Relation-like set
[:[:( the Arrows of a . (c,b)),( the Arrows of a . (d,c)):],( the Arrows of a . (d,b)):] is Relation-like set
bool [:[:( the Arrows of a . (c,b)),( the Arrows of a . (d,c)):],( the Arrows of a . (d,b)):] is non empty set
~ ( the Comp of a . (d,c,b)) is Relation-like [:( the Arrows of a . (d,c)),( the Arrows of a . (c,b)):] -defined the Arrows of a . (d,b) -valued Function-like quasi_total Element of bool [:[:( the Arrows of a . (d,c)),( the Arrows of a . (c,b)):],( the Arrows of a . (d,b)):]
[:( the Arrows of a . (d,c)),( the Arrows of a . (c,b)):] is Relation-like set
[:[:( the Arrows of a . (d,c)),( the Arrows of a . (c,b)):],( the Arrows of a . (d,b)):] is Relation-like set
bool [:[:( the Arrows of a . (d,c)),( the Arrows of a . (c,b)):],( the Arrows of a . (d,b)):] is non empty set
f is Element of the carrier of FF
fa is Element of the carrier of FF
fb is Element of the carrier of FF
the Comp of FF . (f,fa,fb) is Relation-like [:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):] -defined the Arrows of FF . (f,fb) -valued Function-like quasi_total Element of bool [:[:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):],( the Arrows of FF . (f,fb)):]
the Arrows of FF . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of FF . [fa,fb] is set
the Arrows of FF . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of FF . [f,fa] is set
[:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):] is Relation-like set
the Arrows of FF . (f,fb) is set
[f,fb] is V22() set
{f,fb} is non empty set
{{f,fb},{f}} is non empty set
the Arrows of FF . [f,fb] is set
[:[:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):],( the Arrows of FF . (f,fb)):] is Relation-like set
bool [:[:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):],( the Arrows of FF . (f,fb)):] is non empty set
~ ( the Comp of FF . (f,fa,fb)) is Relation-like [:( the Arrows of FF . (f,fa)),( the Arrows of FF . (fa,fb)):] -defined the Arrows of FF . (f,fb) -valued Function-like quasi_total Element of bool [:[:( the Arrows of FF . (f,fa)),( the Arrows of FF . (fa,fb)):],( the Arrows of FF . (f,fb)):]
[:( the Arrows of FF . (f,fa)),( the Arrows of FF . (fa,fb)):] is Relation-like set
[:[:( the Arrows of FF . (f,fa)),( the Arrows of FF . (fa,fb)):],( the Arrows of FF . (f,fb)):] is Relation-like set
bool [:[:( the Arrows of FF . (f,fa)),( the Arrows of FF . (fa,fb)):],( the Arrows of FF . (f,fb)):] is non empty set
dom ( the Comp of FF . (f,fa,fb)) is Relation-like the Arrows of FF . (fa,fb) -defined the Arrows of FF . (f,fa) -valued Element of bool [:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):]
bool [:( the Arrows of FF . (fa,fb)),( the Arrows of FF . (f,fa)):] is non empty set
A is non empty AltCatStr
c<sub>2</sub> is non empty AltCatStr
the carrier of A is non empty set
the carrier of c<sub>2</sub> is non empty set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
~ the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Comp of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|},{| the Arrows of c<sub>2</sub>|}
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
{| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
{| the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
FF is Element of the carrier of A
A is non empty AltCatStr
c<sub>2</sub> is non empty AltCatStr
the carrier of A is non empty set
the carrier of c<sub>2</sub> is non empty set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
~ the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Comp of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|},{| the Arrows of c<sub>2</sub>|}
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
{| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
{| the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
b is Element of the carrier of c<sub>2</sub>
c is Element of the carrier of c<sub>2</sub>
<^c,b^> is set
the Arrows of c<sub>2</sub> . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of c<sub>2</sub> . [c,b] is set
A is non empty AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is non empty AltCatStr
the carrier of c<sub>2</sub> is non empty set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
b is Element of the carrier of c<sub>2</sub>
c is Element of the carrier of c<sub>2</sub>
d is Element of <^FF,a^>
<^c,b^> is set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of c<sub>2</sub> . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of c<sub>2</sub> . [c,b] is set
A is non empty transitive AltCatStr
c<sub>2</sub> is non empty transitive AltCatStr
the carrier of c<sub>2</sub> is non empty set
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
dom the Arrows of A is Relation-like the carrier of A -defined the carrier of A -valued non empty Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
dom the Arrows of c<sub>2</sub> is Relation-like the carrier of c<sub>2</sub> -defined the carrier of c<sub>2</sub> -valued non empty Element of bool [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
bool [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
c is Element of the carrier of c<sub>2</sub>
FF is Element of the carrier of A
d is Element of the carrier of c<sub>2</sub>
a is Element of the carrier of A
f is Element of the carrier of c<sub>2</sub>
b is Element of the carrier of A
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
<^FF,a^> is set
the Arrows of A . (FF,a) is set
the Arrows of A . [FF,a] is set
~ the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
(~ the Arrows of A) . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{{a,FF},{a}} is non empty set
(~ the Arrows of A) . [a,FF] is set
<^d,c^> is set
the Arrows of c<sub>2</sub> . (d,c) is set
[d,c] is V22() set
{d,c} is non empty set
{d} is non empty set
{{d,c},{d}} is non empty set
the Arrows of c<sub>2</sub> . [d,c] is set
<^a,b^> is set
the Arrows of A . (a,b) is set
the Arrows of A . [a,b] is set
(~ the Arrows of A) . (b,a) is set
[b,a] is V22() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
(~ the Arrows of A) . [b,a] is set
<^f,d^> is set
the Arrows of c<sub>2</sub> . (f,d) is set
[f,d] is V22() set
{f,d} is non empty set
{f} is non empty set
{{f,d},{f}} is non empty set
the Arrows of c<sub>2</sub> . [f,d] is set
the Comp of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|},{| the Arrows of c<sub>2</sub>|}
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
{| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
{| the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
the Comp of c<sub>2</sub> . (f,d,c) is Relation-like [:( the Arrows of c<sub>2</sub> . (d,c)),( the Arrows of c<sub>2</sub> . (f,d)):] -defined the Arrows of c<sub>2</sub> . (f,c) -valued Function-like quasi_total Element of bool [:[:( the Arrows of c<sub>2</sub> . (d,c)),( the Arrows of c<sub>2</sub> . (f,d)):],( the Arrows of c<sub>2</sub> . (f,c)):]
[:( the Arrows of c<sub>2</sub> . (d,c)),( the Arrows of c<sub>2</sub> . (f,d)):] is Relation-like set
the Arrows of c<sub>2</sub> . (f,c) is set
[f,c] is V22() set
{f,c} is non empty set
{{f,c},{f}} is non empty set
the Arrows of c<sub>2</sub> . [f,c] is set
[:[:( the Arrows of c<sub>2</sub> . (d,c)),( the Arrows of c<sub>2</sub> . (f,d)):],( the Arrows of c<sub>2</sub> . (f,c)):] is Relation-like set
bool [:[:( the Arrows of c<sub>2</sub> . (d,c)),( the Arrows of c<sub>2</sub> . (f,d)):],( the Arrows of c<sub>2</sub> . (f,c)):] is non empty set
the Arrows of A . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of A . [FF,b] is set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
the Comp of A . (FF,a,b) is Relation-like [:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):] -defined the Arrows of A . (FF,b) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):],( the Arrows of A . (FF,b)):]
[:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):] is Relation-like set
[:[:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):],( the Arrows of A . (FF,b)):] is Relation-like set
bool [:[:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):],( the Arrows of A . (FF,b)):] is non empty set
~ ( the Comp of A . (FF,a,b)) is Relation-like [:( the Arrows of A . (FF,a)),( the Arrows of A . (a,b)):] -defined the Arrows of A . (FF,b) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (FF,a)),( the Arrows of A . (a,b)):],( the Arrows of A . (FF,b)):]
[:( the Arrows of A . (FF,a)),( the Arrows of A . (a,b)):] is Relation-like set
[:[:( the Arrows of A . (FF,a)),( the Arrows of A . (a,b)):],( the Arrows of A . (FF,b)):] is Relation-like set
bool [:[:( the Arrows of A . (FF,a)),( the Arrows of A . (a,b)):],( the Arrows of A . (FF,b)):] is non empty set
<^FF,b^> is set
dom ( the Comp of A . (FF,a,b)) is Relation-like the Arrows of A . (a,b) -defined the Arrows of A . (FF,a) -valued Element of bool [:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):]
bool [:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):] is non empty set
fb is Element of <^a,b^>
fa is Element of <^FF,a^>
[fb,fa] is V22() set
{fb,fa} is non empty set
{fb} is non empty set
{{fb,fa},{fb}} is non empty set
g is Element of <^d,c^>
g is Element of <^f,d^>
g * g is Element of <^f,c^>
<^f,c^> is set
(~ ( the Comp of A . (FF,a,b))) . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
(~ ( the Comp of A . (FF,a,b))) . [fa,fb] is set
( the Comp of A . (FF,a,b)) . (fb,fa) is set
( the Comp of A . (FF,a,b)) . [fb,fa] is set
fb * fa is Element of <^FF,b^>
FF is set
a is set
b is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
d is set
c is set
[d,c] is V22() set
{d,c} is non empty set
{d} is non empty set
{{d,c},{d}} is non empty set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
b is set
a is set
[b,a] is V22() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
FF is set
a is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
b is Element of the carrier of A
c is Element of the carrier of A
the Arrows of c<sub>2</sub> . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,FF] is set
f is Element of the carrier of c<sub>2</sub>
d is Element of the carrier of c<sub>2</sub>
<^f,d^> is set
the Arrows of c<sub>2</sub> . (f,d) is set
[f,d] is V22() set
{f,d} is non empty set
{f} is non empty set
{{f,d},{f}} is non empty set
the Arrows of c<sub>2</sub> . [f,d] is set
<^b,c^> is set
the Arrows of A . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of A . [b,c] is set
the Arrows of A . (FF,a) is set
the Arrows of A . [FF,a] is set
FF is Element of the carrier of A
a is Element of the carrier of A
b is Element of the carrier of A
the Arrows of A . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of A . [a,FF] is set
the Arrows of A . (b,a) is set
[b,a] is V22() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
the Arrows of A . [b,a] is set
the Arrows of A . (b,FF) is set
[b,FF] is V22() set
{b,FF} is non empty set
{{b,FF},{b}} is non empty set
the Arrows of A . [b,FF] is set
the Comp of A . (b,a,FF) is Relation-like [:( the Arrows of A . (a,FF)),( the Arrows of A . (b,a)):] -defined the Arrows of A . (b,FF) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (a,FF)),( the Arrows of A . (b,a)):],( the Arrows of A . (b,FF)):]
[:( the Arrows of A . (a,FF)),( the Arrows of A . (b,a)):] is Relation-like set
[:[:( the Arrows of A . (a,FF)),( the Arrows of A . (b,a)):],( the Arrows of A . (b,FF)):] is Relation-like set
bool [:[:( the Arrows of A . (a,FF)),( the Arrows of A . (b,a)):],( the Arrows of A . (b,FF)):] is non empty set
~ ( the Comp of A . (b,a,FF)) is Relation-like [:( the Arrows of A . (b,a)),( the Arrows of A . (a,FF)):] -defined the Arrows of A . (b,FF) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (b,a)),( the Arrows of A . (a,FF)):],( the Arrows of A . (b,FF)):]
[:( the Arrows of A . (b,a)),( the Arrows of A . (a,FF)):] is Relation-like set
[:[:( the Arrows of A . (b,a)),( the Arrows of A . (a,FF)):],( the Arrows of A . (b,FF)):] is Relation-like set
bool [:[:( the Arrows of A . (b,a)),( the Arrows of A . (a,FF)):],( the Arrows of A . (b,FF)):] is non empty set
c is Element of the carrier of c<sub>2</sub>
d is Element of the carrier of c<sub>2</sub>
f is Element of the carrier of c<sub>2</sub>
the Comp of c<sub>2</sub> . (c,d,f) is Relation-like [:( the Arrows of c<sub>2</sub> . (d,f)),( the Arrows of c<sub>2</sub> . (c,d)):] -defined the Arrows of c<sub>2</sub> . (c,f) -valued Function-like quasi_total Element of bool [:[:( the Arrows of c<sub>2</sub> . (d,f)),( the Arrows of c<sub>2</sub> . (c,d)):],( the Arrows of c<sub>2</sub> . (c,f)):]
the Arrows of c<sub>2</sub> . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of c<sub>2</sub> . [d,f] is set
the Arrows of c<sub>2</sub> . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
the Arrows of c<sub>2</sub> . [c,d] is set
[:( the Arrows of c<sub>2</sub> . (d,f)),( the Arrows of c<sub>2</sub> . (c,d)):] is Relation-like set
the Arrows of c<sub>2</sub> . (c,f) is set
[c,f] is V22() set
{c,f} is non empty set
{{c,f},{c}} is non empty set
the Arrows of c<sub>2</sub> . [c,f] is set
[:[:( the Arrows of c<sub>2</sub> . (d,f)),( the Arrows of c<sub>2</sub> . (c,d)):],( the Arrows of c<sub>2</sub> . (c,f)):] is Relation-like set
bool [:[:( the Arrows of c<sub>2</sub> . (d,f)),( the Arrows of c<sub>2</sub> . (c,d)):],( the Arrows of c<sub>2</sub> . (c,f)):] is non empty set
<^c,d^> is set
<^a,FF^> is set
<^d,f^> is set
<^b,a^> is set
<^c,f^> is set
<^b,FF^> is set
[:<^a,FF^>,<^b,a^>:] is Relation-like set
dom ( the Comp of A . (b,a,FF)) is Relation-like the Arrows of A . (a,FF) -defined the Arrows of A . (b,a) -valued Element of bool [:( the Arrows of A . (a,FF)),( the Arrows of A . (b,a)):]
bool [:( the Arrows of A . (a,FF)),( the Arrows of A . (b,a)):] is non empty set
[:<^b,a^>,<^a,FF^>:] is Relation-like set
dom ( the Comp of c<sub>2</sub> . (c,d,f)) is Relation-like the Arrows of c<sub>2</sub> . (d,f) -defined the Arrows of c<sub>2</sub> . (c,d) -valued Element of bool [:( the Arrows of c<sub>2</sub> . (d,f)),( the Arrows of c<sub>2</sub> . (c,d)):]
bool [:( the Arrows of c<sub>2</sub> . (d,f)),( the Arrows of c<sub>2</sub> . (c,d)):] is non empty set
fa is set
fb is set
g is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
c<sub>13</sub> is set
g is set
[c<sub>13</sub>,g] is V22() set
{c<sub>13</sub>,g} is non empty set
{c<sub>13</sub>} is non empty set
{{c<sub>13</sub>,g},{c<sub>13</sub>}} is non empty set
[g,c<sub>13</sub>] is V22() set
{g,c<sub>13</sub>} is non empty set
{g} is non empty set
{{g,c<sub>13</sub>},{g}} is non empty set
g is set
fb is set
[g,fb] is V22() set
{g,fb} is non empty set
{g} is non empty set
{{g,fb},{g}} is non empty set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
fa is set
fb is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
( the Comp of c<sub>2</sub> . (c,d,f)) . (fb,fa) is set
[fb,fa] is V22() set
{fb,fa} is non empty set
{fb} is non empty set
{{fb,fa},{fb}} is non empty set
( the Comp of c<sub>2</sub> . (c,d,f)) . [fb,fa] is set
c<sub>13</sub> is Element of <^c,d^>
g9 is Element of <^d,f^>
g9 * c<sub>13</sub> is Element of <^c,f^>
g is Element of <^b,a^>
g is Element of <^a,FF^>
g * g is Element of <^b,FF^>
( the Comp of A . (b,a,FF)) . (fa,fb) is set
( the Comp of A . (b,a,FF)) . [fa,fb] is set
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
the carrier of c<sub>2</sub> is non empty set
FF is Element of the carrier of A
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
a is Element of the carrier of c<sub>2</sub>
idm a is retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of c<sub>2</sub> . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,a] is set
c is Element of the carrier of A
<^FF,c^> is set
the Arrows of A . (FF,c) is set
[FF,c] is V22() set
{FF,c} is non empty set
{{FF,c},{FF}} is non empty set
the Arrows of A . [FF,c] is set
f is Element of the carrier of c<sub>2</sub>
<^f,a^> is set
the Arrows of c<sub>2</sub> . (f,a) is set
[f,a] is V22() set
{f,a} is non empty set
{f} is non empty set
{{f,a},{f}} is non empty set
the Arrows of c<sub>2</sub> . [f,a] is set
d is Element of <^FF,c^>
b is Element of <^FF,FF^>
d * b is Element of <^FF,c^>
fa is Element of <^f,a^>
(idm a) * fa is Element of <^f,a^>
A is non empty transitive AltCatStr
c<sub>2</sub> is non empty transitive AltCatStr
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
the carrier of A is non empty set
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
the carrier of c<sub>2</sub> is non empty set
FF is Element of the carrier of c<sub>2</sub>
a is Element of the carrier of c<sub>2</sub>
<^FF,a^> is set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of c<sub>2</sub> . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,a] is set
b is Element of the carrier of c<sub>2</sub>
<^a,b^> is set
the Arrows of c<sub>2</sub> . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,b] is set
fa is Element of the carrier of A
f is Element of the carrier of A
<^fa,f^> is set
the Arrows of A . (fa,f) is set
[fa,f] is V22() set
{fa,f} is non empty set
{fa} is non empty set
{{fa,f},{fa}} is non empty set
the Arrows of A . [fa,f] is set
fb is Element of the carrier of A
<^fb,fa^> is set
the Arrows of A . (fb,fa) is set
[fb,fa] is V22() set
{fb,fa} is non empty set
{fb} is non empty set
{{fb,fa},{fb}} is non empty set
the Arrows of A . [fb,fa] is set
c is Element of <^FF,a^>
d is Element of <^a,b^>
d * c is Element of <^FF,b^>
<^FF,b^> is set
the Arrows of c<sub>2</sub> . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,b] is set
g is Element of <^fb,fa^>
g is Element of <^fa,f^>
g * g is Element of <^fb,f^>
<^fb,f^> is set
the Arrows of A . (fb,f) is set
[fb,f] is V22() set
{fb,f} is non empty set
{{fb,f},{fb}} is non empty set
the Arrows of A . [fb,f] is set
the Comp of A . (b,a,FF) is Relation-like Function-like set
( the Comp of A . (b,a,FF)) . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
( the Comp of A . (b,a,FF)) . [c,d] is set
FF is Element of the carrier of c<sub>2</sub>
a is Element of the carrier of c<sub>2</sub>
b is Element of the carrier of c<sub>2</sub>
c is Element of the carrier of c<sub>2</sub>
d is set
<^FF,a^> is set
the Arrows of c<sub>2</sub> . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,a] is set
g is Element of the carrier of A
fb is Element of the carrier of A
<^g,fb^> is set
the Arrows of A . (g,fb) is set
[g,fb] is V22() set
{g,fb} is non empty set
{g} is non empty set
{{g,fb},{g}} is non empty set
the Arrows of A . [g,fb] is set
f is set
<^a,b^> is set
the Arrows of c<sub>2</sub> . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,b] is set
g is Element of the carrier of A
<^g,g^> is set
the Arrows of A . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of A . [g,g] is set
fa is set
<^b,c^> is set
the Arrows of c<sub>2</sub> . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of c<sub>2</sub> . [b,c] is set
c<sub>13</sub> is Element of the carrier of A
<^c<sub>13</sub>,g^> is set
the Arrows of A . (c<sub>13</sub>,g) is set
[c<sub>13</sub>,g] is V22() set
{c<sub>13</sub>,g} is non empty set
{c<sub>13</sub>} is non empty set
{{c<sub>13</sub>,g},{c<sub>13</sub>}} is non empty set
the Arrows of A . [c<sub>13</sub>,g] is set
<^g,fb^> is set
the Arrows of A . (g,fb) is set
[g,fb] is V22() set
{g,fb} is non empty set
{{g,fb},{g}} is non empty set
the Arrows of A . [g,fb] is set
<^c<sub>13</sub>,g^> is set
the Arrows of A . (c<sub>13</sub>,g) is set
[c<sub>13</sub>,g] is V22() set
{c<sub>13</sub>,g} is non empty set
{{c<sub>13</sub>,g},{c<sub>13</sub>}} is non empty set
the Arrows of A . [c<sub>13</sub>,g] is set
the Comp of A . (b,a,FF) is Relation-like Function-like set
( the Comp of A . (b,a,FF)) . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
( the Comp of A . (b,a,FF)) . [d,f] is set
the Comp of A . (c,b,FF) is Relation-like Function-like set
( the Comp of A . (c,b,FF)) . (H<sub>1</sub>(FF,a,b,d,f),fa) is set
[(( the Comp of A . (b,a,FF)) . (d,f)),fa] is V22() set
{(( the Comp of A . (b,a,FF)) . (d,f)),fa} is non empty set
{(( the Comp of A . (b,a,FF)) . (d,f))} is non empty set
{{(( the Comp of A . (b,a,FF)) . (d,f)),fa},{(( the Comp of A . (b,a,FF)) . (d,f))}} is non empty set
( the Comp of A . (c,b,FF)) . [(( the Comp of A . (b,a,FF)) . (d,f)),fa] is set
a1 is Element of <^g,g^>
g9 is Element of <^g,fb^>
g9 * a1 is Element of <^g,fb^>
( the Comp of A . (c,b,FF)) . ((g9 * a1),fa) is set
[(g9 * a1),fa] is V22() set
{(g9 * a1),fa} is non empty set
{(g9 * a1)} is non empty set
{{(g9 * a1),fa},{(g9 * a1)}} is non empty set
( the Comp of A . (c,b,FF)) . [(g9 * a1),fa] is set
b1 is Element of <^c<sub>13</sub>,g^>
(g9 * a1) * b1 is Element of <^c<sub>13</sub>,fb^>
<^c<sub>13</sub>,fb^> is set
the Arrows of A . (c<sub>13</sub>,fb) is set
[c<sub>13</sub>,fb] is V22() set
{c<sub>13</sub>,fb} is non empty set
{{c<sub>13</sub>,fb},{c<sub>13</sub>}} is non empty set
the Arrows of A . [c<sub>13</sub>,fb] is set
a1 * b1 is Element of <^c<sub>13</sub>,g^>
g9 * (a1 * b1) is Element of <^c<sub>13</sub>,fb^>
the Comp of A . (c,a,FF) is Relation-like Function-like set
( the Comp of A . (c,a,FF)) . (d,(a1 * b1)) is set
[d,(a1 * b1)] is V22() set
{d,(a1 * b1)} is non empty set
{{d,(a1 * b1)},{d}} is non empty set
( the Comp of A . (c,a,FF)) . [d,(a1 * b1)] is set
the Comp of A . (c,b,a) is Relation-like Function-like set
( the Comp of A . (c,b,a)) . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
( the Comp of A . (c,b,a)) . [f,fa] is set
( the Comp of A . (c,a,FF)) . (d,H<sub>1</sub>(a,b,c,f,fa)) is set
[d,(( the Comp of A . (c,b,a)) . (f,fa))] is V22() set
{d,(( the Comp of A . (c,b,a)) . (f,fa))} is non empty set
{{d,(( the Comp of A . (c,b,a)) . (f,fa))},{d}} is non empty set
( the Comp of A . (c,a,FF)) . [d,(( the Comp of A . (c,b,a)) . (f,fa))] is set
A is non empty transitive AltCatStr
c<sub>2</sub> is non empty transitive AltCatStr
FF is non empty transitive with_units reflexive AltCatStr
the Comp of FF is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) Function-yielding V63() ManySortedFunction of {| the Arrows of FF, the Arrows of FF|},{| the Arrows of FF|}
the carrier of FF is non empty set
[: the carrier of FF, the carrier of FF, the carrier of FF:] is non empty set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
{| the Arrows of FF, the Arrows of FF|} is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) set
{| the Arrows of FF|} is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) set
the carrier of c<sub>2</sub> is non empty set
a is Element of the carrier of c<sub>2</sub>
b is Element of the carrier of c<sub>2</sub>
<^a,b^> is set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of c<sub>2</sub> . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,b] is set
c is Element of the carrier of c<sub>2</sub>
<^b,c^> is set
the Arrows of c<sub>2</sub> . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of c<sub>2</sub> . [b,c] is set
fb is Element of the carrier of FF
fa is Element of the carrier of FF
<^fb,fa^> is set
the Arrows of FF . (fb,fa) is set
[fb,fa] is V22() set
{fb,fa} is non empty set
{fb} is non empty set
{{fb,fa},{fb}} is non empty set
the Arrows of FF . [fb,fa] is set
g is Element of the carrier of FF
<^g,fb^> is set
the Arrows of FF . (g,fb) is set
[g,fb] is V22() set
{g,fb} is non empty set
{g} is non empty set
{{g,fb},{g}} is non empty set
the Arrows of FF . [g,fb] is set
d is Element of <^a,b^>
f is Element of <^b,c^>
f * d is Element of <^a,c^>
<^a,c^> is set
the Arrows of c<sub>2</sub> . (a,c) is set
[a,c] is V22() set
{a,c} is non empty set
{{a,c},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,c] is set
c<sub>13</sub> is Element of <^g,fb^>
g is Element of <^fb,fa^>
g * c<sub>13</sub> is Element of <^g,fa^>
<^g,fa^> is set
the Arrows of FF . (g,fa) is set
[g,fa] is V22() set
{g,fa} is non empty set
{{g,fa},{g}} is non empty set
the Arrows of FF . [g,fa] is set
the Comp of FF . (c,b,a) is Relation-like Function-like set
( the Comp of FF . (c,b,a)) . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
( the Comp of FF . (c,b,a)) . [d,f] is set
a is Element of the carrier of c<sub>2</sub>
b is Element of the carrier of FF
idm b is retraction coretraction mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of FF . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of FF . [b,b] is set
c is set
d is set
<^a,a^> is set
the Arrows of c<sub>2</sub> . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,a] is set
f is Element of the carrier of c<sub>2</sub>
fa is set
<^a,f^> is set
the Arrows of c<sub>2</sub> . (a,f) is set
[a,f] is V22() set
{a,f} is non empty set
{{a,f},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,f] is set
fb is Element of the carrier of FF
<^fb,b^> is set
the Arrows of FF . (fb,b) is set
[fb,b] is V22() set
{fb,b} is non empty set
{fb} is non empty set
{{fb,b},{fb}} is non empty set
the Arrows of FF . [fb,b] is set
the Comp of FF . (f,a,a) is Relation-like Function-like set
( the Comp of FF . (f,a,a)) . (d,fa) is set
[d,fa] is V22() set
{d,fa} is non empty set
{d} is non empty set
{{d,fa},{d}} is non empty set
( the Comp of FF . (f,a,a)) . [d,fa] is set
g is Element of <^fb,b^>
(idm b) * g is Element of <^fb,b^>
a is Element of the carrier of c<sub>2</sub>
b is Element of the carrier of FF
idm b is retraction coretraction mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of FF . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of FF . [b,b] is set
c is set
d is set
<^a,a^> is set
the Arrows of c<sub>2</sub> . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,a] is set
f is Element of the carrier of c<sub>2</sub>
fa is set
<^f,a^> is set
the Arrows of c<sub>2</sub> . (f,a) is set
[f,a] is V22() set
{f,a} is non empty set
{f} is non empty set
{{f,a},{f}} is non empty set
the Arrows of c<sub>2</sub> . [f,a] is set
fb is Element of the carrier of FF
<^b,fb^> is set
the Arrows of FF . (b,fb) is set
[b,fb] is V22() set
{b,fb} is non empty set
{{b,fb},{b}} is non empty set
the Arrows of FF . [b,fb] is set
the Comp of FF . (a,a,f) is Relation-like Function-like set
( the Comp of FF . (a,a,f)) . (fa,d) is set
[fa,d] is V22() set
{fa,d} is non empty set
{fa} is non empty set
{{fa,d},{fa}} is non empty set
( the Comp of FF . (a,a,f)) . [fa,d] is set
g is Element of <^b,fb^>
g * (idm b) is Element of <^b,fb^>
A is non empty AltCatStr
c<sub>2</sub> is non empty AltCatStr
FF is non empty AltCatStr
the carrier of c<sub>2</sub> is non empty set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Comp of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|},{| the Arrows of c<sub>2</sub>|}
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
{| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
{| the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
AltCatStr(# the carrier of c<sub>2</sub>, the Arrows of c<sub>2</sub>, the Comp of c<sub>2</sub> #) is non empty strict AltCatStr
the carrier of FF is non empty set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
the Comp of FF is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) Function-yielding V63() ManySortedFunction of {| the Arrows of FF, the Arrows of FF|},{| the Arrows of FF|}
[: the carrier of FF, the carrier of FF, the carrier of FF:] is non empty set
{| the Arrows of FF, the Arrows of FF|} is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) set
{| the Arrows of FF|} is Relation-like [: the carrier of FF, the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF, the carrier of FF:]) set
AltCatStr(# the carrier of FF, the Arrows of FF, the Comp of FF #) is non empty strict AltCatStr
the carrier of A is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
~ the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
dom the Comp of c<sub>2</sub> is non empty Element of bool [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
bool [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
dom the Comp of FF is non empty Element of bool [: the carrier of FF, the carrier of FF, the carrier of FF:]
bool [: the carrier of FF, the carrier of FF, the carrier of FF:] is non empty set
a is set
b is set
c is set
d is set
[b,c,d] is V22() V23() set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
[[b,c],d] is V22() set
{[b,c],d} is non empty set
{[b,c]} is Relation-like Function-like non empty set
{{[b,c],d},{[b,c]}} is non empty set
f is Element of the carrier of A
fa is Element of the carrier of A
fb is Element of the carrier of A
g is Element of the carrier of c<sub>2</sub>
g is Element of the carrier of c<sub>2</sub>
c<sub>13</sub> is Element of the carrier of c<sub>2</sub>
the Comp of c<sub>2</sub> . (g,g,c<sub>13</sub>) is Relation-like [:( the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>)),( the Arrows of c<sub>2</sub> . (g,g)):] -defined the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>) -valued Function-like quasi_total Element of bool [:[:( the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>)),( the Arrows of c<sub>2</sub> . (g,g)):],( the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>)):]
the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>) is set
[g,c<sub>13</sub>] is V22() set
{g,c<sub>13</sub>} is non empty set
{g} is non empty set
{{g,c<sub>13</sub>},{g}} is non empty set
the Arrows of c<sub>2</sub> . [g,c<sub>13</sub>] is set
the Arrows of c<sub>2</sub> . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of c<sub>2</sub> . [g,g] is set
[:( the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>)),( the Arrows of c<sub>2</sub> . (g,g)):] is Relation-like set
the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>) is set
[g,c<sub>13</sub>] is V22() set
{g,c<sub>13</sub>} is non empty set
{{g,c<sub>13</sub>},{g}} is non empty set
the Arrows of c<sub>2</sub> . [g,c<sub>13</sub>] is set
[:[:( the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>)),( the Arrows of c<sub>2</sub> . (g,g)):],( the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>)):] is Relation-like set
bool [:[:( the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>)),( the Arrows of c<sub>2</sub> . (g,g)):],( the Arrows of c<sub>2</sub> . (g,c<sub>13</sub>)):] is non empty set
the Arrows of A . (fa,f) is set
[fa,f] is V22() set
{fa,f} is non empty set
{fa} is non empty set
{{fa,f},{fa}} is non empty set
the Arrows of A . [fa,f] is set
the Arrows of A . (fb,fa) is set
[fb,fa] is V22() set
{fb,fa} is non empty set
{fb} is non empty set
{{fb,fa},{fb}} is non empty set
the Arrows of A . [fb,fa] is set
the Arrows of A . (fb,f) is set
[fb,f] is V22() set
{fb,f} is non empty set
{{fb,f},{fb}} is non empty set
the Arrows of A . [fb,f] is set
the Comp of A . (fb,fa,f) is Relation-like [:( the Arrows of A . (fa,f)),( the Arrows of A . (fb,fa)):] -defined the Arrows of A . (fb,f) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (fa,f)),( the Arrows of A . (fb,fa)):],( the Arrows of A . (fb,f)):]
[:( the Arrows of A . (fa,f)),( the Arrows of A . (fb,fa)):] is Relation-like set
[:[:( the Arrows of A . (fa,f)),( the Arrows of A . (fb,fa)):],( the Arrows of A . (fb,f)):] is Relation-like set
bool [:[:( the Arrows of A . (fa,f)),( the Arrows of A . (fb,fa)):],( the Arrows of A . (fb,f)):] is non empty set
~ ( the Comp of A . (fb,fa,f)) is Relation-like [:( the Arrows of A . (fb,fa)),( the Arrows of A . (fa,f)):] -defined the Arrows of A . (fb,f) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (fb,fa)),( the Arrows of A . (fa,f)):],( the Arrows of A . (fb,f)):]
[:( the Arrows of A . (fb,fa)),( the Arrows of A . (fa,f)):] is Relation-like set
[:[:( the Arrows of A . (fb,fa)),( the Arrows of A . (fa,f)):],( the Arrows of A . (fb,f)):] is Relation-like set
bool [:[:( the Arrows of A . (fb,fa)),( the Arrows of A . (fa,f)):],( the Arrows of A . (fb,f)):] is non empty set
g9 is Element of the carrier of FF
a1 is Element of the carrier of FF
b1 is Element of the carrier of FF
the Comp of FF . (g9,a1,b1) is Relation-like [:( the Arrows of FF . (a1,b1)),( the Arrows of FF . (g9,a1)):] -defined the Arrows of FF . (g9,b1) -valued Function-like quasi_total Element of bool [:[:( the Arrows of FF . (a1,b1)),( the Arrows of FF . (g9,a1)):],( the Arrows of FF . (g9,b1)):]
the Arrows of FF . (a1,b1) is set
[a1,b1] is V22() set
{a1,b1} is non empty set
{a1} is non empty set
{{a1,b1},{a1}} is non empty set
the Arrows of FF . [a1,b1] is set
the Arrows of FF . (g9,a1) is set
[g9,a1] is V22() set
{g9,a1} is non empty set
{g9} is non empty set
{{g9,a1},{g9}} is non empty set
the Arrows of FF . [g9,a1] is set
[:( the Arrows of FF . (a1,b1)),( the Arrows of FF . (g9,a1)):] is Relation-like set
the Arrows of FF . (g9,b1) is set
[g9,b1] is V22() set
{g9,b1} is non empty set
{{g9,b1},{g9}} is non empty set
the Arrows of FF . [g9,b1] is set
[:[:( the Arrows of FF . (a1,b1)),( the Arrows of FF . (g9,a1)):],( the Arrows of FF . (g9,b1)):] is Relation-like set
bool [:[:( the Arrows of FF . (a1,b1)),( the Arrows of FF . (g9,a1)):],( the Arrows of FF . (g9,b1)):] is non empty set
the Comp of c<sub>2</sub> . a is Relation-like Function-like set
the Comp of FF . a is Relation-like Function-like set
a is Element of the carrier of A
b is Element of the carrier of A
c is Element of the carrier of A
the Arrows of A . (b,a) is set
[b,a] is V22() set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
the Arrows of A . [b,a] is set
the Arrows of A . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of A . [c,b] is set
the Arrows of A . (c,a) is set
[c,a] is V22() set
{c,a} is non empty set
{{c,a},{c}} is non empty set
the Arrows of A . [c,a] is set
the Comp of A . (c,b,a) is Relation-like [:( the Arrows of A . (b,a)),( the Arrows of A . (c,b)):] -defined the Arrows of A . (c,a) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (b,a)),( the Arrows of A . (c,b)):],( the Arrows of A . (c,a)):]
[:( the Arrows of A . (b,a)),( the Arrows of A . (c,b)):] is Relation-like set
[:[:( the Arrows of A . (b,a)),( the Arrows of A . (c,b)):],( the Arrows of A . (c,a)):] is Relation-like set
bool [:[:( the Arrows of A . (b,a)),( the Arrows of A . (c,b)):],( the Arrows of A . (c,a)):] is non empty set
~ ( the Comp of A . (c,b,a)) is Relation-like [:( the Arrows of A . (c,b)),( the Arrows of A . (b,a)):] -defined the Arrows of A . (c,a) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (c,b)),( the Arrows of A . (b,a)):],( the Arrows of A . (c,a)):]
[:( the Arrows of A . (c,b)),( the Arrows of A . (b,a)):] is Relation-like set
[:[:( the Arrows of A . (c,b)),( the Arrows of A . (b,a)):],( the Arrows of A . (c,a)):] is Relation-like set
bool [:[:( the Arrows of A . (c,b)),( the Arrows of A . (b,a)):],( the Arrows of A . (c,a)):] is non empty set
d is Element of the carrier of FF
f is Element of the carrier of FF
fa is Element of the carrier of FF
the Comp of FF . (d,f,fa) is Relation-like [:( the Arrows of FF . (f,fa)),( the Arrows of FF . (d,f)):] -defined the Arrows of FF . (d,fa) -valued Function-like quasi_total Element of bool [:[:( the Arrows of FF . (f,fa)),( the Arrows of FF . (d,f)):],( the Arrows of FF . (d,fa)):]
the Arrows of FF . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of FF . [f,fa] is set
the Arrows of FF . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of FF . [d,f] is set
[:( the Arrows of FF . (f,fa)),( the Arrows of FF . (d,f)):] is Relation-like set
the Arrows of FF . (d,fa) is set
[d,fa] is V22() set
{d,fa} is non empty set
{{d,fa},{d}} is non empty set
the Arrows of FF . [d,fa] is set
[:[:( the Arrows of FF . (f,fa)),( the Arrows of FF . (d,f)):],( the Arrows of FF . (d,fa)):] is Relation-like set
bool [:[:( the Arrows of FF . (f,fa)),( the Arrows of FF . (d,f)):],( the Arrows of FF . (d,fa)):] is non empty set
A is non empty transitive AltCatStr
c<sub>2</sub> is non empty transitive strict AltCatStr
FF is non empty transitive strict AltCatStr
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
a is Element of the carrier of A
b is set
the Arrows of A . (FF,c<sub>2</sub>) is set
[FF,c<sub>2</sub>] is V22() set
{FF,c<sub>2</sub>} is non empty set
{FF} is non empty set
{{FF,c<sub>2</sub>},{FF}} is non empty set
the Arrows of A . [FF,c<sub>2</sub>] is set
f is Element of the carrier of A
d is Element of the carrier of A
<^f,d^> is set
the Arrows of A . (f,d) is set
[f,d] is V22() set
{f,d} is non empty set
{f} is non empty set
{{f,d},{f}} is non empty set
the Arrows of A . [f,d] is set
c is set
the Arrows of A . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of A . [a,FF] is set
fa is Element of the carrier of A
<^fa,f^> is set
the Arrows of A . (fa,f) is set
[fa,f] is V22() set
{fa,f} is non empty set
{fa} is non empty set
{{fa,f},{fa}} is non empty set
the Arrows of A . [fa,f] is set
<^fa,d^> is set
the Arrows of A . (fa,d) is set
[fa,d] is V22() set
{fa,d} is non empty set
{{fa,d},{fa}} is non empty set
the Arrows of A . [fa,d] is set
the Comp of A . (a,FF,c<sub>2</sub>) is Relation-like Function-like set
( the Comp of A . (a,FF,c<sub>2</sub>)) . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
( the Comp of A . (a,FF,c<sub>2</sub>)) . [b,c] is set
g is Element of <^fa,f^>
fb is Element of <^f,d^>
fb * g is Element of <^fa,d^>
the Arrows of A . (a,c<sub>2</sub>) is set
[a,c<sub>2</sub>] is V22() set
{a,c<sub>2</sub>} is non empty set
{{a,c<sub>2</sub>},{a}} is non empty set
the Arrows of A . [a,c<sub>2</sub>] is set
c<sub>2</sub> is non empty transitive strict AltCatStr
the carrier of c<sub>2</sub> is non empty set
c<sub>2</sub> is non empty transitive strict AltCatStr
the carrier of c<sub>2</sub> is non empty set
c is Element of the carrier of c<sub>2</sub>
FF is Element of the carrier of A
d is Element of the carrier of c<sub>2</sub>
a is Element of the carrier of A
f is Element of the carrier of c<sub>2</sub>
b is Element of the carrier of A
<^FF,a^> is set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
<^d,c^> is set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of c<sub>2</sub> . (d,c) is set
[d,c] is V22() set
{d,c} is non empty set
{d} is non empty set
{{d,c},{d}} is non empty set
the Arrows of c<sub>2</sub> . [d,c] is set
<^a,b^> is set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
<^f,d^> is set
the Arrows of c<sub>2</sub> . (f,d) is set
[f,d] is V22() set
{f,d} is non empty set
{f} is non empty set
{{f,d},{f}} is non empty set
the Arrows of c<sub>2</sub> . [f,d] is set
g is Element of <^d,c^>
fa is Element of <^FF,a^>
g is Element of <^f,d^>
fb is Element of <^a,b^>
g * g is Element of <^f,c^>
<^f,c^> is set
the Arrows of c<sub>2</sub> . (f,c) is set
[f,c] is V22() set
{f,c} is non empty set
{{f,c},{f}} is non empty set
the Arrows of c<sub>2</sub> . [f,c] is set
the Comp of A . (FF,a,b) is Relation-like [:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):] -defined the Arrows of A . (FF,b) -valued Function-like quasi_total Element of bool [:[:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):],( the Arrows of A . (FF,b)):]
[:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):] is Relation-like set
the Arrows of A . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of A . [FF,b] is set
[:[:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):],( the Arrows of A . (FF,b)):] is Relation-like set
bool [:[:( the Arrows of A . (a,b)),( the Arrows of A . (FF,a)):],( the Arrows of A . (FF,b)):] is non empty set
( the Comp of A . (FF,a,b)) . (fb,fa) is set
[fb,fa] is V22() set
{fb,fa} is non empty set
{fb} is non empty set
{{fb,fa},{fb}} is non empty set
( the Comp of A . (FF,a,b)) . [fb,fa] is set
fb * fa is Element of <^FF,b^>
<^FF,b^> is set
A is non empty transitive associative AltCatStr
(A) is non empty transitive strict AltCatStr
A is non empty transitive with_units reflexive AltCatStr
(A) is non empty transitive strict AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
the carrier of c<sub>2</sub> is non empty set
FF is Element of the carrier of A
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
d is Element of the carrier of c<sub>2</sub>
c is Element of the carrier of c<sub>2</sub>
<^d,c^> is set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Arrows of c<sub>2</sub> . (d,c) is set
[d,c] is V22() set
{d,c} is non empty set
{d} is non empty set
{{d,c},{d}} is non empty set
the Arrows of c<sub>2</sub> . [d,c] is set
the Arrows of c<sub>2</sub> . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,FF] is set
b is Element of <^FF,a^>
the Arrows of c<sub>2</sub> . (H<sub>1</sub>(a),H<sub>1</sub>(FF)) is set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
b is Element of the carrier of A
<^a,b^> is set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
fa is Element of the carrier of c<sub>2</sub>
f is Element of the carrier of c<sub>2</sub>
<^fa,f^> is set
the Arrows of c<sub>2</sub> . (fa,f) is set
[fa,f] is V22() set
{fa,f} is non empty set
{fa} is non empty set
{{fa,f},{fa}} is non empty set
the Arrows of c<sub>2</sub> . [fa,f] is set
fb is Element of the carrier of c<sub>2</sub>
<^fb,fa^> is set
the Arrows of c<sub>2</sub> . (fb,fa) is set
[fb,fa] is V22() set
{fb,fa} is non empty set
{fb} is non empty set
{{fb,fa},{fb}} is non empty set
the Arrows of c<sub>2</sub> . [fb,fa] is set
g is Element of <^fa,f^>
c is Element of <^FF,a^>
g is Element of <^fb,fa^>
d is Element of <^a,b^>
d * c is Element of <^FF,b^>
<^FF,b^> is set
the Arrows of A . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of A . [FF,b] is set
g * g is Element of <^fb,f^>
<^fb,f^> is set
the Arrows of c<sub>2</sub> . (fb,f) is set
[fb,f] is V22() set
{fb,f} is non empty set
{{fb,f},{fb}} is non empty set
the Arrows of c<sub>2</sub> . [fb,f] is set
a is Element of the carrier of c<sub>2</sub>
FF is Element of the carrier of A
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
idm a is retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of c<sub>2</sub> . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,a] is set
FF is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
a is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
b is Element of the carrier of A
FF . b is Element of the carrier of c<sub>2</sub>
the ObjectMap of FF is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the ObjectMap of FF . (b,b) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of FF . [b,b] is set
( the ObjectMap of FF . (b,b)) `1 is set
a . b is Element of the carrier of c₂
the ObjectMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c₂, the carrier of c₂:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:]
the ObjectMap of a . (b,b) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of a . [b,b] is set
( the ObjectMap of a . (b,b)) `1 is set
b is Element of the carrier of A
c is Element of the carrier of A
<^b,c^> is set
the Arrows of A . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of A . [b,c] is set
d is Element of <^b,c^>
FF . d is Element of <^(FF . c),(FF . b)^>
FF . c is Element of the carrier of c<sub>2</sub>
the ObjectMap of FF . (c,c) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of FF . [c,c] is set
( the ObjectMap of FF . (c,c)) `1 is set
FF . b is Element of the carrier of c₂
the ObjectMap of FF . (b,b) is Element of [: the carrier of c₂, the carrier of c₂:]
[b,b] is V22() set
{b,b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of FF . [b,b] is set
( the ObjectMap of FF . (b,b)) `1 is set
<^(FF . c),(FF . b)^> is set
the Arrows of c<sub>2</sub> . ((FF . c),(FF . b)) is set
[(FF . c),(FF . b)] is V22() set
{(FF . c),(FF . b)} is non empty set
{(FF . c)} is non empty set
{{(FF . c),(FF . b)},{(FF . c)}} is non empty set
the Arrows of c<sub>2</sub> . [(FF . c),(FF . b)] is set
a . d is Element of <^(a . c),(a . b)^>
a . c is Element of the carrier of c<sub>2</sub>
the ObjectMap of a . (c,c) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of a . [c,c] is set
( the ObjectMap of a . (c,c)) `1 is set
a . b is Element of the carrier of c₂
the ObjectMap of a . (b,b) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of a . [b,b] is set
( the ObjectMap of a . (b,b)) `1 is set
<^(a . c),(a . b)^> is set
the Arrows of c<sub>2</sub> . ((a . c),(a . b)) is set
[(a . c),(a . b)] is V22() set
{(a . c),(a . b)} is non empty set
{(a . c)} is non empty set
{{(a . c),(a . b)},{(a . c)}} is non empty set
the Arrows of c<sub>2</sub> . [(a . c),(a . b)] is set
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
(c<sub>2</sub>,A) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of c<sub>2</sub>,A
(A,c<sub>2</sub>) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
(A,c<sub>2</sub>) * (c<sub>2</sub>,A) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
id c<sub>2</sub> is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of c<sub>2</sub>,c<sub>2</sub>
the carrier of c<sub>2</sub> is non empty set
FF is Element of the carrier of c<sub>2</sub>
((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF is Element of the carrier of c<sub>2</sub>
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the ObjectMap of ((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) quasi_total Element of bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
[:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the ObjectMap of ((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . (FF,FF) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the ObjectMap of ((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . [FF,FF] is set
( the ObjectMap of ((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . (FF,FF)) `1 is set
(c₂,A) . FF is Element of the carrier of A
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the ObjectMap of (c₂,A) is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) quasi_total Element of bool [:[: the carrier of c₂, the carrier of c₂:],[: the carrier of A, the carrier of A:]:]
[:[: the carrier of c₂, the carrier of c₂:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of c₂, the carrier of c₂:],[: the carrier of A, the carrier of A:]:] is non empty set
the ObjectMap of (c₂,A) . (FF,FF) is Element of [: the carrier of A, the carrier of A:]
the ObjectMap of (c₂,A) . [FF,FF] is set
( the ObjectMap of (c₂,A) . (FF,FF)) `1 is set
(A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF) is Element of the carrier of c<sub>2</sub>
the ObjectMap of (A,c<sub>2</sub>) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the ObjectMap of (A,c<sub>2</sub>) . (((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)] is V22() set
{((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)} is non empty set
{((c<sub>2</sub>,A) . FF)} is non empty set
{{((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)},{((c<sub>2</sub>,A) . FF)}} is non empty set
the ObjectMap of (A,c<sub>2</sub>) . [((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)] is set
( the ObjectMap of (A,c<sub>2</sub>) . (((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF))) `1 is set
(id c₂) . FF is Element of the carrier of c₂
the ObjectMap of (id c₂) is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined [: the carrier of c₂, the carrier of c₂:] -valued Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) quasi_total Element of bool [:[: the carrier of c₂, the carrier of c₂:],[: the carrier of c₂, the carrier of c₂:]:]
the ObjectMap of (id c₂) . (FF,FF) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of (id c₂) . [FF,FF] is set
( the ObjectMap of (id c₂) . (FF,FF)) `1 is set
FF is Element of the carrier of c<sub>2</sub>
a is Element of the carrier of c<sub>2</sub>
<^FF,a^> is set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
the Arrows of c<sub>2</sub> . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,a] is set
(c<sub>2</sub>,A) . a is Element of the carrier of A
the ObjectMap of (c<sub>2</sub>,A) . (a,a) is Element of [: the carrier of A, the carrier of A:]
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the ObjectMap of (c<sub>2</sub>,A) . [a,a] is set
( the ObjectMap of (c<sub>2</sub>,A) . (a,a)) `1 is set
(c₂,A) . FF is Element of the carrier of A
the ObjectMap of (c₂,A) . (FF,FF) is Element of [: the carrier of A, the carrier of A:]
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the ObjectMap of (c₂,A) . [FF,FF] is set
( the ObjectMap of (c₂,A) . (FF,FF)) `1 is set
<^((c<sub>2</sub>,A) . a),((c<sub>2</sub>,A) . FF)^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A . (((c<sub>2</sub>,A) . a),((c<sub>2</sub>,A) . FF)) is set
[((c<sub>2</sub>,A) . a),((c<sub>2</sub>,A) . FF)] is V22() set
{((c<sub>2</sub>,A) . a),((c<sub>2</sub>,A) . FF)} is non empty set
{((c<sub>2</sub>,A) . a)} is non empty set
{{((c<sub>2</sub>,A) . a),((c<sub>2</sub>,A) . FF)},{((c<sub>2</sub>,A) . a)}} is non empty set
the Arrows of A . [((c<sub>2</sub>,A) . a),((c<sub>2</sub>,A) . FF)] is set
b is Element of <^FF,a^>
((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . b is Element of <^(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF),(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . a)^>
((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF is Element of the carrier of c<sub>2</sub>
the ObjectMap of ((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . (FF,FF) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of ((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . [FF,FF] is set
( the ObjectMap of ((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . (FF,FF)) `1 is set
((A,c₂) * (c₂,A)) . a is Element of the carrier of c₂
the ObjectMap of ((A,c₂) * (c₂,A)) . (a,a) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of ((A,c₂) * (c₂,A)) . [a,a] is set
( the ObjectMap of ((A,c₂) * (c₂,A)) . (a,a)) `1 is set
<^(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF),(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . a)^> is set
the Arrows of c<sub>2</sub> . ((((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF),(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . a)) is set
[(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF),(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . a)] is V22() set
{(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF),(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . a)} is non empty set
{(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF)} is non empty set
{{(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF),(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . a)},{(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF)}} is non empty set
the Arrows of c<sub>2</sub> . [(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . FF),(((A,c<sub>2</sub>) * (c<sub>2</sub>,A)) . a)] is set
(c<sub>2</sub>,A) . b is Element of <^((c<sub>2</sub>,A) . a),((c<sub>2</sub>,A) . FF)^>
(A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . b) is Element of <^((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF)),((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . a))^>
(A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF) is Element of the carrier of c<sub>2</sub>
the ObjectMap of (A,c<sub>2</sub>) . (((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)] is V22() set
{((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)} is non empty set
{((c<sub>2</sub>,A) . FF)} is non empty set
{{((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)},{((c<sub>2</sub>,A) . FF)}} is non empty set
the ObjectMap of (A,c<sub>2</sub>) . [((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF)] is set
( the ObjectMap of (A,c<sub>2</sub>) . (((c<sub>2</sub>,A) . FF),((c<sub>2</sub>,A) . FF))) `1 is set
(A,c₂) . ((c₂,A) . a) is Element of the carrier of c₂
the ObjectMap of (A,c₂) . (((c₂,A) . a),((c₂,A) . a)) is Element of [: the carrier of c₂, the carrier of c₂:]
[((c₂,A) . a),((c₂,A) . a)] is V22() set
{((c₂,A) . a),((c₂,A) . a)} is non empty set
{{((c₂,A) . a),((c₂,A) . a)},{((c₂,A) . a)}} is non empty set
the ObjectMap of (A,c₂) . [((c₂,A) . a),((c₂,A) . a)] is set
( the ObjectMap of (A,c₂) . (((c₂,A) . a),((c₂,A) . a))) `1 is set
<^((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF)),((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . a))^> is set
the Arrows of c<sub>2</sub> . (((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF)),((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . a))) is set
[((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF)),((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . a))] is V22() set
{((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF)),((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . a))} is non empty set
{((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF))} is non empty set
{{((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF)),((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . a))},{((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF))}} is non empty set
the Arrows of c<sub>2</sub> . [((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . FF)),((A,c<sub>2</sub>) . ((c<sub>2</sub>,A) . a))] is set
(id c<sub>2</sub>) . b is Element of <^((id c<sub>2</sub>) . FF),((id c<sub>2</sub>) . a)^>
(id c<sub>2</sub>) . FF is Element of the carrier of c<sub>2</sub>
the ObjectMap of (id c<sub>2</sub>) . (FF,FF) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of (id c<sub>2</sub>) . [FF,FF] is set
( the ObjectMap of (id c<sub>2</sub>) . (FF,FF)) `1 is set
(id c₂) . a is Element of the carrier of c₂
the ObjectMap of (id c₂) . (a,a) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of (id c₂) . [a,a] is set
( the ObjectMap of (id c₂) . (a,a)) `1 is set
<^((id c<sub>2</sub>) . FF),((id c<sub>2</sub>) . a)^> is set
the Arrows of c<sub>2</sub> . (((id c<sub>2</sub>) . FF),((id c<sub>2</sub>) . a)) is set
[((id c<sub>2</sub>) . FF),((id c<sub>2</sub>) . a)] is V22() set
{((id c<sub>2</sub>) . FF),((id c<sub>2</sub>) . a)} is non empty set
{((id c<sub>2</sub>) . FF)} is non empty set
{{((id c<sub>2</sub>) . FF),((id c<sub>2</sub>) . a)},{((id c<sub>2</sub>) . FF)}} is non empty set
the Arrows of c<sub>2</sub> . [((id c<sub>2</sub>) . FF),((id c<sub>2</sub>) . a)] is set
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
(A,c<sub>2</sub>) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
the carrier of A is non empty set
a is Element of the carrier of A
(A,c<sub>2</sub>) . a is Element of the carrier of c<sub>2</sub>
the carrier of c<sub>2</sub> is non empty set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the ObjectMap of (A,c<sub>2</sub>) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the ObjectMap of (A,c<sub>2</sub>) . (a,a) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the ObjectMap of (A,c<sub>2</sub>) . [a,a] is set
( the ObjectMap of (A,c<sub>2</sub>) . (a,a)) `1 is set
a is Element of the carrier of A
b is Element of the carrier of A
<^a,b^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
c is Element of <^a,b^>
(A,c₂) . c is Element of <^((A,c₂) . b),((A,c₂) . a)^>
(A,c₂) . b is Element of the carrier of c₂
the carrier of c₂ is non empty set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the ObjectMap of (A,c₂) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c₂, the carrier of c₂:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c₂, the carrier of c₂:]:] is non empty set
the ObjectMap of (A,c₂) . (b,b) is Element of [: the carrier of c₂, the carrier of c₂:]
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of (A,c₂) . [b,b] is set
( the ObjectMap of (A,c₂) . (b,b)) `1 is set
(A,c<sub>2</sub>) . a is Element of the carrier of c<sub>2</sub>
the ObjectMap of (A,c<sub>2</sub>) . (a,a) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[a,a] is V22() set
{a,a} is non empty set
{{a,a},{a}} is non empty set
the ObjectMap of (A,c<sub>2</sub>) . [a,a] is set
( the ObjectMap of (A,c<sub>2</sub>) . (a,a)) `1 is set
<^((A,c₂) . b),((A,c₂) . a)^> is set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
the Arrows of c₂ . (((A,c₂) . b),((A,c₂) . a)) is set
[((A,c₂) . b),((A,c₂) . a)] is V22() set
{((A,c₂) . b),((A,c₂) . a)} is non empty set
{((A,c₂) . b)} is non empty set
{{((A,c₂) . b),((A,c₂) . a)},{((A,c₂) . b)}} is non empty set
the Arrows of c₂ . [((A,c₂) . b),((A,c₂) . a)] is set
a is Element of the carrier of A
b is Element of the carrier of A
a is Element of the carrier of A
b is Element of the carrier of A
<^a,b^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
c is Element of <^a,b^>
d is Element of <^a,b^>
the carrier of c₂ is non empty set
a is Element of the carrier of c₂
b is Element of the carrier of c₂
<^a,b^> is set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the Arrows of c₂ . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of c₂ . [a,b] is set
d is Element of the carrier of A
c is Element of the carrier of A
<^d,c^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (d,c) is set
[d,c] is V22() set
{d,c} is non empty set
{d} is non empty set
{{d,c},{d}} is non empty set
the Arrows of A . [d,c] is set
f is Element of <^a,b^>
A is non empty transitive associative with_units reflexive AltCatStr
(A) is non empty transitive strict associative with_units reflexive AltCatStr
(A,(A)) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,(A)
((A),A) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of (A),A
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
(A,c₂) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c₂
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
(A,c₂) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c₂
a is feasible id-preserving Functor of FF,A
b is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of FF,A
(A,c₂) * b is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,c₂
a is feasible id-preserving Functor of c₂,FF
b is reflexive feasible Contravariant id-preserving comp-reversing contravariant Functor of c₂,FF
b * (A,c₂) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,FF
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
a is non empty transitive associative with_units reflexive AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
a is non empty transitive associative with_units reflexive AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
<^a,FF^> is set
the Arrows of A . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of A . [a,FF] is set
the carrier of c₂ is non empty set
b is Element of the carrier of c₂
c is Element of the carrier of c₂
<^c,b^> is set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the Arrows of c₂ . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of c₂ . [c,b] is set
f is Element of <^c,b^>
d is Element of <^FF,a^>
fa is Element of <^a,FF^>
<^b,c^> is set
the Arrows of c₂ . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of c₂ . [b,c] is set
fb is Element of <^b,c^>
d * fa is Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of A . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of A . [a,a] is set
idm a is retraction coretraction iso mono epi Element of <^a,a^>
idm c is retraction coretraction iso mono epi Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of c₂ . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of c₂ . [c,c] is set
fb * f is Element of <^c,c^>
fa is Element of <^a,FF^>
<^b,c^> is set
the Arrows of c₂ . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of c₂ . [b,c] is set
fb is Element of <^b,c^>
fa * d is Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
idm b is retraction coretraction iso mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of c₂ . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of c₂ . [b,b] is set
f * fb is Element of <^b,b^>
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
the carrier of c₂ is non empty set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
<^a,FF^> is set
the Arrows of A . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of A . [a,FF] is set
b is Element of the carrier of c₂
c is Element of the carrier of c₂
<^c,b^> is set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the Arrows of c₂ . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of c₂ . [c,b] is set
<^b,c^> is set
the Arrows of c₂ . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of c₂ . [b,c] is set
f is Element of <^c,b^>
d is Element of <^FF,a^>
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
the carrier of c₂ is non empty set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
<^a,FF^> is set
the Arrows of A . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of A . [a,FF] is set
b is Element of the carrier of c₂
c is Element of the carrier of c₂
<^c,b^> is set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the Arrows of c₂ . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of c₂ . [c,b] is set
<^b,c^> is set
the Arrows of c₂ . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of c₂ . [b,c] is set
f is Element of <^c,b^>
d is Element of <^FF,a^>
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
the carrier of c₂ is non empty set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
<^a,FF^> is set
the Arrows of A . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of A . [a,FF] is set
b is Element of the carrier of c₂
c is Element of the carrier of c₂
<^c,b^> is set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the Arrows of c₂ . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of c₂ . [c,b] is set
<^b,c^> is set
the Arrows of c₂ . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of c₂ . [b,c] is set
d is Element of <^FF,a^>
d " is Element of <^a,FF^>
f is Element of <^c,b^>
f " is Element of <^b,c^>
(d ") * d is Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
d * (d ") is Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of A . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of A . [a,a] is set
idm a is retraction coretraction iso mono epi Element of <^a,a^>
fa is Element of <^b,c^>
f * fa is Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of c₂ . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of c₂ . [b,b] is set
fa * f is Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of c₂ . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of c₂ . [c,c] is set
idm b is retraction coretraction iso mono epi Element of <^b,b^>
idm c is retraction coretraction iso mono epi Element of <^c,c^>
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
the carrier of c₂ is non empty set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
<^a,FF^> is set
the Arrows of A . (a,FF) is set
[a,FF] is V22() set
{a,FF} is non empty set
{a} is non empty set
{{a,FF},{a}} is non empty set
the Arrows of A . [a,FF] is set
b is Element of the carrier of c₂
c is Element of the carrier of c₂
<^c,b^> is set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
the Arrows of c₂ . (c,b) is set
[c,b] is V22() set
{c,b} is non empty set
{c} is non empty set
{{c,b},{c}} is non empty set
the Arrows of c₂ . [c,b] is set
<^b,c^> is set
the Arrows of c₂ . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of c₂ . [b,c] is set
d is non empty transitive associative with_units reflexive AltCatStr
f is non empty transitive associative with_units reflexive AltCatStr
the carrier of d is non empty set
fa is Element of the carrier of d
fb is Element of the carrier of d
<^fa,fb^> is set
the Arrows of d is Relation-like [: the carrier of d, the carrier of d:] -defined Function-like non empty V14([: the carrier of d, the carrier of d:]) set
[: the carrier of d, the carrier of d:] is Relation-like non empty set
the Arrows of d . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of d . [fa,fb] is set
<^fb,fa^> is set
the Arrows of d . (fb,fa) is set
[fb,fa] is V22() set
{fb,fa} is non empty set
{fb} is non empty set
{{fb,fa},{fb}} is non empty set
the Arrows of d . [fb,fa] is set
the carrier of f is non empty set
g is Element of the carrier of f
g is Element of the carrier of f
<^g,g^> is set
the Arrows of f is Relation-like [: the carrier of f, the carrier of f:] -defined Function-like non empty V14([: the carrier of f, the carrier of f:]) set
[: the carrier of f, the carrier of f:] is Relation-like non empty set
the Arrows of f . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of f . [g,g] is set
g9 is Element of <^g,g^>
c₁₃ is Element of <^fa,fb^>
c₁₃ " is Element of <^fb,fa^>
c₁₃ * (c₁₃ ") is Element of <^fb,fb^>
<^fb,fb^> is non empty set
the Arrows of d . (fb,fb) is set
[fb,fb] is V22() set
{fb,fb} is non empty set
{{fb,fb},{fb}} is non empty set
the Arrows of d . [fb,fb] is set
idm fb is retraction coretraction iso mono epi Element of <^fb,fb^>
(c₁₃ ") * c₁₃ is Element of <^fa,fa^>
<^fa,fa^> is non empty set
the Arrows of d . (fa,fa) is set
[fa,fa] is V22() set
{fa,fa} is non empty set
{{fa,fa},{fa}} is non empty set
the Arrows of d . [fa,fa] is set
idm fa is retraction coretraction iso mono epi Element of <^fa,fa^>
g9 " is Element of <^g,g^>
<^g,g^> is set
the Arrows of f . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of f . [g,g] is set
idm g is retraction coretraction iso mono epi Element of <^g,g^>
<^g,g^> is non empty set
the Arrows of f . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of f . [g,g] is set
idm g is retraction coretraction iso mono epi Element of <^g,g^>
<^g,g^> is non empty set
the Arrows of f . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of f . [g,g] is set
g9 * (g9 ") is Element of <^g,g^>
(g9 ") * g9 is Element of <^g,g^>
f is Element of <^c,b^>
d is Element of <^FF,a^>
A is non empty transitive associative with_units reflexive AltCatStr
c₂ is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
a is non empty transitive associative with_units reflexive AltCatStr
(A,c₂) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c₂
(FF,a) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,a
b is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of c₂,FF
c is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of c₂,FF
(FF,a) * c is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of c₂,a
((FF,a) * c) * (A,c₂) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
(FF,a) * b is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of c₂,a
((FF,a) * b) * (A,c₂) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,a
the carrier of c₂ is non empty set
d is Relation-like the carrier of c₂ -defined Function-like non empty V14( the carrier of c₂) natural_transformation of b,c
the carrier of A is non empty set
g is Element of the carrier of A
(((FF,a) * c) * (A,c₂)) . g is Element of the carrier of a
the carrier of a is non empty set
[: the carrier of a, the carrier of a:] is Relation-like non empty set
the ObjectMap of (((FF,a) * c) * (A,c₂)) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]:] is non empty set
the ObjectMap of (((FF,a) * c) * (A,c₂)) . (g,g) is Element of [: the carrier of a, the carrier of a:]
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of (((FF,a) * c) * (A,c₂)) . [g,g] is set
( the ObjectMap of (((FF,a) * c) * (A,c₂)) . (g,g)) `1 is set
(A,c<sub>2</sub>) . g is Element of the carrier of c<sub>2</sub>
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the ObjectMap of (A,c<sub>2</sub>) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]:] is non empty set
the ObjectMap of (A,c<sub>2</sub>) . (g,g) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of (A,c<sub>2</sub>) . [g,g] is set
( the ObjectMap of (A,c<sub>2</sub>) . (g,g)) `1 is set
((FF,a) * c) . ((A,c₂) . g) is Element of the carrier of a
the ObjectMap of ((FF,a) * c) is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) quasi_total Element of bool [:[: the carrier of c₂, the carrier of c₂:],[: the carrier of a, the carrier of a:]:]
[:[: the carrier of c₂, the carrier of c₂:],[: the carrier of a, the carrier of a:]:] is Relation-like non empty set
bool [:[: the carrier of c₂, the carrier of c₂:],[: the carrier of a, the carrier of a:]:] is non empty set
the ObjectMap of ((FF,a) * c) . (((A,c₂) . g),((A,c₂) . g)) is Element of [: the carrier of a, the carrier of a:]
[((A,c₂) . g),((A,c₂) . g)] is V22() set
{((A,c₂) . g),((A,c₂) . g)} is non empty set
{((A,c₂) . g)} is non empty set
{{((A,c₂) . g),((A,c₂) . g)},{((A,c₂) . g)}} is non empty set
the ObjectMap of ((FF,a) * c) . [((A,c₂) . g),((A,c₂) . g)] is set
( the ObjectMap of ((FF,a) * c) . (((A,c₂) . g),((A,c₂) . g))) `1 is set
(((FF,a) * b) * (A,c<sub>2</sub>)) . g is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of a, the carrier of a:]:]
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (g,g) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . [g,g] is set
( the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (g,g)) `1 is set
((FF,a) * b) . ((A,c₂) . g) is Element of the carrier of a
the ObjectMap of ((FF,a) * b) is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) quasi_total Element of bool [:[: the carrier of c₂, the carrier of c₂:],[: the carrier of a, the carrier of a:]:]
the ObjectMap of ((FF,a) * b) . (((A,c₂) . g),((A,c₂) . g)) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of ((FF,a) * b) . [((A,c₂) . g),((A,c₂) . g)] is set
( the ObjectMap of ((FF,a) * b) . (((A,c₂) . g),((A,c₂) . g))) `1 is set
c . ((A,c<sub>2</sub>) . g) is Element of the carrier of FF
the carrier of FF is non empty set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
the ObjectMap of c is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined [: the carrier of FF, the carrier of FF:] -valued Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) quasi_total Element of bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:]
[:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:] is Relation-like non empty set
bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:] is non empty set
the ObjectMap of c . (((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g)) is Element of [: the carrier of FF, the carrier of FF:]
the ObjectMap of c . [((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g)] is set
( the ObjectMap of c . (((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g))) `1 is set
(FF,a) . (c . ((A,c₂) . g)) is Element of the carrier of a
the ObjectMap of (FF,a) is Relation-like [: the carrier of FF, the carrier of FF:] -defined [: the carrier of a, the carrier of a:] -valued Function-like non empty V14([: the carrier of FF, the carrier of FF:]) quasi_total Element of bool [:[: the carrier of FF, the carrier of FF:],[: the carrier of a, the carrier of a:]:]
[:[: the carrier of FF, the carrier of FF:],[: the carrier of a, the carrier of a:]:] is Relation-like non empty set
bool [:[: the carrier of FF, the carrier of FF:],[: the carrier of a, the carrier of a:]:] is non empty set
the ObjectMap of (FF,a) . ((c . ((A,c₂) . g)),(c . ((A,c₂) . g))) is Element of [: the carrier of a, the carrier of a:]
[(c . ((A,c₂) . g)),(c . ((A,c₂) . g))] is V22() set
{(c . ((A,c₂) . g)),(c . ((A,c₂) . g))} is non empty set
{(c . ((A,c₂) . g))} is non empty set
{{(c . ((A,c₂) . g)),(c . ((A,c₂) . g))},{(c . ((A,c₂) . g))}} is non empty set
the ObjectMap of (FF,a) . [(c . ((A,c₂) . g)),(c . ((A,c₂) . g))] is set
( the ObjectMap of (FF,a) . ((c . ((A,c₂) . g)),(c . ((A,c₂) . g)))) `1 is set
b . ((A,c<sub>2</sub>) . g) is Element of the carrier of FF
the ObjectMap of b is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined [: the carrier of FF, the carrier of FF:] -valued Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) quasi_total Element of bool [:[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:],[: the carrier of FF, the carrier of FF:]:]
the ObjectMap of b . (((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g)) is Element of [: the carrier of FF, the carrier of FF:]
the ObjectMap of b . [((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g)] is set
( the ObjectMap of b . (((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g))) `1 is set
(FF,a) . (b . ((A,c₂) . g)) is Element of the carrier of a
the ObjectMap of (FF,a) . ((b . ((A,c₂) . g)),(b . ((A,c₂) . g))) is Element of [: the carrier of a, the carrier of a:]
[(b . ((A,c₂) . g)),(b . ((A,c₂) . g))] is V22() set
{(b . ((A,c₂) . g)),(b . ((A,c₂) . g))} is non empty set
{(b . ((A,c₂) . g))} is non empty set
{{(b . ((A,c₂) . g)),(b . ((A,c₂) . g))},{(b . ((A,c₂) . g))}} is non empty set
the ObjectMap of (FF,a) . [(b . ((A,c₂) . g)),(b . ((A,c₂) . g))] is set
( the ObjectMap of (FF,a) . ((b . ((A,c₂) . g)),(b . ((A,c₂) . g)))) `1 is set
<^((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)^> is set
the Arrows of a is Relation-like [: the carrier of a, the carrier of a:] -defined Function-like non empty V14([: the carrier of a, the carrier of a:]) set
the Arrows of a . (((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)) is set
[((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)] is V22() set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)} is non empty set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g)} is non empty set
{{((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)},{((((FF,a) * c) * (A,c<sub>2</sub>)) . g)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)] is set
<^(b . ((A,c<sub>2</sub>) . g)),(c . ((A,c<sub>2</sub>) . g))^> is set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
the Arrows of FF . ((b . ((A,c<sub>2</sub>) . g)),(c . ((A,c<sub>2</sub>) . g))) is set
[(b . ((A,c<sub>2</sub>) . g)),(c . ((A,c<sub>2</sub>) . g))] is V22() set
{(b . ((A,c<sub>2</sub>) . g)),(c . ((A,c<sub>2</sub>) . g))} is non empty set
{{(b . ((A,c<sub>2</sub>) . g)),(c . ((A,c<sub>2</sub>) . g))},{(b . ((A,c<sub>2</sub>) . g))}} is non empty set
the Arrows of FF . [(b . ((A,c<sub>2</sub>) . g)),(c . ((A,c<sub>2</sub>) . g))] is set
g is Element of the carrier of A
(((FF,a) * c) * (A,c<sub>2</sub>)) . g is Element of the carrier of a
the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . (g,g) is Element of [: the carrier of a, the carrier of a:]
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . [g,g] is set
( the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . (g,g)) `1 is set
(((FF,a) * b) * (A,c₂)) . g is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c₂)) . (g,g) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * b) * (A,c₂)) . [g,g] is set
( the ObjectMap of (((FF,a) * b) * (A,c₂)) . (g,g)) `1 is set
<^((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)) is set
[((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)] is V22() set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)} is non empty set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g)} is non empty set
{{((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)},{((((FF,a) * c) * (A,c<sub>2</sub>)) . g)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c<sub>2</sub>)) . g),((((FF,a) * b) * (A,c<sub>2</sub>)) . g)] is set
(A,c<sub>2</sub>) . g is Element of the carrier of c<sub>2</sub>
the ObjectMap of (A,c<sub>2</sub>) . (g,g) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of (A,c<sub>2</sub>) . [g,g] is set
( the ObjectMap of (A,c<sub>2</sub>) . (g,g)) `1 is set
b . ((A,c₂) . g) is Element of the carrier of FF
the ObjectMap of b . (((A,c₂) . g),((A,c₂) . g)) is Element of [: the carrier of FF, the carrier of FF:]
[((A,c₂) . g),((A,c₂) . g)] is V22() set
{((A,c₂) . g),((A,c₂) . g)} is non empty set
{((A,c₂) . g)} is non empty set
{{((A,c₂) . g),((A,c₂) . g)},{((A,c₂) . g)}} is non empty set
the ObjectMap of b . [((A,c₂) . g),((A,c₂) . g)] is set
( the ObjectMap of b . (((A,c₂) . g),((A,c₂) . g))) `1 is set
c . ((A,c<sub>2</sub>) . g) is Element of the carrier of FF
the ObjectMap of c . (((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g)) is Element of [: the carrier of FF, the carrier of FF:]
the ObjectMap of c . [((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g)] is set
( the ObjectMap of c . (((A,c<sub>2</sub>) . g),((A,c<sub>2</sub>) . g))) `1 is set
<^(b . ((A,c₂) . g)),(c . ((A,c₂) . g))^> is set
the Arrows of FF . ((b . ((A,c₂) . g)),(c . ((A,c₂) . g))) is set
[(b . ((A,c₂) . g)),(c . ((A,c₂) . g))] is V22() set
{(b . ((A,c₂) . g)),(c . ((A,c₂) . g))} is non empty set
{(b . ((A,c₂) . g))} is non empty set
{{(b . ((A,c₂) . g)),(c . ((A,c₂) . g))},{(b . ((A,c₂) . g))}} is non empty set
the Arrows of FF . [(b . ((A,c₂) . g)),(c . ((A,c₂) . g))] is set
dom d is non empty Element of bool the carrier of c₂
bool the carrier of c₂ is non empty set
g is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) set
c₁₃ is Element of the carrier of A
g . c₁₃ is set
(((FF,a) * c) * (A,c₂)) . c₁₃ is Element of the carrier of a
the ObjectMap of (((FF,a) * c) * (A,c₂)) . (c₁₃,c₁₃) is Element of [: the carrier of a, the carrier of a:]
[c₁₃,c₁₃] is V22() set
{c₁₃,c₁₃} is non empty set
{c₁₃} is non empty set
{{c₁₃,c₁₃},{c₁₃}} is non empty set
the ObjectMap of (((FF,a) * c) * (A,c₂)) . [c₁₃,c₁₃] is set
( the ObjectMap of (((FF,a) * c) * (A,c₂)) . (c₁₃,c₁₃)) `1 is set
(((FF,a) * b) * (A,c<sub>2</sub>)) . c<sub>13</sub> is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (c<sub>13</sub>,c<sub>13</sub>) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . [c<sub>13</sub>,c<sub>13</sub>] is set
( the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (c<sub>13</sub>,c<sub>13</sub>)) `1 is set
<^((((FF,a) * c) * (A,c₂)) . c₁₃),((((FF,a) * b) * (A,c₂)) . c₁₃)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c₂)) . c₁₃),((((FF,a) * b) * (A,c₂)) . c₁₃)) is set
[((((FF,a) * c) * (A,c₂)) . c₁₃),((((FF,a) * b) * (A,c₂)) . c₁₃)] is V22() set
{((((FF,a) * c) * (A,c₂)) . c₁₃),((((FF,a) * b) * (A,c₂)) . c₁₃)} is non empty set
{((((FF,a) * c) * (A,c₂)) . c₁₃)} is non empty set
{{((((FF,a) * c) * (A,c₂)) . c₁₃),((((FF,a) * b) * (A,c₂)) . c₁₃)},{((((FF,a) * c) * (A,c₂)) . c₁₃)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c₂)) . c₁₃),((((FF,a) * b) * (A,c₂)) . c₁₃)] is set
(A,c₂) . c₁₃ is Element of the carrier of c₂
the ObjectMap of (A,c₂) . (c₁₃,c₁₃) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of (A,c₂) . [c₁₃,c₁₃] is set
( the ObjectMap of (A,c₂) . (c₁₃,c₁₃)) `1 is set
d . ((A,c<sub>2</sub>) . c<sub>13</sub>) is set
d ! ((A,c<sub>2</sub>) . c<sub>13</sub>) is Element of <^(b . ((A,c<sub>2</sub>) . c<sub>13</sub>)),(c . ((A,c<sub>2</sub>) . c<sub>13</sub>))^>
b . ((A,c<sub>2</sub>) . c<sub>13</sub>) is Element of the carrier of FF
the ObjectMap of b . (((A,c<sub>2</sub>) . c<sub>13</sub>),((A,c<sub>2</sub>) . c<sub>13</sub>)) is Element of [: the carrier of FF, the carrier of FF:]
[((A,c<sub>2</sub>) . c<sub>13</sub>),((A,c<sub>2</sub>) . c<sub>13</sub>)] is V22() set
{((A,c<sub>2</sub>) . c<sub>13</sub>),((A,c<sub>2</sub>) . c<sub>13</sub>)} is non empty set
{((A,c<sub>2</sub>) . c<sub>13</sub>)} is non empty set
{{((A,c<sub>2</sub>) . c<sub>13</sub>),((A,c<sub>2</sub>) . c<sub>13</sub>)},{((A,c<sub>2</sub>) . c<sub>13</sub>)}} is non empty set
the ObjectMap of b . [((A,c<sub>2</sub>) . c<sub>13</sub>),((A,c<sub>2</sub>) . c<sub>13</sub>)] is set
( the ObjectMap of b . (((A,c<sub>2</sub>) . c<sub>13</sub>),((A,c<sub>2</sub>) . c<sub>13</sub>))) `1 is set
c . ((A,c₂) . c₁₃) is Element of the carrier of FF
the ObjectMap of c . (((A,c₂) . c₁₃),((A,c₂) . c₁₃)) is Element of [: the carrier of FF, the carrier of FF:]
the ObjectMap of c . [((A,c₂) . c₁₃),((A,c₂) . c₁₃)] is set
( the ObjectMap of c . (((A,c₂) . c₁₃),((A,c₂) . c₁₃))) `1 is set
<^(b . ((A,c<sub>2</sub>) . c<sub>13</sub>)),(c . ((A,c<sub>2</sub>) . c<sub>13</sub>))^> is set
the Arrows of FF . ((b . ((A,c<sub>2</sub>) . c<sub>13</sub>)),(c . ((A,c<sub>2</sub>) . c<sub>13</sub>))) is set
[(b . ((A,c<sub>2</sub>) . c<sub>13</sub>)),(c . ((A,c<sub>2</sub>) . c<sub>13</sub>))] is V22() set
{(b . ((A,c<sub>2</sub>) . c<sub>13</sub>)),(c . ((A,c<sub>2</sub>) . c<sub>13</sub>))} is non empty set
{(b . ((A,c<sub>2</sub>) . c<sub>13</sub>))} is non empty set
{{(b . ((A,c<sub>2</sub>) . c<sub>13</sub>)),(c . ((A,c<sub>2</sub>) . c<sub>13</sub>))},{(b . ((A,c<sub>2</sub>) . c<sub>13</sub>))}} is non empty set
the Arrows of FF . [(b . ((A,c<sub>2</sub>) . c<sub>13</sub>)),(c . ((A,c<sub>2</sub>) . c<sub>13</sub>))] is set
g9 is Element of the carrier of A
a1 is Element of the carrier of A
<^g9,a1^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A . (g9,a1) is set
[g9,a1] is V22() set
{g9,a1} is non empty set
{g9} is non empty set
{{g9,a1},{g9}} is non empty set
the Arrows of A . [g9,a1] is set
(A,c<sub>2</sub>) . a1 is Element of the carrier of c<sub>2</sub>
the ObjectMap of (A,c<sub>2</sub>) . (a1,a1) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
[a1,a1] is V22() set
{a1,a1} is non empty set
{a1} is non empty set
{{a1,a1},{a1}} is non empty set
the ObjectMap of (A,c<sub>2</sub>) . [a1,a1] is set
( the ObjectMap of (A,c<sub>2</sub>) . (a1,a1)) `1 is set
(A,c₂) . g9 is Element of the carrier of c₂
the ObjectMap of (A,c₂) . (g9,g9) is Element of [: the carrier of c₂, the carrier of c₂:]
[g9,g9] is V22() set
{g9,g9} is non empty set
{{g9,g9},{g9}} is non empty set
the ObjectMap of (A,c₂) . [g9,g9] is set
( the ObjectMap of (A,c₂) . (g9,g9)) `1 is set
b1 is Element of <^g9,a1^>
(A,c<sub>2</sub>) . b1 is Element of <^((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . g9)^>
<^((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . g9)^> is set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
the Arrows of c<sub>2</sub> . (((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . g9)) is set
[((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . g9)] is V22() set
{((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . g9)} is non empty set
{((A,c<sub>2</sub>) . a1)} is non empty set
{{((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . g9)},{((A,c<sub>2</sub>) . a1)}} is non empty set
the Arrows of c<sub>2</sub> . [((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . g9)] is set
d ! ((A,c<sub>2</sub>) . g9) is Element of <^(b . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))^>
b . ((A,c<sub>2</sub>) . g9) is Element of the carrier of FF
the ObjectMap of b . (((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)) is Element of [: the carrier of FF, the carrier of FF:]
[((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)] is V22() set
{((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)} is non empty set
{((A,c<sub>2</sub>) . g9)} is non empty set
{{((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)},{((A,c<sub>2</sub>) . g9)}} is non empty set
the ObjectMap of b . [((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)] is set
( the ObjectMap of b . (((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9))) `1 is set
c . ((A,c₂) . g9) is Element of the carrier of FF
the ObjectMap of c . (((A,c₂) . g9),((A,c₂) . g9)) is Element of [: the carrier of FF, the carrier of FF:]
the ObjectMap of c . [((A,c₂) . g9),((A,c₂) . g9)] is set
( the ObjectMap of c . (((A,c₂) . g9),((A,c₂) . g9))) `1 is set
<^(b . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))^> is set
the Arrows of FF . ((b . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))) is set
[(b . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))] is V22() set
{(b . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))} is non empty set
{(b . ((A,c<sub>2</sub>) . g9))} is non empty set
{{(b . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))},{(b . ((A,c<sub>2</sub>) . g9))}} is non empty set
the Arrows of FF . [(b . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))] is set
d . g9 is set
d ! ((A,c<sub>2</sub>) . a1) is Element of <^(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))^>
b . ((A,c<sub>2</sub>) . a1) is Element of the carrier of FF
the ObjectMap of b . (((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)) is Element of [: the carrier of FF, the carrier of FF:]
[((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)] is V22() set
{((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)} is non empty set
{{((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)},{((A,c<sub>2</sub>) . a1)}} is non empty set
the ObjectMap of b . [((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)] is set
( the ObjectMap of b . (((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1))) `1 is set
c . ((A,c₂) . a1) is Element of the carrier of FF
the ObjectMap of c . (((A,c₂) . a1),((A,c₂) . a1)) is Element of [: the carrier of FF, the carrier of FF:]
the ObjectMap of c . [((A,c₂) . a1),((A,c₂) . a1)] is set
( the ObjectMap of c . (((A,c₂) . a1),((A,c₂) . a1))) `1 is set
<^(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))^> is set
the Arrows of FF . ((b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))) is set
[(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))] is V22() set
{(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))} is non empty set
{(b . ((A,c<sub>2</sub>) . a1))} is non empty set
{{(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))},{(b . ((A,c<sub>2</sub>) . a1))}} is non empty set
the Arrows of FF . [(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))] is set
d . a1 is set
c<sub>13</sub> is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) transformation of ((FF,a) * c) * (A,c<sub>2</sub>),((FF,a) * b) * (A,c<sub>2</sub>)
c<sub>13</sub> ! g9 is Element of <^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)^>
(((FF,a) * c) * (A,c<sub>2</sub>)) . g9 is Element of the carrier of a
the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . (g9,g9) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . [g9,g9] is set
( the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . (g9,g9)) `1 is set
(((FF,a) * b) * (A,c₂)) . g9 is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c₂)) . (g9,g9) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * b) * (A,c₂)) . [g9,g9] is set
( the ObjectMap of (((FF,a) * b) * (A,c₂)) . (g9,g9)) `1 is set
<^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)) is set
[((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)] is V22() set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)} is non empty set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9)} is non empty set
{{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)},{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)] is set
c<sub>13</sub> ! a1 is Element of <^((((FF,a) * c) * (A,c<sub>2</sub>)) . a1),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^>
(((FF,a) * c) * (A,c<sub>2</sub>)) . a1 is Element of the carrier of a
the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . (a1,a1) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . [a1,a1] is set
( the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . (a1,a1)) `1 is set
(((FF,a) * b) * (A,c₂)) . a1 is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c₂)) . (a1,a1) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * b) * (A,c₂)) . [a1,a1] is set
( the ObjectMap of (((FF,a) * b) * (A,c₂)) . (a1,a1)) `1 is set
<^((((FF,a) * c) * (A,c<sub>2</sub>)) . a1),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c<sub>2</sub>)) . a1),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)) is set
[((((FF,a) * c) * (A,c<sub>2</sub>)) . a1),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)] is V22() set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . a1),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)} is non empty set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)} is non empty set
{{((((FF,a) * c) * (A,c<sub>2</sub>)) . a1),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)},{((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c<sub>2</sub>)) . a1),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)] is set
<^(b . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . g9))^> is set
the Arrows of FF . ((b . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . g9))) is set
[(b . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . g9))] is V22() set
{(b . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . g9))} is non empty set
{{(b . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . g9))},{(b . ((A,c<sub>2</sub>) . a1))}} is non empty set
the Arrows of FF . [(b . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . g9))] is set
<^(c . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))^> is set
the Arrows of FF . ((c . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))) is set
[(c . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))] is V22() set
{(c . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))} is non empty set
{(c . ((A,c<sub>2</sub>) . a1))} is non empty set
{{(c . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))},{(c . ((A,c<sub>2</sub>) . a1))}} is non empty set
the Arrows of FF . [(c . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))] is set
(((FF,a) * b) * (A,c<sub>2</sub>)) . b1 is Element of <^((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^>
<^((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^> is set
the Arrows of a . (((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)) is set
[((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)] is V22() set
{((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)} is non empty set
{((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)} is non empty set
{{((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)},{((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)}} is non empty set
the Arrows of a . [((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)] is set
((FF,a) * b) . ((A,c<sub>2</sub>) . b1) is Element of <^(((FF,a) * b) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * b) . ((A,c<sub>2</sub>) . a1))^>
((FF,a) * b) . ((A,c<sub>2</sub>) . g9) is Element of the carrier of a
the ObjectMap of ((FF,a) * b) . (((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of ((FF,a) * b) . [((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)] is set
( the ObjectMap of ((FF,a) * b) . (((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9))) `1 is set
((FF,a) * b) . ((A,c₂) . a1) is Element of the carrier of a
the ObjectMap of ((FF,a) * b) . (((A,c₂) . a1),((A,c₂) . a1)) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of ((FF,a) * b) . [((A,c₂) . a1),((A,c₂) . a1)] is set
( the ObjectMap of ((FF,a) * b) . (((A,c₂) . a1),((A,c₂) . a1))) `1 is set
<^(((FF,a) * b) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * b) . ((A,c<sub>2</sub>) . a1))^> is set
the Arrows of a . ((((FF,a) * b) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * b) . ((A,c<sub>2</sub>) . a1))) is set
[(((FF,a) * b) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * b) . ((A,c<sub>2</sub>) . a1))] is V22() set
{(((FF,a) * b) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * b) . ((A,c<sub>2</sub>) . a1))} is non empty set
{(((FF,a) * b) . ((A,c<sub>2</sub>) . g9))} is non empty set
{{(((FF,a) * b) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * b) . ((A,c<sub>2</sub>) . a1))},{(((FF,a) * b) . ((A,c<sub>2</sub>) . g9))}} is non empty set
the Arrows of a . [(((FF,a) * b) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * b) . ((A,c<sub>2</sub>) . a1))] is set
(((FF,a) * c) * (A,c<sub>2</sub>)) . b1 is Element of <^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)^>
<^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)) is set
[((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)] is V22() set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)} is non empty set
{{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)},{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)] is set
((FF,a) * c) . ((A,c<sub>2</sub>) . b1) is Element of <^(((FF,a) * c) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * c) . ((A,c<sub>2</sub>) . a1))^>
((FF,a) * c) . ((A,c<sub>2</sub>) . g9) is Element of the carrier of a
the ObjectMap of ((FF,a) * c) . (((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of ((FF,a) * c) . [((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9)] is set
( the ObjectMap of ((FF,a) * c) . (((A,c<sub>2</sub>) . g9),((A,c<sub>2</sub>) . g9))) `1 is set
((FF,a) * c) . ((A,c₂) . a1) is Element of the carrier of a
the ObjectMap of ((FF,a) * c) . (((A,c₂) . a1),((A,c₂) . a1)) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of ((FF,a) * c) . [((A,c₂) . a1),((A,c₂) . a1)] is set
( the ObjectMap of ((FF,a) * c) . (((A,c₂) . a1),((A,c₂) . a1))) `1 is set
<^(((FF,a) * c) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * c) . ((A,c<sub>2</sub>) . a1))^> is set
the Arrows of a . ((((FF,a) * c) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * c) . ((A,c<sub>2</sub>) . a1))) is set
[(((FF,a) * c) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * c) . ((A,c<sub>2</sub>) . a1))] is V22() set
{(((FF,a) * c) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * c) . ((A,c<sub>2</sub>) . a1))} is non empty set
{(((FF,a) * c) . ((A,c<sub>2</sub>) . g9))} is non empty set
{{(((FF,a) * c) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * c) . ((A,c<sub>2</sub>) . a1))},{(((FF,a) * c) . ((A,c<sub>2</sub>) . g9))}} is non empty set
the Arrows of a . [(((FF,a) * c) . ((A,c<sub>2</sub>) . g9)),(((FF,a) * c) . ((A,c<sub>2</sub>) . a1))] is set
b . ((A,c<sub>2</sub>) . b1) is Element of <^(b . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . g9))^>
(FF,a) . (b . ((A,c<sub>2</sub>) . b1)) is Element of <^((FF,a) . (b . ((A,c<sub>2</sub>) . g9))),((FF,a) . (b . ((A,c<sub>2</sub>) . a1)))^>
(FF,a) . (b . ((A,c<sub>2</sub>) . g9)) is Element of the carrier of a
the ObjectMap of (FF,a) . ((b . ((A,c<sub>2</sub>) . g9)),(b . ((A,c<sub>2</sub>) . g9))) is Element of [: the carrier of a, the carrier of a:]
[(b . ((A,c<sub>2</sub>) . g9)),(b . ((A,c<sub>2</sub>) . g9))] is V22() set
{(b . ((A,c<sub>2</sub>) . g9)),(b . ((A,c<sub>2</sub>) . g9))} is non empty set
{{(b . ((A,c<sub>2</sub>) . g9)),(b . ((A,c<sub>2</sub>) . g9))},{(b . ((A,c<sub>2</sub>) . g9))}} is non empty set
the ObjectMap of (FF,a) . [(b . ((A,c<sub>2</sub>) . g9)),(b . ((A,c<sub>2</sub>) . g9))] is set
( the ObjectMap of (FF,a) . ((b . ((A,c<sub>2</sub>) . g9)),(b . ((A,c<sub>2</sub>) . g9)))) `1 is set
(FF,a) . (b . ((A,c₂) . a1)) is Element of the carrier of a
the ObjectMap of (FF,a) . ((b . ((A,c₂) . a1)),(b . ((A,c₂) . a1))) is Element of [: the carrier of a, the carrier of a:]
[(b . ((A,c₂) . a1)),(b . ((A,c₂) . a1))] is V22() set
{(b . ((A,c₂) . a1)),(b . ((A,c₂) . a1))} is non empty set
{{(b . ((A,c₂) . a1)),(b . ((A,c₂) . a1))},{(b . ((A,c₂) . a1))}} is non empty set
the ObjectMap of (FF,a) . [(b . ((A,c₂) . a1)),(b . ((A,c₂) . a1))] is set
( the ObjectMap of (FF,a) . ((b . ((A,c₂) . a1)),(b . ((A,c₂) . a1)))) `1 is set
<^((FF,a) . (b . ((A,c<sub>2</sub>) . g9))),((FF,a) . (b . ((A,c<sub>2</sub>) . a1)))^> is set
the Arrows of a . (((FF,a) . (b . ((A,c<sub>2</sub>) . g9))),((FF,a) . (b . ((A,c<sub>2</sub>) . a1)))) is set
[((FF,a) . (b . ((A,c<sub>2</sub>) . g9))),((FF,a) . (b . ((A,c<sub>2</sub>) . a1)))] is V22() set
{((FF,a) . (b . ((A,c<sub>2</sub>) . g9))),((FF,a) . (b . ((A,c<sub>2</sub>) . a1)))} is non empty set
{((FF,a) . (b . ((A,c<sub>2</sub>) . g9)))} is non empty set
{{((FF,a) . (b . ((A,c<sub>2</sub>) . g9))),((FF,a) . (b . ((A,c<sub>2</sub>) . a1)))},{((FF,a) . (b . ((A,c<sub>2</sub>) . g9)))}} is non empty set
the Arrows of a . [((FF,a) . (b . ((A,c<sub>2</sub>) . g9))),((FF,a) . (b . ((A,c<sub>2</sub>) . a1)))] is set
c . ((A,c<sub>2</sub>) . b1) is Element of <^(c . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))^>
(FF,a) . (c . ((A,c<sub>2</sub>) . b1)) is Element of <^((FF,a) . (c . ((A,c<sub>2</sub>) . g9))),((FF,a) . (c . ((A,c<sub>2</sub>) . a1)))^>
(FF,a) . (c . ((A,c<sub>2</sub>) . g9)) is Element of the carrier of a
the ObjectMap of (FF,a) . ((c . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))) is Element of [: the carrier of a, the carrier of a:]
[(c . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))] is V22() set
{(c . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))} is non empty set
{(c . ((A,c<sub>2</sub>) . g9))} is non empty set
{{(c . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))},{(c . ((A,c<sub>2</sub>) . g9))}} is non empty set
the ObjectMap of (FF,a) . [(c . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9))] is set
( the ObjectMap of (FF,a) . ((c . ((A,c<sub>2</sub>) . g9)),(c . ((A,c<sub>2</sub>) . g9)))) `1 is set
(FF,a) . (c . ((A,c₂) . a1)) is Element of the carrier of a
the ObjectMap of (FF,a) . ((c . ((A,c₂) . a1)),(c . ((A,c₂) . a1))) is Element of [: the carrier of a, the carrier of a:]
[(c . ((A,c₂) . a1)),(c . ((A,c₂) . a1))] is V22() set
{(c . ((A,c₂) . a1)),(c . ((A,c₂) . a1))} is non empty set
{{(c . ((A,c₂) . a1)),(c . ((A,c₂) . a1))},{(c . ((A,c₂) . a1))}} is non empty set
the ObjectMap of (FF,a) . [(c . ((A,c₂) . a1)),(c . ((A,c₂) . a1))] is set
( the ObjectMap of (FF,a) . ((c . ((A,c₂) . a1)),(c . ((A,c₂) . a1)))) `1 is set
<^((FF,a) . (c . ((A,c<sub>2</sub>) . g9))),((FF,a) . (c . ((A,c<sub>2</sub>) . a1)))^> is set
the Arrows of a . (((FF,a) . (c . ((A,c<sub>2</sub>) . g9))),((FF,a) . (c . ((A,c<sub>2</sub>) . a1)))) is set
[((FF,a) . (c . ((A,c<sub>2</sub>) . g9))),((FF,a) . (c . ((A,c<sub>2</sub>) . a1)))] is V22() set
{((FF,a) . (c . ((A,c<sub>2</sub>) . g9))),((FF,a) . (c . ((A,c<sub>2</sub>) . a1)))} is non empty set
{((FF,a) . (c . ((A,c<sub>2</sub>) . g9)))} is non empty set
{{((FF,a) . (c . ((A,c<sub>2</sub>) . g9))),((FF,a) . (c . ((A,c<sub>2</sub>) . a1)))},{((FF,a) . (c . ((A,c<sub>2</sub>) . g9)))}} is non empty set
the Arrows of a . [((FF,a) . (c . ((A,c<sub>2</sub>) . g9))),((FF,a) . (c . ((A,c<sub>2</sub>) . a1)))] is set
(c<sub>13</sub> ! a1) * ((((FF,a) * c) * (A,c<sub>2</sub>)) . b1) is Element of <^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^>
<^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)) is set
[((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)] is V22() set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)} is non empty set
{{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)},{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)] is set
(c . ((A,c<sub>2</sub>) . b1)) * (d ! ((A,c<sub>2</sub>) . a1)) is Element of <^(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))^>
<^(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))^> is set
the Arrows of FF . ((b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))) is set
[(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))] is V22() set
{(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))} is non empty set
{{(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))},{(b . ((A,c<sub>2</sub>) . a1))}} is non empty set
the Arrows of FF . [(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))] is set
(d ! ((A,c<sub>2</sub>) . g9)) * (b . ((A,c<sub>2</sub>) . b1)) is Element of <^(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . g9))^>
((((FF,a) * b) * (A,c<sub>2</sub>)) . b1) * (c<sub>13</sub> ! g9) is Element of <^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^>
g9 is Element of the carrier of A
a1 is Element of the carrier of A
<^g9,a1^> is set
the Arrows of A . (g9,a1) is set
[g9,a1] is V22() set
{g9,a1} is non empty set
{g9} is non empty set
{{g9,a1},{g9}} is non empty set
the Arrows of A . [g9,a1] is set
(((FF,a) * c) * (A,c<sub>2</sub>)) . g9 is Element of the carrier of a
the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . (g9,g9) is Element of [: the carrier of a, the carrier of a:]
[g9,g9] is V22() set
{g9,g9} is non empty set
{{g9,g9},{g9}} is non empty set
the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . [g9,g9] is set
( the ObjectMap of (((FF,a) * c) * (A,c<sub>2</sub>)) . (g9,g9)) `1 is set
(((FF,a) * c) * (A,c₂)) . a1 is Element of the carrier of a
the ObjectMap of (((FF,a) * c) * (A,c₂)) . (a1,a1) is Element of [: the carrier of a, the carrier of a:]
[a1,a1] is V22() set
{a1,a1} is non empty set
{a1} is non empty set
{{a1,a1},{a1}} is non empty set
the ObjectMap of (((FF,a) * c) * (A,c₂)) . [a1,a1] is set
( the ObjectMap of (((FF,a) * c) * (A,c₂)) . (a1,a1)) `1 is set
(((FF,a) * b) * (A,c<sub>2</sub>)) . a1 is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (a1,a1) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . [a1,a1] is set
( the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (a1,a1)) `1 is set
b1 is Element of <^g9,a1^>
(((FF,a) * c) * (A,c₂)) . b1 is Element of <^((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * c) * (A,c₂)) . a1)^>
<^((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * c) * (A,c₂)) . a1)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * c) * (A,c₂)) . a1)) is set
[((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * c) * (A,c₂)) . a1)] is V22() set
{((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * c) * (A,c₂)) . a1)} is non empty set
{((((FF,a) * c) * (A,c₂)) . g9)} is non empty set
{{((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * c) * (A,c₂)) . a1)},{((((FF,a) * c) * (A,c₂)) . g9)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * c) * (A,c₂)) . a1)] is set
c₁₃ ! a1 is Element of <^((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)^>
<^((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)) is set
[((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)] is V22() set
{((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)} is non empty set
{((((FF,a) * c) * (A,c₂)) . a1)} is non empty set
{{((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)},{((((FF,a) * c) * (A,c₂)) . a1)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)] is set
(c₁₃ ! a1) * ((((FF,a) * c) * (A,c₂)) . b1) is Element of <^((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * b) * (A,c₂)) . a1)^>
<^((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * b) * (A,c₂)) . a1)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * b) * (A,c₂)) . a1)) is set
[((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * b) * (A,c₂)) . a1)] is V22() set
{((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * b) * (A,c₂)) . a1)} is non empty set
{{((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * b) * (A,c₂)) . a1)},{((((FF,a) * c) * (A,c₂)) . g9)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c₂)) . g9),((((FF,a) * b) * (A,c₂)) . a1)] is set
(((FF,a) * b) * (A,c₂)) . g9 is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c₂)) . (g9,g9) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * b) * (A,c₂)) . [g9,g9] is set
( the ObjectMap of (((FF,a) * b) * (A,c₂)) . (g9,g9)) `1 is set
c<sub>13</sub> ! g9 is Element of <^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)^>
<^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)) is set
[((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)] is V22() set
{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)} is non empty set
{{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)},{((((FF,a) * c) * (A,c<sub>2</sub>)) . g9)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)] is set
(((FF,a) * b) * (A,c<sub>2</sub>)) . b1 is Element of <^((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^>
<^((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^> is set
the Arrows of a . (((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)) is set
[((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)] is V22() set
{((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)} is non empty set
{((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)} is non empty set
{{((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)},{((((FF,a) * b) * (A,c<sub>2</sub>)) . g9)}} is non empty set
the Arrows of a . [((((FF,a) * b) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)] is set
((((FF,a) * b) * (A,c<sub>2</sub>)) . b1) * (c<sub>13</sub> ! g9) is Element of <^((((FF,a) * c) * (A,c<sub>2</sub>)) . g9),((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)^>
a1 is Element of the carrier of A
(((FF,a) * b) * (A,c<sub>2</sub>)) . a1 is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (a1,a1) is Element of [: the carrier of a, the carrier of a:]
[a1,a1] is V22() set
{a1,a1} is non empty set
{a1} is non empty set
{{a1,a1},{a1}} is non empty set
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . [a1,a1] is set
( the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (a1,a1)) `1 is set
(((FF,a) * c) * (A,c₂)) . a1 is Element of the carrier of a
the ObjectMap of (((FF,a) * c) * (A,c₂)) . (a1,a1) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * c) * (A,c₂)) . [a1,a1] is set
( the ObjectMap of (((FF,a) * c) * (A,c₂)) . (a1,a1)) `1 is set
<^((((FF,a) * b) * (A,c<sub>2</sub>)) . a1),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)^> is set
the Arrows of a . (((((FF,a) * b) * (A,c<sub>2</sub>)) . a1),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)) is set
[((((FF,a) * b) * (A,c<sub>2</sub>)) . a1),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)] is V22() set
{((((FF,a) * b) * (A,c<sub>2</sub>)) . a1),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)} is non empty set
{((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)} is non empty set
{{((((FF,a) * b) * (A,c<sub>2</sub>)) . a1),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)},{((((FF,a) * b) * (A,c<sub>2</sub>)) . a1)}} is non empty set
the Arrows of a . [((((FF,a) * b) * (A,c<sub>2</sub>)) . a1),((((FF,a) * c) * (A,c<sub>2</sub>)) . a1)] is set
(A,c<sub>2</sub>) . a1 is Element of the carrier of c<sub>2</sub>
the ObjectMap of (A,c<sub>2</sub>) . (a1,a1) is Element of [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]
the ObjectMap of (A,c<sub>2</sub>) . [a1,a1] is set
( the ObjectMap of (A,c<sub>2</sub>) . (a1,a1)) `1 is set
b . ((A,c₂) . a1) is Element of the carrier of FF
the ObjectMap of b . (((A,c₂) . a1),((A,c₂) . a1)) is Element of [: the carrier of FF, the carrier of FF:]
[((A,c₂) . a1),((A,c₂) . a1)] is V22() set
{((A,c₂) . a1),((A,c₂) . a1)} is non empty set
{((A,c₂) . a1)} is non empty set
{{((A,c₂) . a1),((A,c₂) . a1)},{((A,c₂) . a1)}} is non empty set
the ObjectMap of b . [((A,c₂) . a1),((A,c₂) . a1)] is set
( the ObjectMap of b . (((A,c₂) . a1),((A,c₂) . a1))) `1 is set
c . ((A,c<sub>2</sub>) . a1) is Element of the carrier of FF
the ObjectMap of c . (((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)) is Element of [: the carrier of FF, the carrier of FF:]
the ObjectMap of c . [((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)] is set
( the ObjectMap of c . (((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1))) `1 is set
<^(c . ((A,c₂) . a1)),(b . ((A,c₂) . a1))^> is set
the Arrows of FF . ((c . ((A,c₂) . a1)),(b . ((A,c₂) . a1))) is set
[(c . ((A,c₂) . a1)),(b . ((A,c₂) . a1))] is V22() set
{(c . ((A,c₂) . a1)),(b . ((A,c₂) . a1))} is non empty set
{(c . ((A,c₂) . a1))} is non empty set
{{(c . ((A,c₂) . a1)),(b . ((A,c₂) . a1))},{(c . ((A,c₂) . a1))}} is non empty set
the Arrows of FF . [(c . ((A,c₂) . a1)),(b . ((A,c₂) . a1))] is set
g9 is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) natural_transformation of ((FF,a) * c) * (A,c₂),((FF,a) * b) * (A,c₂)
a1 is Element of the carrier of A
(((FF,a) * c) * (A,c₂)) . a1 is Element of the carrier of a
the ObjectMap of (((FF,a) * c) * (A,c₂)) . (a1,a1) is Element of [: the carrier of a, the carrier of a:]
[a1,a1] is V22() set
{a1,a1} is non empty set
{a1} is non empty set
{{a1,a1},{a1}} is non empty set
the ObjectMap of (((FF,a) * c) * (A,c₂)) . [a1,a1] is set
( the ObjectMap of (((FF,a) * c) * (A,c₂)) . (a1,a1)) `1 is set
(((FF,a) * b) * (A,c<sub>2</sub>)) . a1 is Element of the carrier of a
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (a1,a1) is Element of [: the carrier of a, the carrier of a:]
the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . [a1,a1] is set
( the ObjectMap of (((FF,a) * b) * (A,c<sub>2</sub>)) . (a1,a1)) `1 is set
g9 ! a1 is Element of <^((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)^>
<^((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)^> is set
the Arrows of a . (((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)) is set
[((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)] is V22() set
{((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)} is non empty set
{((((FF,a) * c) * (A,c₂)) . a1)} is non empty set
{{((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)},{((((FF,a) * c) * (A,c₂)) . a1)}} is non empty set
the Arrows of a . [((((FF,a) * c) * (A,c₂)) . a1),((((FF,a) * b) * (A,c₂)) . a1)] is set
(A,c₂) . a1 is Element of the carrier of c₂
the ObjectMap of (A,c₂) . (a1,a1) is Element of [: the carrier of c₂, the carrier of c₂:]
the ObjectMap of (A,c₂) . [a1,a1] is set
( the ObjectMap of (A,c₂) . (a1,a1)) `1 is set
c . ((A,c<sub>2</sub>) . a1) is Element of the carrier of FF
the ObjectMap of c . (((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)) is Element of [: the carrier of FF, the carrier of FF:]
[((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)] is V22() set
{((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)} is non empty set
{((A,c<sub>2</sub>) . a1)} is non empty set
{{((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)},{((A,c<sub>2</sub>) . a1)}} is non empty set
the ObjectMap of c . [((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1)] is set
( the ObjectMap of c . (((A,c<sub>2</sub>) . a1),((A,c<sub>2</sub>) . a1))) `1 is set
b . ((A,c₂) . a1) is Element of the carrier of FF
the ObjectMap of b . (((A,c₂) . a1),((A,c₂) . a1)) is Element of [: the carrier of FF, the carrier of FF:]
the ObjectMap of b . [((A,c₂) . a1),((A,c₂) . a1)] is set
( the ObjectMap of b . (((A,c₂) . a1),((A,c₂) . a1))) `1 is set
d . a1 is set
d ! ((A,c<sub>2</sub>) . a1) is Element of <^(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))^>
<^(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))^> is set
the Arrows of FF . ((b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))) is set
[(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))] is V22() set
{(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))} is non empty set
{(b . ((A,c<sub>2</sub>) . a1))} is non empty set
{{(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))},{(b . ((A,c<sub>2</sub>) . a1))}} is non empty set
the Arrows of FF . [(b . ((A,c<sub>2</sub>) . a1)),(c . ((A,c<sub>2</sub>) . a1))] is set
<^(c . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . a1))^> is set
the Arrows of FF . ((c . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . a1))) is set
[(c . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . a1))] is V22() set
{(c . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . a1))} is non empty set
{(c . ((A,c<sub>2</sub>) . a1))} is non empty set
{{(c . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . a1))},{(c . ((A,c<sub>2</sub>) . a1))}} is non empty set
the Arrows of FF . [(c . ((A,c<sub>2</sub>) . a1)),(b . ((A,c<sub>2</sub>) . a1))] is set
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
a is non empty transitive associative with_units reflexive AltCatStr
id A is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A,A
id FF is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of FF,FF
b is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of A,FF
c is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of FF,A
c * b is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,A
b * c is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,FF
(c<sub>2</sub>,A) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of c<sub>2</sub>,A
(FF,a) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,a
(FF,a) * b is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,a
((FF,a) * b) * (c<sub>2</sub>,A) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,a
d is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,a
id c<sub>2</sub> is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of c<sub>2</sub>,c<sub>2</sub>
id a is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of a,a
(a,FF) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of a,FF
(A,c<sub>2</sub>) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
(A,c<sub>2</sub>) * c is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,c<sub>2</sub>
((A,c<sub>2</sub>) * c) * (a,FF) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,c<sub>2</sub>
f is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,c<sub>2</sub>
f * d is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
d * f is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
c * (id FF) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,A
the ObjectMap of c is Relation-like [: the carrier of FF, the carrier of FF:] -defined [: the carrier of A, the carrier of A:] -valued Function-like non empty V14([: the carrier of FF, the carrier of FF:]) quasi_total Element of bool [:[: the carrier of FF, the carrier of FF:],[: the carrier of A, the carrier of A:]:]
the carrier of FF is non empty set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[:[: the carrier of FF, the carrier of FF:],[: the carrier of A, the carrier of A:]:] is Relation-like non empty set
bool [:[: the carrier of FF, the carrier of FF:],[: the carrier of A, the carrier of A:]:] is non empty set
the MorphMap of c is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) Function-yielding V63() MSUnTrans of the ObjectMap of c, the Arrows of FF, the Arrows of A
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
FunctorStr(# the ObjectMap of c, the MorphMap of c #) is strict FunctorStr over FF,A
(A,c<sub>2</sub>) * (id A) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
(a,FF) * (FF,a) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of FF,FF
(A,c<sub>2</sub>) * (c * b) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
((A,c<sub>2</sub>) * (c * b)) * (c<sub>2</sub>,A) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
((A,c<sub>2</sub>) * c) * b is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,c<sub>2</sub>
(((A,c<sub>2</sub>) * c) * b) * (c<sub>2</sub>,A) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
b * (c<sub>2</sub>,A) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of c<sub>2</sub>,FF
((A,c<sub>2</sub>) * c) * (b * (c<sub>2</sub>,A)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
(A,c<sub>2</sub>) * (c * (id FF)) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,c<sub>2</sub>
((A,c<sub>2</sub>) * (c * (id FF))) * (b * (c<sub>2</sub>,A)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
((A,c<sub>2</sub>) * c) * (id FF) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,c<sub>2</sub>
(((A,c<sub>2</sub>) * c) * (id FF)) * (b * (c<sub>2</sub>,A)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
f * (FF,a) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,c<sub>2</sub>
(f * (FF,a)) * (b * (c<sub>2</sub>,A)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
(FF,a) * (b * (c<sub>2</sub>,A)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,a
f * ((FF,a) * (b * (c<sub>2</sub>,A))) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
((A,c<sub>2</sub>) * (id A)) * (c<sub>2</sub>,A) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of c<sub>2</sub>,c<sub>2</sub>
b * (id A) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,FF
the ObjectMap of b is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of FF, the carrier of FF:] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of FF, the carrier of FF:]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of FF, the carrier of FF:]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of FF, the carrier of FF:]:] is non empty set
the MorphMap of b is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() MSUnTrans of the ObjectMap of b, the Arrows of A, the Arrows of FF
FunctorStr(# the ObjectMap of b, the MorphMap of b #) is strict FunctorStr over A,FF
(FF,a) * (id FF) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,a
(c<sub>2</sub>,A) * (A,c<sub>2</sub>) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,A
(FF,a) * (b * c) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,a
((FF,a) * (b * c)) * (a,FF) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
((FF,a) * b) * c is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of FF,a
(((FF,a) * b) * c) * (a,FF) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
c * (a,FF) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of a,A
((FF,a) * b) * (c * (a,FF)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
(FF,a) * (b * (id A)) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,a
((FF,a) * (b * (id A))) * (c * (a,FF)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
((FF,a) * b) * (id A) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,a
(((FF,a) * b) * (id A)) * (c * (a,FF)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
d * (A,c<sub>2</sub>) is reflexive feasible strict Contravariant id-preserving comp-reversing contravariant Functor of A,a
(d * (A,c<sub>2</sub>)) * (c * (a,FF)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
(A,c<sub>2</sub>) * (c * (a,FF)) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,c<sub>2</sub>
d * ((A,c<sub>2</sub>) * (c * (a,FF))) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
((FF,a) * (id FF)) * (a,FF) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of a,a
FF is non empty transitive associative with_units reflexive AltCatStr
a is non empty transitive associative with_units reflexive AltCatStr
(a) is non empty transitive strict associative with_units reflexive AltCatStr
(FF) is non empty transitive strict associative with_units reflexive AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
(c<sub>2</sub>) is non empty transitive strict associative with_units reflexive AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
(FF) is non empty transitive strict associative with_units reflexive AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
(c<sub>2</sub>) is non empty transitive strict associative with_units reflexive AltCatStr
(FF) is non empty transitive strict associative with_units reflexive AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
c<sub>2</sub> is non empty transitive associative with_units reflexive AltCatStr
FF is non empty transitive associative with_units reflexive AltCatStr
(c<sub>2</sub>) is non empty transitive strict associative with_units reflexive AltCatStr
FF is set
A is set
c<sub>2</sub> is set
Funcs (A,c<sub>2</sub>) is functional set
proj1 FF is set
proj2 FF is set
a is Relation-like Function-like set
proj1 a is set
proj2 a is set
a is Relation-like Function-like set
proj1 a is set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one non empty V14( the carrier of A) quasi_total Element of bool [: the carrier of A, the carrier of A:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
bool [: the carrier of A, the carrier of A:] is non empty set
c<sub>2</sub> is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
c<sub>2</sub> . FF is set
c<sub>2</sub> . a is set
Funcs ((c<sub>2</sub> . FF),(c<sub>2</sub> . a)) is functional set
c<sub>2</sub> is set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
FF is Element of the carrier of A
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
b is Element of the carrier of A
a is set
idm b is retraction coretraction iso mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of A . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of A . [b,b] is set
proj1 (idm b) is set
b is Element of the carrier of A
FF is set
idm b is retraction coretraction iso mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of A . [b,b] is set
proj1 (idm b) is set
c is Element of the carrier of A
a is set
idm c is retraction coretraction iso mono epi Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of A . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of A . [c,c] is set
proj1 (idm c) is set
d is set
f is set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
(A,c<sub>2</sub>) is set
idm c<sub>2</sub> is retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,c<sub>2</sub>] is set
proj1 (idm c<sub>2</sub>) is set
FF is set
a is set
A is non empty set
EnsCat A is non empty transitive strict quasi-functional semi-functional pseudo-functional associative with_units reflexive () AltCatStr
the carrier of (EnsCat A) is non empty set
c<sub>2</sub> is Element of the carrier of (EnsCat A)
idm c<sub>2</sub> is retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of (EnsCat A) is Relation-like [: the carrier of (EnsCat A), the carrier of (EnsCat A):] -defined Function-like non empty V14([: the carrier of (EnsCat A), the carrier of (EnsCat A):]) set
[: the carrier of (EnsCat A), the carrier of (EnsCat A):] is Relation-like non empty set
the Arrows of (EnsCat A) . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of (EnsCat A) . [c<sub>2</sub>,c<sub>2</sub>] is set
id c<sub>2</sub> is Relation-like c<sub>2</sub> -defined c<sub>2</sub> -valued Function-like one-to-one V14(c<sub>2</sub>) quasi_total Element of bool [:c<sub>2</sub>,c<sub>2</sub>:]
[:c<sub>2</sub>,c<sub>2</sub>:] is Relation-like set
bool [:c<sub>2</sub>,c<sub>2</sub>:] is non empty set
Funcs (c<sub>2</sub>,c<sub>2</sub>) is functional non empty set
a is Element of the carrier of (EnsCat A)
<^c<sub>2</sub>,a^> is set
the Arrows of (EnsCat A) . (c<sub>2</sub>,a) is set
[c<sub>2</sub>,a] is V22() set
{c<sub>2</sub>,a} is non empty set
{{c<sub>2</sub>,a},{c<sub>2</sub>}} is non empty set
the Arrows of (EnsCat A) . [c<sub>2</sub>,a] is set
Funcs (c<sub>2</sub>,a) is functional set
b is Element of <^c<sub>2</sub>,a^>
c is Relation-like Function-like set
proj1 c is set
FF is Element of <^c<sub>2</sub>,c<sub>2</sub>^>
b * FF is Element of <^c<sub>2</sub>,a^>
(id c<sub>2</sub>) (#) c is Relation-like c<sub>2</sub> -defined Function-like set
A is non empty set
EnsCat A is non empty transitive strict quasi-functional semi-functional pseudo-functional associative with_units reflexive () AltCatStr
the carrier of (EnsCat A) is non empty set
c<sub>2</sub> is Element of the carrier of (EnsCat A)
((EnsCat A),c<sub>2</sub>) is set
idm c<sub>2</sub> is retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of (EnsCat A) is Relation-like [: the carrier of (EnsCat A), the carrier of (EnsCat A):] -defined Function-like non empty V14([: the carrier of (EnsCat A), the carrier of (EnsCat A):]) set
[: the carrier of (EnsCat A), the carrier of (EnsCat A):] is Relation-like non empty set
the Arrows of (EnsCat A) . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of (EnsCat A) . [c<sub>2</sub>,c<sub>2</sub>] is set
proj1 (idm c<sub>2</sub>) is set
id c<sub>2</sub> is Relation-like c<sub>2</sub> -defined c<sub>2</sub> -valued Function-like one-to-one V14(c<sub>2</sub>) quasi_total Element of bool [:c<sub>2</sub>,c<sub>2</sub>:]
[:c<sub>2</sub>,c<sub>2</sub>:] is Relation-like set
bool [:c<sub>2</sub>,c<sub>2</sub>:] is non empty set
proj1 (id c<sub>2</sub>) is set
A is non empty set
EnsCat A is non empty transitive strict quasi-functional semi-functional pseudo-functional associative with_units reflexive () AltCatStr
the carrier of (EnsCat A) is non empty set
c<sub>2</sub> is Element of the carrier of (EnsCat A)
idm c<sub>2</sub> is retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of (EnsCat A) is Relation-like [: the carrier of (EnsCat A), the carrier of (EnsCat A):] -defined Function-like non empty V14([: the carrier of (EnsCat A), the carrier of (EnsCat A):]) set
[: the carrier of (EnsCat A), the carrier of (EnsCat A):] is Relation-like non empty set
the Arrows of (EnsCat A) . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of (EnsCat A) . [c<sub>2</sub>,c<sub>2</sub>] is set
((EnsCat A),c<sub>2</sub>) is set
proj1 (idm c<sub>2</sub>) is set
id ((EnsCat A),c<sub>2</sub>) is Relation-like ((EnsCat A),c<sub>2</sub>) -defined ((EnsCat A),c<sub>2</sub>) -valued Function-like one-to-one V14(((EnsCat A),c<sub>2</sub>)) quasi_total Element of bool [:((EnsCat A),c<sub>2</sub>),((EnsCat A),c<sub>2</sub>):]
[:((EnsCat A),c<sub>2</sub>),((EnsCat A),c<sub>2</sub>):] is Relation-like set
bool [:((EnsCat A),c<sub>2</sub>),((EnsCat A),c<sub>2</sub>):] is non empty set
id c<sub>2</sub> is Relation-like c<sub>2</sub> -defined c<sub>2</sub> -valued Function-like one-to-one V14(c<sub>2</sub>) quasi_total Element of bool [:c<sub>2</sub>,c<sub>2</sub>:]
[:c<sub>2</sub>,c<sub>2</sub>:] is Relation-like set
bool [:c<sub>2</sub>,c<sub>2</sub>:] is non empty set
A is non empty transitive associative with_units reflexive AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
EnsCat NAT is non empty transitive strict quasi-functional semi-functional pseudo-functional associative with_units reflexive () () () AltCatStr
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
(A,FF) is set
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
(A,a) is set
idm a is retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of A . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of A . [a,a] is set
proj1 (idm a) is set
Funcs ((A,FF),(A,a)) is functional set
c<sub>2</sub> . FF is set
Funcs ((c<sub>2</sub> . FF),(c<sub>2</sub> . FF)) is functional non empty set
c<sub>2</sub> . a is set
Funcs ((c<sub>2</sub> . a),(c<sub>2</sub> . a)) is functional non empty set
b is Relation-like Function-like set
proj1 b is set
proj2 b is set
c is Relation-like Function-like set
proj1 c is set
proj2 c is set
c<sub>2</sub> is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
c<sub>2</sub> . FF is set
c<sub>2</sub> . a is set
Funcs ((c<sub>2</sub> . FF),(c<sub>2</sub> . a)) is functional set
(A,FF) is set
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
(A,a) is set
idm a is retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of A . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of A . [a,a] is set
proj1 (idm a) is set
A is non empty transitive associative with_units reflexive () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
(A,c<sub>2</sub>) is set
idm c<sub>2</sub> is retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of A . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,c<sub>2</sub>] is set
proj1 (idm c<sub>2</sub>) is set
(A,FF) is set
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
[:(A,c<sub>2</sub>),(A,FF):] is Relation-like set
bool [:(A,c<sub>2</sub>),(A,FF):] is non empty set
a is Element of <^c<sub>2</sub>,FF^>
Funcs ((A,c<sub>2</sub>),(A,FF)) is functional set
A is non empty transitive associative with_units reflexive () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
a is Element of <^c<sub>2</sub>,FF^>
A is non empty transitive associative with_units reflexive () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
(A,c<sub>2</sub>) is set
idm c<sub>2</sub> is Relation-like Function-like retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of A . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,c<sub>2</sub>] is set
proj1 (idm c<sub>2</sub>) is set
(A,FF) is set
idm FF is Relation-like Function-like retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
a is Relation-like Function-like Element of <^c<sub>2</sub>,FF^>
proj1 a is set
proj2 a is set
Funcs ((A,c<sub>2</sub>),(A,FF)) is functional set
A is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
b is Relation-like Function-like Element of <^c<sub>2</sub>,FF^>
c is Relation-like Function-like Element of <^FF,a^>
c * b is Relation-like Function-like Element of <^c<sub>2</sub>,a^>
<^c<sub>2</sub>,a^> is set
the Arrows of A . (c<sub>2</sub>,a) is set
[c<sub>2</sub>,a] is V22() set
{c<sub>2</sub>,a} is non empty set
{{c<sub>2</sub>,a},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,a] is set
b (#) c is Relation-like Function-like set
A is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
(A,c<sub>2</sub>) is set
idm c<sub>2</sub> is Relation-like Function-like retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,c<sub>2</sub>] is set
proj1 (idm c<sub>2</sub>) is set
id (A,c<sub>2</sub>) is Relation-like (A,c<sub>2</sub>) -defined (A,c<sub>2</sub>) -valued Function-like one-to-one V14((A,c<sub>2</sub>)) quasi_total Element of bool [:(A,c<sub>2</sub>),(A,c<sub>2</sub>):]
[:(A,c<sub>2</sub>),(A,c<sub>2</sub>):] is Relation-like set
bool [:(A,c<sub>2</sub>),(A,c<sub>2</sub>):] is non empty set
a is Element of the carrier of A
<^c<sub>2</sub>,a^> is set
the Arrows of A . (c<sub>2</sub>,a) is set
[c<sub>2</sub>,a] is V22() set
{c<sub>2</sub>,a} is non empty set
{{c<sub>2</sub>,a},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,a] is set
b is Relation-like Function-like Element of <^c<sub>2</sub>,a^>
proj1 b is set
FF is Relation-like Function-like Element of <^c<sub>2</sub>,c<sub>2</sub>^>
b * FF is Relation-like Function-like Element of <^c<sub>2</sub>,a^>
(id (A,c<sub>2</sub>)) (#) b is Relation-like (A,c<sub>2</sub>) -defined Function-like set
F<sub>1</sub>() is non empty set
FF is set
A is Element of F<sub>1</sub>()
c<sub>2</sub> is Element of F<sub>1</sub>()
F<sub>2</sub>(A,c<sub>2</sub>) is set
F<sub>3</sub>(A) is set
F<sub>3</sub>(c<sub>2</sub>) is set
Funcs (F<sub>3</sub>(A),F<sub>3</sub>(c<sub>2</sub>)) is functional set
A is Element of F<sub>1</sub>()
c<sub>2</sub> is Element of F<sub>1</sub>()
F<sub>2</sub>(A,c<sub>2</sub>) is set
FF is Element of F<sub>1</sub>()
F<sub>2</sub>(c<sub>2</sub>,FF) is set
F<sub>2</sub>(A,FF) is set
a is set
b is set
a (#) b is Relation-like set
c is Relation-like Function-like set
d is Relation-like Function-like set
c (#) d is Relation-like Function-like set
A is Element of F<sub>1</sub>()
c<sub>2</sub> is Element of F<sub>1</sub>()
F<sub>2</sub>(A,c<sub>2</sub>) is set
FF is Element of F<sub>1</sub>()
F<sub>2</sub>(c<sub>2</sub>,FF) is set
a is Element of F<sub>1</sub>()
F<sub>2</sub>(FF,a) is set
b is set
c is set
d is set
b (#) c is Relation-like set
H<sub>1</sub>(A,c<sub>2</sub>,FF,b,c) (#) d is Relation-like set
c (#) d is Relation-like set
b (#) H<sub>1</sub>(c<sub>2</sub>,FF,a,c,d) is Relation-like set
f is Relation-like Function-like set
fa is Relation-like Function-like set
f (#) fa is Relation-like Function-like set
fb is Relation-like Function-like set
(f (#) fa) (#) fb is Relation-like Function-like set
fa (#) fb is Relation-like Function-like set
f (#) (fa (#) fb) is Relation-like Function-like set
A is Element of F<sub>1</sub>()
F<sub>2</sub>(A,A) is set
F<sub>3</sub>(A) is set
[:F<sub>3</sub>(A),F<sub>3</sub>(A):] is Relation-like set
bool [:F<sub>3</sub>(A),F<sub>3</sub>(A):] is non empty set
id F<sub>3</sub>(A) is Relation-like F<sub>3</sub>(A) -defined F<sub>3</sub>(A) -valued Function-like one-to-one V14(F<sub>3</sub>(A)) quasi_total Element of bool [:F<sub>3</sub>(A),F<sub>3</sub>(A):]
c<sub>2</sub> is Relation-like F<sub>3</sub>(A) -defined F<sub>3</sub>(A) -valued Function-like one-to-one V14(F<sub>3</sub>(A)) quasi_total Element of bool [:F<sub>3</sub>(A),F<sub>3</sub>(A):]
FF is Element of F<sub>1</sub>()
F<sub>2</sub>(A,FF) is set
a is set
c<sub>2</sub> (#) a is Relation-like set
F<sub>3</sub>(FF) is set
Funcs (F<sub>3</sub>(A),F<sub>3</sub>(FF)) is functional set
b is Relation-like Function-like set
proj1 b is set
proj2 b is set
A is Element of F<sub>1</sub>()
F<sub>2</sub>(A,A) is set
F<sub>3</sub>(A) is set
[:F<sub>3</sub>(A),F<sub>3</sub>(A):] is Relation-like set
bool [:F<sub>3</sub>(A),F<sub>3</sub>(A):] is non empty set
id F<sub>3</sub>(A) is Relation-like F<sub>3</sub>(A) -defined F<sub>3</sub>(A) -valued Function-like one-to-one V14(F<sub>3</sub>(A)) quasi_total Element of bool [:F<sub>3</sub>(A),F<sub>3</sub>(A):]
c<sub>2</sub> is Relation-like F<sub>3</sub>(A) -defined F<sub>3</sub>(A) -valued Function-like one-to-one V14(F<sub>3</sub>(A)) quasi_total Element of bool [:F<sub>3</sub>(A),F<sub>3</sub>(A):]
FF is Element of F<sub>1</sub>()
F<sub>2</sub>(FF,A) is set
a is set
a (#) c<sub>2</sub> is Relation-like set
F<sub>3</sub>(FF) is set
Funcs (F<sub>3</sub>(FF),F<sub>3</sub>(A)) is functional set
b is Relation-like Function-like set
proj1 b is set
proj2 b is set
A is non empty transitive strict associative with_units reflexive AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Relation-like the carrier of A -defined Function-like non empty V14( the carrier of A) set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
c<sub>2</sub> . FF is set
c<sub>2</sub> . a is set
Funcs ((c<sub>2</sub> . FF),(c<sub>2</sub> . a)) is functional set
F<sub>2</sub>(FF,a) is set
F<sub>3</sub>(FF) is set
F<sub>3</sub>(a) is set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
b is Element of the carrier of A
<^a,b^> is set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
<^FF,b^> is set
the Arrows of A . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of A . [FF,b] is set
c is Element of <^FF,a^>
d is Element of <^a,b^>
d * c is Element of <^FF,b^>
f is Relation-like Function-like set
fa is Relation-like Function-like set
f (#) fa is Relation-like Function-like set
FF is Element of the carrier of A
F<sub>3</sub>(FF) is set
id F<sub>3</sub>(FF) is Relation-like F<sub>3</sub>(FF) -defined F<sub>3</sub>(FF) -valued Function-like one-to-one V14(F<sub>3</sub>(FF)) quasi_total Element of bool [:F<sub>3</sub>(FF),F<sub>3</sub>(FF):]
[:F<sub>3</sub>(FF),F<sub>3</sub>(FF):] is Relation-like set
bool [:F<sub>3</sub>(FF),F<sub>3</sub>(FF):] is non empty set
F<sub>2</sub>(FF,FF) is set
<^FF,FF^> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
b is Element of the carrier of A
<^FF,b^> is set
the Arrows of A . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of A . [FF,b] is set
F<sub>2</sub>(FF,b) is set
F<sub>3</sub>(b) is set
Funcs (F<sub>3</sub>(FF),F<sub>3</sub>(b)) is functional set
c is Element of <^FF,b^>
d is Relation-like Function-like set
proj1 d is set
proj2 d is set
a is Element of <^FF,FF^>
c * a is Element of <^FF,b^>
(id F<sub>3</sub>(FF)) (#) d is Relation-like F<sub>3</sub>(FF) -defined Function-like set
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
FF is set
(A,FF) is set
a is Element of the carrier of A
idm a is retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of A . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of A . [a,a] is set
proj1 (idm a) is set
F<sub>3</sub>(a) is set
id F<sub>3</sub>(a) is Relation-like F<sub>3</sub>(a) -defined F<sub>3</sub>(a) -valued Function-like one-to-one V14(F<sub>3</sub>(a)) quasi_total Element of bool [:F<sub>3</sub>(a),F<sub>3</sub>(a):]
[:F<sub>3</sub>(a),F<sub>3</sub>(a):] is Relation-like set
bool [:F<sub>3</sub>(a),F<sub>3</sub>(a):] is non empty set
proj1 (id F<sub>3</sub>(a)) is set
c<sub>2</sub> . FF is set
FF is Element of the carrier of A
idm FF is retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
(A,FF) is set
proj1 (idm FF) is set
id (A,FF) is Relation-like (A,FF) -defined (A,FF) -valued Function-like one-to-one V14((A,FF)) quasi_total Element of bool [:(A,FF),(A,FF):]
[:(A,FF),(A,FF):] is Relation-like set
bool [:(A,FF),(A,FF):] is non empty set
F<sub>3</sub>(FF) is set
id F<sub>3</sub>(FF) is Relation-like F<sub>3</sub>(FF) -defined F<sub>3</sub>(FF) -valued Function-like one-to-one V14(F<sub>3</sub>(FF)) quasi_total Element of bool [:F<sub>3</sub>(FF),F<sub>3</sub>(FF):]
[:F<sub>3</sub>(FF),F<sub>3</sub>(FF):] is Relation-like set
bool [:F<sub>3</sub>(FF),F<sub>3</sub>(FF):] is non empty set
c<sub>2</sub> . FF is set
id (c<sub>2</sub> . FF) is Relation-like c<sub>2</sub> . FF -defined c<sub>2</sub> . FF -valued Function-like one-to-one V14(c<sub>2</sub> . FF) quasi_total Element of bool [:(c<sub>2</sub> . FF),(c<sub>2</sub> . FF):]
[:(c<sub>2</sub> . FF),(c<sub>2</sub> . FF):] is Relation-like set
bool [:(c<sub>2</sub> . FF),(c<sub>2</sub> . FF):] is non empty set
FF is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
the carrier of FF is non empty set
a is Element of the carrier of FF
(FF,a) is set
idm a is Relation-like Function-like retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
the Arrows of FF . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of FF . [a,a] is set
proj1 (idm a) is set
c<sub>2</sub> . a is set
F<sub>3</sub>(a) is set
a is Element of the carrier of FF
b is Element of the carrier of FF
<^a,b^> is set
the Arrows of FF . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of FF . [a,b] is set
F<sub>2</sub>(a,b) is set
F<sub>1</sub>() is non empty set
c<sub>2</sub> is set
[:F<sub>1</sub>(),F<sub>1</sub>():] is Relation-like non empty set
FF is set
a is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
F<sub>2</sub>(FF) is set
F<sub>2</sub>(a) is set
Funcs (F<sub>2</sub>(FF),F<sub>2</sub>(a)) is functional set
b is set
c is set
c<sub>2</sub> is Relation-like Function-like set
proj1 c<sub>2</sub> is set
FF is set
a is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
c<sub>2</sub> . [FF,a] is set
b is set
c is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
F<sub>2</sub>(b) is set
F<sub>2</sub>(c) is set
Funcs (F<sub>2</sub>(b),F<sub>2</sub>(c)) is functional set
d is set
F<sub>2</sub>(FF) is set
F<sub>2</sub>(a) is set
Funcs (F<sub>2</sub>(FF),F<sub>2</sub>(a)) is functional set
c is Relation-like Function-like set
FF is Element of F<sub>1</sub>()
a is Element of F<sub>1</sub>()
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
c<sub>2</sub> . [FF,a] is set
d is Relation-like Function-like set
b is Element of F<sub>1</sub>()
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
c<sub>2</sub> . [a,b] is set
F<sub>2</sub>(FF) is set
F<sub>2</sub>(a) is set
Funcs (F<sub>2</sub>(FF),F<sub>2</sub>(a)) is functional set
F<sub>2</sub>(b) is set
Funcs (F<sub>2</sub>(a),F<sub>2</sub>(b)) is functional set
proj1 c is set
proj2 c is set
proj1 d is set
proj2 d is set
c (#) d is Relation-like Function-like set
proj2 (c (#) d) is set
proj1 (c (#) d) is set
Funcs (F<sub>2</sub>(FF),F<sub>2</sub>(b)) is functional set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
c<sub>2</sub> . [FF,b] is set
FF is Element of F<sub>1</sub>()
a is Element of F<sub>1</sub>()
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
c<sub>2</sub> . [FF,a] is set
F<sub>2</sub>(FF) is set
F<sub>2</sub>(a) is set
Funcs (F<sub>2</sub>(FF),F<sub>2</sub>(a)) is functional set
b is set
FF is Element of F<sub>1</sub>()
F<sub>2</sub>(FF) is set
id F<sub>2</sub>(FF) is Relation-like F<sub>2</sub>(FF) -defined F<sub>2</sub>(FF) -valued Function-like one-to-one V14(F<sub>2</sub>(FF)) quasi_total Element of bool [:F<sub>2</sub>(FF),F<sub>2</sub>(FF):]
[:F<sub>2</sub>(FF),F<sub>2</sub>(FF):] is Relation-like set
bool [:F<sub>2</sub>(FF),F<sub>2</sub>(FF):] is non empty set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
c<sub>2</sub> . [FF,FF] is set
dom (id F<sub>2</sub>(FF)) is Element of bool F<sub>2</sub>(FF)
bool F<sub>2</sub>(FF) is non empty set
proj2 (id F<sub>2</sub>(FF)) is set
Funcs (F<sub>2</sub>(FF),F<sub>2</sub>(FF)) is functional non empty set
FF is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
the carrier of FF is non empty set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
a is Element of the carrier of FF
(FF,a) is set
idm a is Relation-like Function-like retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of FF . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of FF . [a,a] is set
proj1 (idm a) is set
F<sub>2</sub>(a) is set
a is Element of F<sub>1</sub>()
b is Element of F<sub>1</sub>()
the Arrows of FF . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of FF . [a,b] is set
F<sub>2</sub>(a) is set
F<sub>2</sub>(b) is set
Funcs (F<sub>2</sub>(a),F<sub>2</sub>(b)) is functional set
c is Relation-like Function-like set
d is Element of the carrier of FF
f is Element of the carrier of FF
the Arrows of FF . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of FF . [d,f] is set
<^d,f^> is set
c<sub>2</sub> . [d,f] is set
F<sub>1</sub>() is non empty set
A is Element of F<sub>1</sub>()
c<sub>2</sub> is Element of F<sub>1</sub>()
a is Relation-like Function-like set
FF is Element of F<sub>1</sub>()
b is Relation-like Function-like set
a (#) b is Relation-like Function-like set
A is Relation-like Function-like set
proj1 A is set
c<sub>2</sub> is Element of F<sub>1</sub>()
A . c<sub>2</sub> is set
F<sub>2</sub>(c<sub>2</sub>) is set
FF is set
a is set
id H<sub>1</sub>(c<sub>2</sub>) is Relation-like H<sub>1</sub>(c<sub>2</sub>) -defined H<sub>1</sub>(c<sub>2</sub>) -valued Function-like one-to-one V14(H<sub>1</sub>(c<sub>2</sub>)) quasi_total Element of bool [:H<sub>1</sub>(c<sub>2</sub>),H<sub>1</sub>(c<sub>2</sub>):]
[:H<sub>1</sub>(c<sub>2</sub>),H<sub>1</sub>(c<sub>2</sub>):] is Relation-like set
bool [:H<sub>1</sub>(c<sub>2</sub>),H<sub>1</sub>(c<sub>2</sub>):] is non empty set
c<sub>2</sub> is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
the carrier of c<sub>2</sub> is non empty set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
FF is Element of the carrier of c<sub>2</sub>
(c<sub>2</sub>,FF) is set
idm FF is Relation-like Function-like retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of c<sub>2</sub> . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,FF] is set
proj1 (idm FF) is set
A . FF is set
F<sub>2</sub>(FF) is set
a is set
b is set
FF is Element of F<sub>1</sub>()
a is Element of F<sub>1</sub>()
the Arrows of c<sub>2</sub> . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,a] is set
(c<sub>2</sub>,FF) is set
(c<sub>2</sub>,a) is set
Funcs ((c<sub>2</sub>,FF),(c<sub>2</sub>,a)) is functional set
A . FF is set
A . a is set
b is Relation-like Function-like set
c is Relation-like Function-like set
F<sub>1</sub>() is non empty set
A is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of c<sub>2</sub> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
AltCatStr(# the carrier of A, the Arrows of A, the Comp of A #) is non empty strict AltCatStr
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Comp of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|},{| the Arrows of c<sub>2</sub>|}
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
{| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
{| the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
AltCatStr(# the carrier of c<sub>2</sub>, the Arrows of c<sub>2</sub>, the Comp of c<sub>2</sub> #) is non empty strict AltCatStr
FF is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of FF is non empty set
a is Element of the carrier of FF
b is Element of the carrier of FF
<^a,b^> is set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
the Arrows of FF . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of FF . [a,b] is set
c is Element of the carrier of FF
<^b,c^> is set
the Arrows of FF . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of FF . [b,c] is set
d is Relation-like Function-like Element of <^a,b^>
f is Relation-like Function-like Element of <^b,c^>
f * d is Relation-like Function-like Element of <^a,c^>
<^a,c^> is set
the Arrows of FF . (a,c) is set
[a,c] is V22() set
{a,c} is non empty set
{{a,c},{a}} is non empty set
the Arrows of FF . [a,c] is set
d (#) f is Relation-like Function-like set
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
b is Element of the carrier of A
<^a,b^> is set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
c is Relation-like Function-like Element of <^FF,a^>
d is Relation-like Function-like Element of <^a,b^>
d * c is Relation-like Function-like Element of <^FF,b^>
<^FF,b^> is set
the Arrows of A . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of A . [FF,b] is set
c (#) d is Relation-like Function-like set
FF is Element of the carrier of c<sub>2</sub>
a is Element of the carrier of c<sub>2</sub>
<^FF,a^> is set
the Arrows of c<sub>2</sub> . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,a] is set
b is Element of the carrier of c<sub>2</sub>
<^a,b^> is set
the Arrows of c<sub>2</sub> . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of c<sub>2</sub> . [a,b] is set
c is Relation-like Function-like Element of <^FF,a^>
d is Relation-like Function-like Element of <^a,b^>
d * c is Relation-like Function-like Element of <^FF,b^>
<^FF,b^> is set
the Arrows of c<sub>2</sub> . (FF,b) is set
[FF,b] is V22() set
{FF,b} is non empty set
{{FF,b},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,b] is set
c (#) d is Relation-like Function-like set
F<sub>1</sub>() is non empty set
A is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of A is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
c<sub>2</sub> is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of c<sub>2</sub> is non empty set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
AltCatStr(# the carrier of A, the Arrows of A, the Comp of A #) is non empty strict AltCatStr
the Comp of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|},{| the Arrows of c<sub>2</sub>|}
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
{| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
{| the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
AltCatStr(# the carrier of c<sub>2</sub>, the Arrows of c<sub>2</sub>, the Comp of c<sub>2</sub> #) is non empty strict AltCatStr
FF is Element of the carrier of A
a is Element of the carrier of A
<^FF,a^> is set
the Arrows of A . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of A . [FF,a] is set
FF is Element of the carrier of c<sub>2</sub>
a is Element of the carrier of c<sub>2</sub>
b is Element of F<sub>1</sub>()
c is Element of F<sub>1</sub>()
<^FF,a^> is set
the Arrows of c<sub>2</sub> . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,a] is set
the Arrows of A . (FF,a) is set
the Arrows of A . [FF,a] is set
fa is set
F<sub>2</sub>(b) is set
F<sub>2</sub>(c) is set
Funcs (F<sub>2</sub>(b),F<sub>2</sub>(c)) is functional set
fa is set
d is Element of the carrier of A
f is Element of the carrier of A
<^d,f^> is set
the Arrows of A . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of A . [d,f] is set
F<sub>1</sub>() is non empty set
A is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of A is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
c<sub>2</sub> is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of c<sub>2</sub> is non empty set
the Arrows of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is Relation-like non empty set
the Comp of A is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of {| the Arrows of A, the Arrows of A|},{| the Arrows of A|}
[: the carrier of A, the carrier of A, the carrier of A:] is non empty set
{| the Arrows of A, the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
{| the Arrows of A|} is Relation-like [: the carrier of A, the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A, the carrier of A:]) set
AltCatStr(# the carrier of A, the Arrows of A, the Comp of A #) is non empty strict AltCatStr
the Comp of c<sub>2</sub> is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) Function-yielding V63() ManySortedFunction of {| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|},{| the Arrows of c<sub>2</sub>|}
[: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] is non empty set
{| the Arrows of c<sub>2</sub>, the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
{| the Arrows of c<sub>2</sub>|} is Relation-like [: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:] -defined Function-like non empty V14([: the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>, the carrier of c<sub>2</sub>:]) set
AltCatStr(# the carrier of c<sub>2</sub>, the Arrows of c<sub>2</sub>, the Comp of c<sub>2</sub> #) is non empty strict AltCatStr
FF is Element of F<sub>1</sub>()
c is set
a is Element of the carrier of A
(A,a) is set
idm a is Relation-like Function-like retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of A . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of A . [a,a] is set
proj1 (idm a) is set
F<sub>2</sub>(FF) is set
b is Element of the carrier of c<sub>2</sub>
(c<sub>2</sub>,b) is set
idm b is Relation-like Function-like retraction coretraction iso mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of c<sub>2</sub> . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of c<sub>2</sub> . [b,b] is set
proj1 (idm b) is set
(A,FF) is set
(c<sub>2</sub>,FF) is set
FF is Element of F<sub>1</sub>()
(A,FF) is set
(c<sub>2</sub>,FF) is set
a is Element of F<sub>1</sub>()
(A,a) is set
(c<sub>2</sub>,a) is set
b is Relation-like Function-like set
the Arrows of c<sub>2</sub> . (FF,a) is set
[FF,a] is V22() set
{FF,a} is non empty set
{FF} is non empty set
{{FF,a},{FF}} is non empty set
the Arrows of c<sub>2</sub> . [FF,a] is set
Funcs (H<sub>1</sub>(FF),H<sub>1</sub>(a)) is functional set
A is non empty transitive semi-functional associative with_units reflexive () () () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
<^FF,c<sub>2</sub>^> is set
the Arrows of A . (FF,c<sub>2</sub>) is set
[FF,c<sub>2</sub>] is V22() set
{FF,c<sub>2</sub>} is non empty set
{FF} is non empty set
{{FF,c<sub>2</sub>},{FF}} is non empty set
the Arrows of A . [FF,c<sub>2</sub>] is set
(A,FF) is set
idm FF is Relation-like Function-like retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
a is Relation-like Function-like Element of <^c<sub>2</sub>,FF^>
proj2 a is set
b is Relation-like Function-like Element of <^FF,c<sub>2</sub>^>
a * b is Relation-like Function-like Element of <^FF,FF^>
b (#) a is Relation-like Function-like set
(A,c<sub>2</sub>) is set
idm c<sub>2</sub> is Relation-like Function-like retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of A . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,c<sub>2</sub>] is set
proj1 (idm c<sub>2</sub>) is set
[:(A,c<sub>2</sub>),(A,FF):] is Relation-like set
bool [:(A,c<sub>2</sub>),(A,FF):] is non empty set
[:(A,FF),(A,c<sub>2</sub>):] is Relation-like set
bool [:(A,FF),(A,c<sub>2</sub>):] is non empty set
id (A,FF) is Relation-like (A,FF) -defined (A,FF) -valued Function-like one-to-one V14((A,FF)) quasi_total Element of bool [:(A,FF),(A,FF):]
[:(A,FF),(A,FF):] is Relation-like set
bool [:(A,FF),(A,FF):] is non empty set
A is non empty transitive semi-functional associative with_units reflexive () () () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
<^FF,c<sub>2</sub>^> is set
the Arrows of A . (FF,c<sub>2</sub>) is set
[FF,c<sub>2</sub>] is V22() set
{FF,c<sub>2</sub>} is non empty set
{FF} is non empty set
{{FF,c<sub>2</sub>},{FF}} is non empty set
the Arrows of A . [FF,c<sub>2</sub>] is set
a is Relation-like Function-like Element of <^c<sub>2</sub>,FF^>
b is Relation-like Function-like Element of <^FF,c<sub>2</sub>^>
b * a is Relation-like Function-like Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of A . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,c<sub>2</sub>] is set
idm c<sub>2</sub> is Relation-like Function-like retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
a (#) b is Relation-like Function-like set
proj1 a is set
(A,c<sub>2</sub>) is set
proj1 (idm c<sub>2</sub>) is set
id (A,c<sub>2</sub>) is Relation-like (A,c<sub>2</sub>) -defined (A,c<sub>2</sub>) -valued Function-like one-to-one V14((A,c<sub>2</sub>)) quasi_total Element of bool [:(A,c<sub>2</sub>),(A,c<sub>2</sub>):]
[:(A,c<sub>2</sub>),(A,c<sub>2</sub>):] is Relation-like set
bool [:(A,c<sub>2</sub>),(A,c<sub>2</sub>):] is non empty set
A is non empty transitive semi-functional associative with_units reflexive () () () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
<^FF,c<sub>2</sub>^> is set
the Arrows of A . (FF,c<sub>2</sub>) is set
[FF,c<sub>2</sub>] is V22() set
{FF,c<sub>2</sub>} is non empty set
{FF} is non empty set
{{FF,c<sub>2</sub>},{FF}} is non empty set
the Arrows of A . [FF,c<sub>2</sub>] is set
(A,FF) is set
idm FF is Relation-like Function-like retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
a is Relation-like Function-like Element of <^c<sub>2</sub>,FF^>
proj2 a is set
A is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
<^FF,c<sub>2</sub>^> is set
the Arrows of A . (FF,c<sub>2</sub>) is set
[FF,c<sub>2</sub>] is V22() set
{FF,c<sub>2</sub>} is non empty set
{FF} is non empty set
{{FF,c<sub>2</sub>},{FF}} is non empty set
the Arrows of A . [FF,c<sub>2</sub>] is set
a is Relation-like Function-like Element of <^c<sub>2</sub>,FF^>
a " is Relation-like Function-like set
b is Relation-like Function-like Element of <^FF,c<sub>2</sub>^>
proj1 b is set
(A,FF) is set
idm FF is Relation-like Function-like retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
proj2 a is set
a (#) (a ") is Relation-like Function-like set
proj1 a is set
id (proj1 a) is Relation-like proj1 a -defined proj1 a -valued Function-like one-to-one V14( proj1 a) quasi_total Element of bool [:(proj1 a),(proj1 a):]
[:(proj1 a),(proj1 a):] is Relation-like set
bool [:(proj1 a),(proj1 a):] is non empty set
(a ") (#) a is Relation-like Function-like set
id (proj2 a) is Relation-like proj2 a -defined proj2 a -valued Function-like one-to-one V14( proj2 a) quasi_total Element of bool [:(proj2 a),(proj2 a):]
[:(proj2 a),(proj2 a):] is Relation-like set
bool [:(proj2 a),(proj2 a):] is non empty set
(A,c<sub>2</sub>) is set
idm c<sub>2</sub> is Relation-like Function-like retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of A . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,c<sub>2</sub>] is set
proj1 (idm c<sub>2</sub>) is set
a * b is Relation-like Function-like Element of <^FF,FF^>
id (A,FF) is Relation-like (A,FF) -defined (A,FF) -valued Function-like one-to-one V14((A,FF)) quasi_total Element of bool [:(A,FF),(A,FF):]
[:(A,FF),(A,FF):] is Relation-like set
bool [:(A,FF),(A,FF):] is non empty set
b * a is Relation-like Function-like Element of <^c<sub>2</sub>,c<sub>2</sub>^>
id (A,c<sub>2</sub>) is Relation-like (A,c<sub>2</sub>) -defined (A,c<sub>2</sub>) -valued Function-like one-to-one V14((A,c<sub>2</sub>)) quasi_total Element of bool [:(A,c<sub>2</sub>),(A,c<sub>2</sub>):]
[:(A,c<sub>2</sub>),(A,c<sub>2</sub>):] is Relation-like set
bool [:(A,c<sub>2</sub>),(A,c<sub>2</sub>):] is non empty set
a " is Relation-like Function-like Element of <^FF,c<sub>2</sub>^>
a * (a ") is Relation-like Function-like Element of <^FF,FF^>
(a ") * a is Relation-like Function-like Element of <^c<sub>2</sub>,c<sub>2</sub>^>
A is non empty transitive semi-functional associative with_units reflexive () () () AltCatStr
the carrier of A is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
<^c<sub>2</sub>,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c<sub>2</sub>,FF) is set
[c<sub>2</sub>,FF] is V22() set
{c<sub>2</sub>,FF} is non empty set
{c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,FF},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,FF] is set
<^FF,c<sub>2</sub>^> is set
the Arrows of A . (FF,c<sub>2</sub>) is set
[FF,c<sub>2</sub>] is V22() set
{FF,c<sub>2</sub>} is non empty set
{FF} is non empty set
{{FF,c<sub>2</sub>},{FF}} is non empty set
the Arrows of A . [FF,c<sub>2</sub>] is set
a is Relation-like Function-like Element of <^c<sub>2</sub>,FF^>
a " is Relation-like Function-like Element of <^FF,c<sub>2</sub>^>
a " is Relation-like Function-like set
(a ") * a is Relation-like Function-like Element of <^c<sub>2</sub>,c<sub>2</sub>^>
<^c<sub>2</sub>,c<sub>2</sub>^> is non empty set
the Arrows of A . (c<sub>2</sub>,c<sub>2</sub>) is set
[c<sub>2</sub>,c<sub>2</sub>] is V22() set
{c<sub>2</sub>,c<sub>2</sub>} is non empty set
{{c<sub>2</sub>,c<sub>2</sub>},{c<sub>2</sub>}} is non empty set
the Arrows of A . [c<sub>2</sub>,c<sub>2</sub>] is set
idm c<sub>2</sub> is Relation-like Function-like retraction coretraction iso mono epi Element of <^c<sub>2</sub>,c<sub>2</sub>^>
a (#) (a ") is Relation-like Function-like set
proj1 (a ") is set
(A,FF) is set
idm FF is Relation-like Function-like retraction coretraction iso mono epi Element of <^FF,FF^>
<^FF,FF^> is non empty set
the Arrows of A . (FF,FF) is set
[FF,FF] is V22() set
{FF,FF} is non empty set
{{FF,FF},{FF}} is non empty set
the Arrows of A . [FF,FF] is set
proj1 (idm FF) is set
proj1 a is set
(A,c<sub>2</sub>) is set
proj1 (idm c<sub>2</sub>) is set
proj2 a is set
id (A,c<sub>2</sub>) is Relation-like (A,c<sub>2</sub>) -defined (A,c<sub>2</sub>) -valued Function-like one-to-one V14((A,c<sub>2</sub>)) quasi_total Element of bool [:(A,c<sub>2</sub>),(A,c<sub>2</sub>):]
[:(A,c<sub>2</sub>),(A,c<sub>2</sub>):] is Relation-like set
bool [:(A,c<sub>2</sub>),(A,c<sub>2</sub>):] is non empty set
F<sub>1</sub>() is non empty transitive semi-functional associative with_units reflexive () AltCatStr
F<sub>2</sub>() is non empty transitive semi-functional associative with_units reflexive () AltCatStr
the carrier of F<sub>1</sub>() is non empty set
the carrier of F<sub>2</sub>() is non empty set
A is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
A is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>2</sub>()
c<sub>2</sub> is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>2</sub>(),F<sub>1</sub>()
c<sub>2</sub> is reflexive feasible Covariant id-preserving comp-preserving covariant Functor of F<sub>2</sub>(),F<sub>1</sub>()
id F<sub>1</sub>() is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of F<sub>1</sub>(),F<sub>1</sub>()
id F<sub>2</sub>() is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of F<sub>2</sub>(),F<sub>2</sub>()
c<sub>2</sub> * A is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F<sub>1</sub>(),F<sub>1</sub>()
A * c<sub>2</sub> is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of F<sub>2</sub>(),F<sub>2</sub>()
b is Element of the carrier of F<sub>1</sub>()
F<sub>7</sub>(b) is Relation-like Function-like set
(c<sub>2</sub> * A) . b is Element of the carrier of F<sub>1</sub>()
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
the ObjectMap of (c<sub>2</sub> * A) is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:]
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is non empty set
the ObjectMap of (c<sub>2</sub> * A) . (b,b) is Element of [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of (c<sub>2</sub> * A) . [b,b] is set
( the ObjectMap of (c<sub>2</sub> * A) . (b,b)) `1 is set
(id F₁()) . b is Element of the carrier of F₁()
the ObjectMap of (id F₁()) is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₁(), the carrier of F₁():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₁(), the carrier of F₁():]:]
the ObjectMap of (id F₁()) . (b,b) is Element of [: the carrier of F₁(), the carrier of F₁():]
the ObjectMap of (id F₁()) . [b,b] is set
( the ObjectMap of (id F₁()) . (b,b)) `1 is set
<^((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
the Arrows of F<sub>1</sub>() . (((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)) is set
[((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)] is V22() set
{((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)} is non empty set
{((c<sub>2</sub> * A) . b)} is non empty set
{{((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)},{((c<sub>2</sub> * A) . b)}} is non empty set
the Arrows of F<sub>1</sub>() . [((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)] is set
<^((id F<sub>1</sub>()) . b),((c<sub>2</sub> * A) . b)^> is set
the Arrows of F<sub>1</sub>() . (((id F<sub>1</sub>()) . b),((c<sub>2</sub> * A) . b)) is set
[((id F<sub>1</sub>()) . b),((c<sub>2</sub> * A) . b)] is V22() set
{((id F<sub>1</sub>()) . b),((c<sub>2</sub> * A) . b)} is non empty set
{((id F<sub>1</sub>()) . b)} is non empty set
{{((id F<sub>1</sub>()) . b),((c<sub>2</sub> * A) . b)},{((id F<sub>1</sub>()) . b)}} is non empty set
the Arrows of F<sub>1</sub>() . [((id F<sub>1</sub>()) . b),((c<sub>2</sub> * A) . b)] is set
A . b is Element of the carrier of F<sub>2</sub>()
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of A is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of A . (b,b) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
the ObjectMap of A . [b,b] is set
( the ObjectMap of A . (b,b)) `1 is set
c₂ . (A . b) is Element of the carrier of F₁()
the ObjectMap of c₂ is Relation-like [: the carrier of F₂(), the carrier of F₂():] -defined [: the carrier of F₁(), the carrier of F₁():] -valued Function-like non empty V14([: the carrier of F₂(), the carrier of F₂():]) quasi_total Element of bool [:[: the carrier of F₂(), the carrier of F₂():],[: the carrier of F₁(), the carrier of F₁():]:]
[:[: the carrier of F₂(), the carrier of F₂():],[: the carrier of F₁(), the carrier of F₁():]:] is Relation-like non empty set
bool [:[: the carrier of F₂(), the carrier of F₂():],[: the carrier of F₁(), the carrier of F₁():]:] is non empty set
the ObjectMap of c₂ . ((A . b),(A . b)) is Element of [: the carrier of F₁(), the carrier of F₁():]
[(A . b),(A . b)] is V22() set
{(A . b),(A . b)} is non empty set
{(A . b)} is non empty set
{{(A . b),(A . b)},{(A . b)}} is non empty set
the ObjectMap of c₂ . [(A . b),(A . b)] is set
( the ObjectMap of c₂ . ((A . b),(A . b))) `1 is set
F<sub>4</sub>((A . b)) is set
F<sub>3</sub>(b) is set
F<sub>4</sub>(F<sub>3</sub>(b)) is set
F<sub>7</sub>(b) " is Relation-like Function-like set
c is Relation-like Function-like Element of <^((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)^>
b is Element of the carrier of F<sub>1</sub>()
c is Element of the carrier of F<sub>1</sub>()
<^b,c^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
the Arrows of F<sub>1</sub>() . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of F<sub>1</sub>() . [b,c] is set
(c<sub>2</sub> * A) . b is Element of the carrier of F<sub>1</sub>()
the ObjectMap of (c<sub>2</sub> * A) is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:]
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is non empty set
the ObjectMap of (c<sub>2</sub> * A) . (b,b) is Element of [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
[b,b] is V22() set
{b,b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of (c<sub>2</sub> * A) . [b,b] is set
( the ObjectMap of (c<sub>2</sub> * A) . (b,b)) `1 is set
(id F₁()) . b is Element of the carrier of F₁()
the ObjectMap of (id F₁()) is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₁(), the carrier of F₁():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₁(), the carrier of F₁():]:]
the ObjectMap of (id F₁()) . (b,b) is Element of [: the carrier of F₁(), the carrier of F₁():]
the ObjectMap of (id F₁()) . [b,b] is set
( the ObjectMap of (id F₁()) . (b,b)) `1 is set
<^((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)^> is set
the Arrows of F<sub>1</sub>() . (((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)) is set
[((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)] is V22() set
{((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)} is non empty set
{((c<sub>2</sub> * A) . b)} is non empty set
{{((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)},{((c<sub>2</sub> * A) . b)}} is non empty set
the Arrows of F<sub>1</sub>() . [((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)] is set
F<sub>7</sub>(b) is Relation-like Function-like set
(c<sub>2</sub> * A) . c is Element of the carrier of F<sub>1</sub>()
the ObjectMap of (c<sub>2</sub> * A) . (c,c) is Element of [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of (c<sub>2</sub> * A) . [c,c] is set
( the ObjectMap of (c<sub>2</sub> * A) . (c,c)) `1 is set
(id F₁()) . c is Element of the carrier of F₁()
the ObjectMap of (id F₁()) . (c,c) is Element of [: the carrier of F₁(), the carrier of F₁():]
the ObjectMap of (id F₁()) . [c,c] is set
( the ObjectMap of (id F₁()) . (c,c)) `1 is set
<^((c<sub>2</sub> * A) . c),((id F<sub>1</sub>()) . c)^> is set
the Arrows of F<sub>1</sub>() . (((c<sub>2</sub> * A) . c),((id F<sub>1</sub>()) . c)) is set
[((c<sub>2</sub> * A) . c),((id F<sub>1</sub>()) . c)] is V22() set
{((c<sub>2</sub> * A) . c),((id F<sub>1</sub>()) . c)} is non empty set
{((c<sub>2</sub> * A) . c)} is non empty set
{{((c<sub>2</sub> * A) . c),((id F<sub>1</sub>()) . c)},{((c<sub>2</sub> * A) . c)}} is non empty set
the Arrows of F<sub>1</sub>() . [((c<sub>2</sub> * A) . c),((id F<sub>1</sub>()) . c)] is set
F<sub>7</sub>(c) is Relation-like Function-like set
<^((c<sub>2</sub> * A) . b),((c<sub>2</sub> * A) . c)^> is set
the Arrows of F<sub>1</sub>() . (((c<sub>2</sub> * A) . b),((c<sub>2</sub> * A) . c)) is set
[((c<sub>2</sub> * A) . b),((c<sub>2</sub> * A) . c)] is V22() set
{((c<sub>2</sub> * A) . b),((c<sub>2</sub> * A) . c)} is non empty set
{{((c<sub>2</sub> * A) . b),((c<sub>2</sub> * A) . c)},{((c<sub>2</sub> * A) . b)}} is non empty set
the Arrows of F<sub>1</sub>() . [((c<sub>2</sub> * A) . b),((c<sub>2</sub> * A) . c)] is set
<^((id F<sub>1</sub>()) . b),((id F<sub>1</sub>()) . c)^> is set
the Arrows of F<sub>1</sub>() . (((id F<sub>1</sub>()) . b),((id F<sub>1</sub>()) . c)) is set
[((id F<sub>1</sub>()) . b),((id F<sub>1</sub>()) . c)] is V22() set
{((id F<sub>1</sub>()) . b),((id F<sub>1</sub>()) . c)} is non empty set
{((id F<sub>1</sub>()) . b)} is non empty set
{{((id F<sub>1</sub>()) . b),((id F<sub>1</sub>()) . c)},{((id F<sub>1</sub>()) . b)}} is non empty set
the Arrows of F<sub>1</sub>() . [((id F<sub>1</sub>()) . b),((id F<sub>1</sub>()) . c)] is set
f is Relation-like Function-like Element of <^b,c^>
(c<sub>2</sub> * A) . f is Relation-like Function-like Element of <^((c<sub>2</sub> * A) . b),((c<sub>2</sub> * A) . c)^>
(id F<sub>1</sub>()) . f is Relation-like Function-like Element of <^((id F<sub>1</sub>()) . b),((id F<sub>1</sub>()) . c)^>
A . b is Element of the carrier of F<sub>2</sub>()
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of A is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of A . (b,b) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
the ObjectMap of A . [b,b] is set
( the ObjectMap of A . (b,b)) `1 is set
A . c is Element of the carrier of F₂()
the ObjectMap of A . (c,c) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of A . [c,c] is set
( the ObjectMap of A . (c,c)) `1 is set
A . f is Relation-like Function-like Element of <^(A . b),(A . c)^>
<^(A . b),(A . c)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . ((A . b),(A . c)) is set
[(A . b),(A . c)] is V22() set
{(A . b),(A . c)} is non empty set
{(A . b)} is non empty set
{{(A . b),(A . c)},{(A . b)}} is non empty set
the Arrows of F<sub>2</sub>() . [(A . b),(A . c)] is set
c<sub>2</sub> . (A . f) is Relation-like Function-like Element of <^(c<sub>2</sub> . (A . b)),(c<sub>2</sub> . (A . c))^>
c<sub>2</sub> . (A . b) is Element of the carrier of F<sub>1</sub>()
the ObjectMap of c<sub>2</sub> is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:]
[:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is non empty set
the ObjectMap of c<sub>2</sub> . ((A . b),(A . b)) is Element of [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
[(A . b),(A . b)] is V22() set
{(A . b),(A . b)} is non empty set
{{(A . b),(A . b)},{(A . b)}} is non empty set
the ObjectMap of c<sub>2</sub> . [(A . b),(A . b)] is set
( the ObjectMap of c<sub>2</sub> . ((A . b),(A . b))) `1 is set
c₂ . (A . c) is Element of the carrier of F₁()
the ObjectMap of c₂ . ((A . c),(A . c)) is Element of [: the carrier of F₁(), the carrier of F₁():]
[(A . c),(A . c)] is V22() set
{(A . c),(A . c)} is non empty set
{(A . c)} is non empty set
{{(A . c),(A . c)},{(A . c)}} is non empty set
the ObjectMap of c₂ . [(A . c),(A . c)] is set
( the ObjectMap of c₂ . ((A . c),(A . c))) `1 is set
<^(c<sub>2</sub> . (A . b)),(c<sub>2</sub> . (A . c))^> is set
the Arrows of F<sub>1</sub>() . ((c<sub>2</sub> . (A . b)),(c<sub>2</sub> . (A . c))) is set
[(c<sub>2</sub> . (A . b)),(c<sub>2</sub> . (A . c))] is V22() set
{(c<sub>2</sub> . (A . b)),(c<sub>2</sub> . (A . c))} is non empty set
{(c<sub>2</sub> . (A . b))} is non empty set
{{(c<sub>2</sub> . (A . b)),(c<sub>2</sub> . (A . c))},{(c<sub>2</sub> . (A . b))}} is non empty set
the Arrows of F<sub>1</sub>() . [(c<sub>2</sub> . (A . b)),(c<sub>2</sub> . (A . c))] is set
F<sub>3</sub>(b) is set
F<sub>3</sub>(c) is set
F<sub>5</sub>(b,c,f) is Relation-like Function-like set
F<sub>6</sub>(F<sub>3</sub>(b),F<sub>3</sub>(c),F<sub>5</sub>(b,c,f)) is Relation-like Function-like set
d is Relation-like Function-like Element of <^((c<sub>2</sub> * A) . c),((id F<sub>1</sub>()) . c)^>
d * ((c<sub>2</sub> * A) . f) is Relation-like Function-like Element of <^((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)^>
<^((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)^> is set
the Arrows of F<sub>1</sub>() . (((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)) is set
[((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)] is V22() set
{((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)} is non empty set
{{((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)},{((c<sub>2</sub> * A) . b)}} is non empty set
the Arrows of F<sub>1</sub>() . [((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)] is set
F<sub>6</sub>(F<sub>3</sub>(b),F<sub>3</sub>(c),F<sub>5</sub>(b,c,f)) (#) F<sub>7</sub>(c) is Relation-like Function-like set
F<sub>7</sub>(b) (#) f is Relation-like Function-like set
F<sub>7</sub>(b) (#) ((id F<sub>1</sub>()) . f) is Relation-like Function-like set
fa is Relation-like Function-like Element of <^((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . b)^>
fb is Relation-like Function-like Element of <^((c<sub>2</sub> * A) . c),((id F<sub>1</sub>()) . c)^>
fb * ((c<sub>2</sub> * A) . f) is Relation-like Function-like Element of <^((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)^>
((id F<sub>1</sub>()) . f) * fa is Relation-like Function-like Element of <^((c<sub>2</sub> * A) . b),((id F<sub>1</sub>()) . c)^>
b is Relation-like the carrier of F<sub>1</sub>() -defined Function-like non empty V14( the carrier of F<sub>1</sub>()) natural_equivalence of c<sub>2</sub> * A, id F<sub>1</sub>()
d is Element of the carrier of F<sub>2</sub>()
F<sub>8</sub>(d) is Relation-like Function-like set
(id F<sub>2</sub>()) . d is Element of the carrier of F<sub>2</sub>()
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the ObjectMap of (id F<sub>2</sub>()) is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of (id F<sub>2</sub>()) . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of (id F<sub>2</sub>()) . [d,d] is set
( the ObjectMap of (id F<sub>2</sub>()) . (d,d)) `1 is set
(A * c₂) . d is Element of the carrier of F₂()
the ObjectMap of (A * c₂) is Relation-like [: the carrier of F₂(), the carrier of F₂():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₂(), the carrier of F₂():]) quasi_total Element of bool [:[: the carrier of F₂(), the carrier of F₂():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of (A * c₂) . (d,d) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of (A * c₂) . [d,d] is set
( the ObjectMap of (A * c₂) . (d,d)) `1 is set
<^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
the Arrows of F<sub>2</sub>() . (((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)) is set
[((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)] is V22() set
{((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)} is non empty set
{((id F<sub>2</sub>()) . d)} is non empty set
{{((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)},{((id F<sub>2</sub>()) . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)] is set
<^((A * c<sub>2</sub>) . d),((id F<sub>2</sub>()) . d)^> is set
the Arrows of F<sub>2</sub>() . (((A * c<sub>2</sub>) . d),((id F<sub>2</sub>()) . d)) is set
[((A * c<sub>2</sub>) . d),((id F<sub>2</sub>()) . d)] is V22() set
{((A * c<sub>2</sub>) . d),((id F<sub>2</sub>()) . d)} is non empty set
{((A * c<sub>2</sub>) . d)} is non empty set
{{((A * c<sub>2</sub>) . d),((id F<sub>2</sub>()) . d)},{((A * c<sub>2</sub>) . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [((A * c<sub>2</sub>) . d),((id F<sub>2</sub>()) . d)] is set
c<sub>2</sub> . d is Element of the carrier of F<sub>1</sub>()
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
the ObjectMap of c<sub>2</sub> is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:]
[:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is non empty set
the ObjectMap of c<sub>2</sub> . (d,d) is Element of [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
the ObjectMap of c<sub>2</sub> . [d,d] is set
( the ObjectMap of c<sub>2</sub> . (d,d)) `1 is set
A . (c₂ . d) is Element of the carrier of F₂()
the ObjectMap of A is Relation-like [: the carrier of F₁(), the carrier of F₁():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₁(), the carrier of F₁():]) quasi_total Element of bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:]
[:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:] is Relation-like non empty set
bool [:[: the carrier of F₁(), the carrier of F₁():],[: the carrier of F₂(), the carrier of F₂():]:] is non empty set
the ObjectMap of A . ((c₂ . d),(c₂ . d)) is Element of [: the carrier of F₂(), the carrier of F₂():]
[(c₂ . d),(c₂ . d)] is V22() set
{(c₂ . d),(c₂ . d)} is non empty set
{(c₂ . d)} is non empty set
{{(c₂ . d),(c₂ . d)},{(c₂ . d)}} is non empty set
the ObjectMap of A . [(c₂ . d),(c₂ . d)] is set
( the ObjectMap of A . ((c₂ . d),(c₂ . d))) `1 is set
F<sub>3</sub>((c<sub>2</sub> . d)) is set
F<sub>4</sub>(d) is set
F<sub>3</sub>(F<sub>4</sub>(d)) is set
F<sub>8</sub>(d) " is Relation-like Function-like set
f is Relation-like Function-like Element of <^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)^>
d is Element of the carrier of F<sub>2</sub>()
f is Element of the carrier of F<sub>2</sub>()
<^d,f^> is set
the Arrows of F<sub>2</sub>() is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) set
[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] is Relation-like non empty set
the Arrows of F<sub>2</sub>() . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of F<sub>2</sub>() . [d,f] is set
(id F<sub>2</sub>()) . d is Element of the carrier of F<sub>2</sub>()
the ObjectMap of (id F<sub>2</sub>()) is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of (id F<sub>2</sub>()) . (d,d) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[d,d] is V22() set
{d,d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of (id F<sub>2</sub>()) . [d,d] is set
( the ObjectMap of (id F<sub>2</sub>()) . (d,d)) `1 is set
(A * c₂) . d is Element of the carrier of F₂()
the ObjectMap of (A * c₂) is Relation-like [: the carrier of F₂(), the carrier of F₂():] -defined [: the carrier of F₂(), the carrier of F₂():] -valued Function-like non empty V14([: the carrier of F₂(), the carrier of F₂():]) quasi_total Element of bool [:[: the carrier of F₂(), the carrier of F₂():],[: the carrier of F₂(), the carrier of F₂():]:]
the ObjectMap of (A * c₂) . (d,d) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of (A * c₂) . [d,d] is set
( the ObjectMap of (A * c₂) . (d,d)) `1 is set
<^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)^> is set
the Arrows of F<sub>2</sub>() . (((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)) is set
[((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)] is V22() set
{((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)} is non empty set
{((id F<sub>2</sub>()) . d)} is non empty set
{{((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)},{((id F<sub>2</sub>()) . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)] is set
F<sub>8</sub>(d) is Relation-like Function-like set
(id F<sub>2</sub>()) . f is Element of the carrier of F<sub>2</sub>()
the ObjectMap of (id F<sub>2</sub>()) . (f,f) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[f,f] is V22() set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
the ObjectMap of (id F<sub>2</sub>()) . [f,f] is set
( the ObjectMap of (id F<sub>2</sub>()) . (f,f)) `1 is set
(A * c₂) . f is Element of the carrier of F₂()
the ObjectMap of (A * c₂) . (f,f) is Element of [: the carrier of F₂(), the carrier of F₂():]
the ObjectMap of (A * c₂) . [f,f] is set
( the ObjectMap of (A * c₂) . (f,f)) `1 is set
<^((id F<sub>2</sub>()) . f),((A * c<sub>2</sub>) . f)^> is set
the Arrows of F<sub>2</sub>() . (((id F<sub>2</sub>()) . f),((A * c<sub>2</sub>) . f)) is set
[((id F<sub>2</sub>()) . f),((A * c<sub>2</sub>) . f)] is V22() set
{((id F<sub>2</sub>()) . f),((A * c<sub>2</sub>) . f)} is non empty set
{((id F<sub>2</sub>()) . f)} is non empty set
{{((id F<sub>2</sub>()) . f),((A * c<sub>2</sub>) . f)},{((id F<sub>2</sub>()) . f)}} is non empty set
the Arrows of F<sub>2</sub>() . [((id F<sub>2</sub>()) . f),((A * c<sub>2</sub>) . f)] is set
F<sub>8</sub>(f) is Relation-like Function-like set
<^((A * c<sub>2</sub>) . d),((A * c<sub>2</sub>) . f)^> is set
the Arrows of F<sub>2</sub>() . (((A * c<sub>2</sub>) . d),((A * c<sub>2</sub>) . f)) is set
[((A * c<sub>2</sub>) . d),((A * c<sub>2</sub>) . f)] is V22() set
{((A * c<sub>2</sub>) . d),((A * c<sub>2</sub>) . f)} is non empty set
{((A * c<sub>2</sub>) . d)} is non empty set
{{((A * c<sub>2</sub>) . d),((A * c<sub>2</sub>) . f)},{((A * c<sub>2</sub>) . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [((A * c<sub>2</sub>) . d),((A * c<sub>2</sub>) . f)] is set
<^((id F<sub>2</sub>()) . d),((id F<sub>2</sub>()) . f)^> is set
the Arrows of F<sub>2</sub>() . (((id F<sub>2</sub>()) . d),((id F<sub>2</sub>()) . f)) is set
[((id F<sub>2</sub>()) . d),((id F<sub>2</sub>()) . f)] is V22() set
{((id F<sub>2</sub>()) . d),((id F<sub>2</sub>()) . f)} is non empty set
{{((id F<sub>2</sub>()) . d),((id F<sub>2</sub>()) . f)},{((id F<sub>2</sub>()) . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [((id F<sub>2</sub>()) . d),((id F<sub>2</sub>()) . f)] is set
fb is Relation-like Function-like Element of <^d,f^>
(id F<sub>2</sub>()) . fb is Relation-like Function-like Element of <^((id F<sub>2</sub>()) . d),((id F<sub>2</sub>()) . f)^>
(A * c<sub>2</sub>) . fb is Relation-like Function-like Element of <^((A * c<sub>2</sub>) . d),((A * c<sub>2</sub>) . f)^>
c<sub>2</sub> . d is Element of the carrier of F<sub>1</sub>()
[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] is Relation-like non empty set
the ObjectMap of c<sub>2</sub> is Relation-like [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -defined [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:]
[:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():],[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]:] is non empty set
the ObjectMap of c<sub>2</sub> . (d,d) is Element of [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]
the ObjectMap of c<sub>2</sub> . [d,d] is set
( the ObjectMap of c<sub>2</sub> . (d,d)) `1 is set
c₂ . f is Element of the carrier of F₁()
the ObjectMap of c₂ . (f,f) is Element of [: the carrier of F₁(), the carrier of F₁():]
the ObjectMap of c₂ . [f,f] is set
( the ObjectMap of c₂ . (f,f)) `1 is set
c<sub>2</sub> . fb is Relation-like Function-like Element of <^(c<sub>2</sub> . d),(c<sub>2</sub> . f)^>
<^(c<sub>2</sub> . d),(c<sub>2</sub> . f)^> is set
the Arrows of F<sub>1</sub>() is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) set
the Arrows of F<sub>1</sub>() . ((c<sub>2</sub> . d),(c<sub>2</sub> . f)) is set
[(c<sub>2</sub> . d),(c<sub>2</sub> . f)] is V22() set
{(c<sub>2</sub> . d),(c<sub>2</sub> . f)} is non empty set
{(c<sub>2</sub> . d)} is non empty set
{{(c<sub>2</sub> . d),(c<sub>2</sub> . f)},{(c<sub>2</sub> . d)}} is non empty set
the Arrows of F<sub>1</sub>() . [(c<sub>2</sub> . d),(c<sub>2</sub> . f)] is set
A . (c<sub>2</sub> . fb) is Relation-like Function-like Element of <^(A . (c<sub>2</sub> . d)),(A . (c<sub>2</sub> . f))^>
A . (c<sub>2</sub> . d) is Element of the carrier of F<sub>2</sub>()
the ObjectMap of A is Relation-like [: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():] -defined [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():] -valued Function-like non empty V14([: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():]) quasi_total Element of bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:]
[:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is Relation-like non empty set
bool [:[: the carrier of F<sub>1</sub>(), the carrier of F<sub>1</sub>():],[: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]:] is non empty set
the ObjectMap of A . ((c<sub>2</sub> . d),(c<sub>2</sub> . d)) is Element of [: the carrier of F<sub>2</sub>(), the carrier of F<sub>2</sub>():]
[(c<sub>2</sub> . d),(c<sub>2</sub> . d)] is V22() set
{(c<sub>2</sub> . d),(c<sub>2</sub> . d)} is non empty set
{{(c<sub>2</sub> . d),(c<sub>2</sub> . d)},{(c<sub>2</sub> . d)}} is non empty set
the ObjectMap of A . [(c<sub>2</sub> . d),(c<sub>2</sub> . d)] is set
( the ObjectMap of A . ((c<sub>2</sub> . d),(c<sub>2</sub> . d))) `1 is set
A . (c₂ . f) is Element of the carrier of F₂()
the ObjectMap of A . ((c₂ . f),(c₂ . f)) is Element of [: the carrier of F₂(), the carrier of F₂():]
[(c₂ . f),(c₂ . f)] is V22() set
{(c₂ . f),(c₂ . f)} is non empty set
{(c₂ . f)} is non empty set
{{(c₂ . f),(c₂ . f)},{(c₂ . f)}} is non empty set
the ObjectMap of A . [(c₂ . f),(c₂ . f)] is set
( the ObjectMap of A . ((c₂ . f),(c₂ . f))) `1 is set
<^(A . (c<sub>2</sub> . d)),(A . (c<sub>2</sub> . f))^> is set
the Arrows of F<sub>2</sub>() . ((A . (c<sub>2</sub> . d)),(A . (c<sub>2</sub> . f))) is set
[(A . (c<sub>2</sub> . d)),(A . (c<sub>2</sub> . f))] is V22() set
{(A . (c<sub>2</sub> . d)),(A . (c<sub>2</sub> . f))} is non empty set
{(A . (c<sub>2</sub> . d))} is non empty set
{{(A . (c<sub>2</sub> . d)),(A . (c<sub>2</sub> . f))},{(A . (c<sub>2</sub> . d))}} is non empty set
the Arrows of F<sub>2</sub>() . [(A . (c<sub>2</sub> . d)),(A . (c<sub>2</sub> . f))] is set
F<sub>4</sub>(d) is set
F<sub>4</sub>(f) is set
F<sub>6</sub>(d,f,fb) is Relation-like Function-like set
F<sub>5</sub>(F<sub>4</sub>(d),F<sub>4</sub>(f),F<sub>6</sub>(d,f,fb)) is Relation-like Function-like set
fa is Relation-like Function-like Element of <^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)^>
((A * c<sub>2</sub>) . fb) * fa is Relation-like Function-like Element of <^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)^>
<^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)^> is set
the Arrows of F<sub>2</sub>() . (((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)) is set
[((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)] is V22() set
{((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)} is non empty set
{{((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)},{((id F<sub>2</sub>()) . d)}} is non empty set
the Arrows of F<sub>2</sub>() . [((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)] is set
F<sub>8</sub>(d) (#) F<sub>5</sub>(F<sub>4</sub>(d),F<sub>4</sub>(f),F<sub>6</sub>(d,f,fb)) is Relation-like Function-like set
fb (#) F<sub>8</sub>(f) is Relation-like Function-like set
((id F<sub>2</sub>()) . fb) (#) F<sub>8</sub>(f) is Relation-like Function-like set
g is Relation-like Function-like Element of <^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . d)^>
g is Relation-like Function-like Element of <^((id F<sub>2</sub>()) . f),((A * c<sub>2</sub>) . f)^>
g * ((id F<sub>2</sub>()) . fb) is Relation-like Function-like Element of <^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)^>
((A * c<sub>2</sub>) . fb) * g is Relation-like Function-like Element of <^((id F<sub>2</sub>()) . d),((A * c<sub>2</sub>) . f)^>
d is Relation-like the carrier of F<sub>2</sub>() -defined Function-like non empty V14( the carrier of F<sub>2</sub>()) natural_equivalence of id F<sub>2</sub>(),A * c<sub>2</sub>
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
disjoin the Arrows of A is Relation-like Function-like set
Union (disjoin the Arrows of A) is set
c<sub>2</sub> is Element of the carrier of A
FF is Element of the carrier of A
a is Element of the carrier of A
b is Relation-like Function-like set
c is Relation-like Function-like set
b (#) c is Relation-like Function-like set
d is Element of the carrier of A
f is Element of the carrier of A
<^d,f^> is set
the Arrows of A . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of A . [d,f] is set
fa is Element of <^d,f^>
fb is Element of the carrier of A
g is Element of the carrier of A
<^fb,g^> is set
the Arrows of A . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of A . [fb,g] is set
g is Element of <^fb,g^>
<^f,g^> is set
the Arrows of A . (f,g) is set
[f,g] is V22() set
{f,g} is non empty set
{f} is non empty set
{{f,g},{f}} is non empty set
the Arrows of A . [f,g] is set
<^d,g^> is set
the Arrows of A . (d,g) is set
[d,g] is V22() set
{d,g} is non empty set
{{d,g},{d}} is non empty set
the Arrows of A . [d,g] is set
c<sub>13</sub> is Element of <^f,g^>
c<sub>13</sub> * fa is Element of <^d,g^>
g9 is Element of <^d,g^>
a1 is Element of the carrier of A
<^a1,d^> is set
the Arrows of A . (a1,d) is set
[a1,d] is V22() set
{a1,d} is non empty set
{a1} is non empty set
{{a1,d},{a1}} is non empty set
the Arrows of A . [a1,d] is set
[a1,g] is V22() set
{a1,g} is non empty set
{{a1,g},{a1}} is non empty set
<^a1,f^> is set
the Arrows of A . (a1,f) is set
[a1,f] is V22() set
{a1,f} is non empty set
{{a1,f},{a1}} is non empty set
the Arrows of A . [a1,f] is set
b1 is Element of <^a1,d^>
[b1,[a1,d]] is V22() set
{b1,[a1,d]} is non empty set
{b1} is non empty set
{{b1,[a1,d]},{b1}} is non empty set
(b (#) c) . [b1,[a1,d]] is set
g9 * b1 is Element of <^a1,g^>
<^a1,g^> is set
the Arrows of A . (a1,g) is set
the Arrows of A . [a1,g] is set
[(g9 * b1),[a1,g]] is V22() set
{(g9 * b1),[a1,g]} is non empty set
{(g9 * b1)} is non empty set
{{(g9 * b1),[a1,g]},{(g9 * b1)}} is non empty set
b . [b1,[a1,d]] is set
fa * b1 is Element of <^a1,f^>
[(fa * b1),[a1,f]] is V22() set
{(fa * b1),[a1,f]} is non empty set
{(fa * b1)} is non empty set
{{(fa * b1),[a1,f]},{(fa * b1)}} is non empty set
proj1 b is set
c . [(fa * b1),[a1,f]] is set
c<sub>13</sub> * (fa * b1) is Element of <^a1,g^>
[(c<sub>13</sub> * (fa * b1)),[a1,g]] is V22() set
{(c<sub>13</sub> * (fa * b1)),[a1,g]} is non empty set
{(c<sub>13</sub> * (fa * b1))} is non empty set
{{(c<sub>13</sub> * (fa * b1)),[a1,g]},{(c<sub>13</sub> * (fa * b1))}} is non empty set
c<sub>2</sub> is Element of the carrier of A
FF is set
id FF is Relation-like FF -defined FF -valued Function-like one-to-one V14(FF) quasi_total Element of bool [:FF,FF:]
[:FF,FF:] is Relation-like set
bool [:FF,FF:] is non empty set
a is Element of the carrier of A
<^a,a^> is non empty set
the Arrows of A . (a,a) is set
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the Arrows of A . [a,a] is set
idm a is retraction coretraction iso mono epi Element of <^a,a^>
b is retraction coretraction iso mono epi Element of <^a,a^>
c is Element of the carrier of A
<^c,a^> is set
the Arrows of A . (c,a) is set
[c,a] is V22() set
{c,a} is non empty set
{c} is non empty set
{{c,a},{c}} is non empty set
the Arrows of A . [c,a] is set
d is Element of <^c,a^>
[d,[c,a]] is V22() set
{d,[c,a]} is non empty set
{d} is non empty set
{{d,[c,a]},{d}} is non empty set
(id FF) . [d,[c,a]] is set
b * d is Element of <^c,a^>
[(b * d),[c,a]] is V22() set
{(b * d),[c,a]} is non empty set
{(b * d)} is non empty set
{{(b * d),[c,a]},{(b * d)}} is non empty set
[d,[c,a]] `1 is set
[d,[c,a]] `2 is set
[d,[c,a]] `22 is set
dom the Arrows of A is Relation-like the carrier of A -defined the carrier of A -valued non empty Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
c₂ is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
the carrier of c₂ is non empty set
the Arrows of c₂ is Relation-like [: the carrier of c₂, the carrier of c₂:] -defined Function-like non empty V14([: the carrier of c₂, the carrier of c₂:]) set
[: the carrier of c₂, the carrier of c₂:] is Relation-like non empty set
FF is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
the carrier of FF is non empty set
the Arrows of FF is Relation-like [: the carrier of FF, the carrier of FF:] -defined Function-like non empty V14([: the carrier of FF, the carrier of FF:]) set
[: the carrier of FF, the carrier of FF:] is Relation-like non empty set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
(A) is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
c₂ is Element of the carrier of A
((A),c₂) is set
FF is set
the carrier of (A) is non empty set
b is Element of the carrier of (A)
((A),b) is set
idm b is Relation-like Function-like retraction coretraction iso mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of (A) is Relation-like [: the carrier of (A), the carrier of (A):] -defined Function-like non empty V14([: the carrier of (A), the carrier of (A):]) set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
the Arrows of (A) . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of (A) . [b,b] is set
proj1 (idm b) is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
disjoin the Arrows of A is Relation-like Function-like set
Union (disjoin the Arrows of A) is set
FF `22 is set
dom the Arrows of A is Relation-like the carrier of A -defined the carrier of A -valued non empty Element of bool [: the carrier of A, the carrier of A:]
bool [: the carrier of A, the carrier of A:] is non empty set
FF `2 is set
FF `1 is set
the Arrows of A . (FF `2) is set
[(FF `1),(FF `2)] is V22() set
{(FF `1),(FF `2)} is non empty set
{(FF `1)} is non empty set
{{(FF `1),(FF `2)},{(FF `1)}} is non empty set
c is set
d is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
f is Element of the carrier of A
fa is Element of the carrier of A
<^fa,c₂^> is set
the Arrows of A . (fa,c₂) is set
[fa,c₂] is V22() set
{fa,c₂} is non empty set
{fa} is non empty set
{{fa,c₂},{fa}} is non empty set
the Arrows of A . [fa,c₂] is set
fb is Element of <^fa,c₂^>
g is Element of <^fa,c₂^>
[g,[fa,c₂]] is V22() set
{g,[fa,c₂]} is non empty set
{g} is non empty set
{{g,[fa,c₂]},{g}} is non empty set
c is Element of the carrier of A
<^c,c₂^> is set
the Arrows of A . (c,c₂) is set
[c,c₂] is V22() set
{c,c₂} is non empty set
{c} is non empty set
{{c,c₂},{c}} is non empty set
the Arrows of A . [c,c₂] is set
d is Element of <^c,c₂^>
[d,[c,c₂]] is V22() set
{d,[c,c₂]} is non empty set
{d} is non empty set
{{d,[c,c₂]},{d}} is non empty set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
(A) is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
c₂ is Element of the carrier of A
((A),c₂) is set
idm c₂ is retraction coretraction iso mono epi Element of <^c₂,c₂^>
<^c₂,c₂^> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c₂,c₂) is set
[c₂,c₂] is V22() set
{c₂,c₂} is non empty set
{c₂} is non empty set
{{c₂,c₂},{c₂}} is non empty set
the Arrows of A . [c₂,c₂] is set
[(idm c₂),[c₂,c₂]] is V22() set
{(idm c₂),[c₂,c₂]} is non empty set
{(idm c₂)} is non empty set
{{(idm c₂),[c₂,c₂]},{(idm c₂)}} is non empty set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
(A) is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
the Arrows of (A) is Relation-like [: the carrier of (A), the carrier of (A):] -defined Function-like non empty V14([: the carrier of (A), the carrier of (A):]) set
the carrier of (A) is non empty set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
c₂ is Element of the carrier of A
FF is Element of the carrier of A
<^c₂,FF^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c₂,FF) is set
[c₂,FF] is V22() set
{c₂,FF} is non empty set
{c₂} is non empty set
{{c₂,FF},{c₂}} is non empty set
the Arrows of A . [c₂,FF] is set
((A),c₂) is non empty set
((A),FF) is non empty set
[:((A),c₂),((A),FF):] is Relation-like non empty set
bool [:((A),c₂),((A),FF):] is non empty set
the Arrows of (A) . (c₂,FF) is set
the Arrows of (A) . [c₂,FF] is set
b is Element of <^c₂,FF^>
c is set
d is Element of the carrier of A
<^d,c₂^> is set
the Arrows of A . (d,c₂) is set
[d,c₂] is V22() set
{d,c₂} is non empty set
{d} is non empty set
{{d,c₂},{d}} is non empty set
the Arrows of A . [d,c₂] is set
f is Element of <^d,c₂^>
[f,[d,c₂]] is V22() set
{f,[d,c₂]} is non empty set
{f} is non empty set
{{f,[d,c₂]},{f}} is non empty set
b * f is Element of <^d,FF^>
<^d,FF^> is set
the Arrows of A . (d,FF) is set
[d,FF] is V22() set
{d,FF} is non empty set
{{d,FF},{d}} is non empty set
the Arrows of A . [d,FF] is set
[(b * f),[d,FF]] is V22() set
{(b * f),[d,FF]} is non empty set
{(b * f)} is non empty set
{{(b * f),[d,FF]},{(b * f)}} is non empty set
c is Relation-like Function-like set
proj1 c is set
proj2 c is set
Funcs (((A),c₂),((A),FF)) is functional non empty FUNCTION_DOMAIN of ((A),c₂),((A),FF)
d is Relation-like ((A),c₂) -defined ((A),FF) -valued Function-like non empty V14(((A),c₂)) quasi_total Element of bool [:((A),c₂),((A),FF):]
f is Element of the carrier of A
fa is Element of the carrier of A
<^f,fa^> is set
the Arrows of A . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of A . [f,fa] is set
fb is Element of <^f,fa^>
g is Element of the carrier of A
<^g,f^> is set
the Arrows of A . (g,f) is set
[g,f] is V22() set
{g,f} is non empty set
{g} is non empty set
{{g,f},{g}} is non empty set
the Arrows of A . [g,f] is set
[g,fa] is V22() set
{g,fa} is non empty set
{{g,fa},{g}} is non empty set
g is Element of <^g,f^>
[g,[g,f]] is V22() set
{g,[g,f]} is non empty set
{g} is non empty set
{{g,[g,f]},{g}} is non empty set
d . [g,[g,f]] is set
fb * g is Element of <^g,fa^>
<^g,fa^> is set
the Arrows of A . (g,fa) is set
the Arrows of A . [g,fa] is set
[(fb * g),[g,fa]] is V22() set
{(fb * g),[g,fa]} is non empty set
{(fb * g)} is non empty set
{{(fb * g),[g,fa]},{(fb * g)}} is non empty set
((A),f) is non empty set
c₁₃ is Element of the carrier of A
<^c₁₃,f^> is set
the Arrows of A . (c₁₃,f) is set
[c₁₃,f] is V22() set
{c₁₃,f} is non empty set
{c₁₃} is non empty set
{{c₁₃,f},{c₁₃}} is non empty set
the Arrows of A . [c₁₃,f] is set
g9 is Element of <^c₁₃,f^>
[g9,[c₁₃,f]] is V22() set
{g9,[c₁₃,f]} is non empty set
{g9} is non empty set
{{g9,[c₁₃,f]},{g9}} is non empty set
fb * g9 is Element of <^c₁₃,fa^>
<^c₁₃,fa^> is set
the Arrows of A . (c₁₃,fa) is set
[c₁₃,fa] is V22() set
{c₁₃,fa} is non empty set
{{c₁₃,fa},{c₁₃}} is non empty set
the Arrows of A . [c₁₃,fa] is set
[(fb * g9),[c₁₃,fa]] is V22() set
{(fb * g9),[c₁₃,fa]} is non empty set
{(fb * g9)} is non empty set
{{(fb * g9),[c₁₃,fa]},{(fb * g9)}} is non empty set
f is Element of the carrier of A
fa is Element of the carrier of A
<^f,fa^> is set
the Arrows of A . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of A . [f,fa] is set
fb is Element of <^f,fa^>
f is Element of the carrier of A
<^f,c₂^> is set
the Arrows of A . (f,c₂) is set
[f,c₂] is V22() set
{f,c₂} is non empty set
{f} is non empty set
{{f,c₂},{f}} is non empty set
the Arrows of A . [f,c₂] is set
[f,FF] is V22() set
{f,FF} is non empty set
{{f,FF},{f}} is non empty set
fa is Element of <^f,c₂^>
[fa,[f,c₂]] is V22() set
{fa,[f,c₂]} is non empty set
{fa} is non empty set
{{fa,[f,c₂]},{fa}} is non empty set
d . [fa,[f,c₂]] is set
b * fa is Element of <^f,FF^>
<^f,FF^> is set
the Arrows of A . (f,FF) is set
the Arrows of A . [f,FF] is set
[(b * fa),[f,FF]] is V22() set
{(b * fa),[f,FF]} is non empty set
{(b * fa)} is non empty set
{{(b * fa),[f,FF]},{(b * fa)}} is non empty set
fb is Element of the carrier of A
<^fb,c₂^> is set
the Arrows of A . (fb,c₂) is set
[fb,c₂] is V22() set
{fb,c₂} is non empty set
{fb} is non empty set
{{fb,c₂},{fb}} is non empty set
the Arrows of A . [fb,c₂] is set
g is Element of <^fb,c₂^>
[g,[fb,c₂]] is V22() set
{g,[fb,c₂]} is non empty set
{g} is non empty set
{{g,[fb,c₂]},{g}} is non empty set
b * g is Element of <^fb,FF^>
<^fb,FF^> is set
the Arrows of A . (fb,FF) is set
[fb,FF] is V22() set
{fb,FF} is non empty set
{{fb,FF},{fb}} is non empty set
the Arrows of A . [fb,FF] is set
[(b * g),[fb,FF]] is V22() set
{(b * g),[fb,FF]} is non empty set
{(b * g)} is non empty set
{{(b * g),[fb,FF]},{(b * g)}} is non empty set
A is non empty transitive associative with_units reflexive AltCatStr
the carrier of A is non empty set
(A) is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
the Arrows of (A) is Relation-like [: the carrier of (A), the carrier of (A):] -defined Function-like non empty V14([: the carrier of (A), the carrier of (A):]) set
the carrier of (A) is non empty set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
c₂ is Element of the carrier of A
FF is Element of the carrier of A
the Arrows of (A) . (c₂,FF) is set
[c₂,FF] is V22() set
{c₂,FF} is non empty set
{c₂} is non empty set
{{c₂,FF},{c₂}} is non empty set
the Arrows of (A) . [c₂,FF] is set
idm c₂ is retraction coretraction iso mono epi Element of <^c₂,c₂^>
<^c₂,c₂^> is non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c₂,c₂) is set
[c₂,c₂] is V22() set
{c₂,c₂} is non empty set
{{c₂,c₂},{c₂}} is non empty set
the Arrows of A . [c₂,c₂] is set
[(idm c₂),[c₂,c₂]] is V22() set
{(idm c₂),[c₂,c₂]} is non empty set
{(idm c₂)} is non empty set
{{(idm c₂),[c₂,c₂]},{(idm c₂)}} is non empty set
b is Relation-like Function-like set
c is Relation-like Function-like set
b . [(idm c₂),[c₂,c₂]] is set
c . [(idm c₂),[c₂,c₂]] is set
((A),c₂) is non empty set
((A),FF) is non empty set
Funcs (((A),c₂),((A),FF)) is functional non empty FUNCTION_DOMAIN of ((A),c₂),((A),FF)
proj1 b is set
proj1 c is set
d is Element of the carrier of A
f is Element of the carrier of A
<^d,f^> is set
the Arrows of A . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of A . [d,f] is set
fa is Element of <^d,f^>
fb is Element of the carrier of A
g is Element of the carrier of A
<^fb,g^> is set
the Arrows of A . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of A . [fb,g] is set
g is Element of <^fb,g^>
<^c₂,FF^> is set
the Arrows of A . (c₂,FF) is set
the Arrows of A . [c₂,FF] is set
c₁₃ is Element of <^c₂,FF^>
c₁₃ * (idm c₂) is Element of <^c₂,FF^>
[(c₁₃ * (idm c₂)),[c₂,FF]] is V22() set
{(c₁₃ * (idm c₂)),[c₂,FF]} is non empty set
{(c₁₃ * (idm c₂))} is non empty set
{{(c₁₃ * (idm c₂)),[c₂,FF]},{(c₁₃ * (idm c₂))}} is non empty set
g9 is Element of <^c₂,FF^>
g9 * (idm c₂) is Element of <^c₂,FF^>
[(g9 * (idm c₂)),[c₂,FF]] is V22() set
{(g9 * (idm c₂)),[c₂,FF]} is non empty set
{(g9 * (idm c₂))} is non empty set
{{(g9 * (idm c₂)),[c₂,FF]},{(g9 * (idm c₂))}} is non empty set
a1 is set
b1 is Element of the carrier of A
<^b1,c₂^> is set
the Arrows of A . (b1,c₂) is set
[b1,c₂] is V22() set
{b1,c₂} is non empty set
{b1} is non empty set
{{b1,c₂},{b1}} is non empty set
the Arrows of A . [b1,c₂] is set
f1 is Element of <^b1,c₂^>
[f1,[b1,c₂]] is V22() set
{f1,[b1,c₂]} is non empty set
{f1} is non empty set
{{f1,[b1,c₂]},{f1}} is non empty set
b . a1 is set
c₁₃ * f1 is Element of <^b1,FF^>
<^b1,FF^> is set
the Arrows of A . (b1,FF) is set
[b1,FF] is V22() set
{b1,FF} is non empty set
{{b1,FF},{b1}} is non empty set
the Arrows of A . [b1,FF] is set
[(c₁₃ * f1),[b1,FF]] is V22() set
{(c₁₃ * f1),[b1,FF]} is non empty set
{(c₁₃ * f1)} is non empty set
{{(c₁₃ * f1),[b1,FF]},{(c₁₃ * f1)}} is non empty set
c . a1 is set
F₁() is set
F₂() is Relation-like F₁() -defined Function-like V14(F₁()) set
F₃() is Relation-like F₁() -defined Function-like V14(F₁()) set
A is set
F₂() . A is set
F₃() . A is set
[:(F₂() . A),(F₃() . A):] is Relation-like set
bool [:(F₂() . A),(F₃() . A):] is non empty set
c₂ is set
FF is set
c₂ is Relation-like Function-like set
proj1 c₂ is set
proj2 c₂ is set
FF is Relation-like F₂() . A -defined F₃() . A -valued Function-like quasi_total Element of bool [:(F₂() . A),(F₃() . A):]
a is set
FF . a is set
A is Relation-like Function-like set
proj1 A is set
FF is set
F₂() . FF is set
F₃() . FF is set
[:(F₂() . FF),(F₃() . FF):] is Relation-like set
bool [:(F₂() . FF),(F₃() . FF):] is non empty set
c₂ is Relation-like F₁() -defined Function-like V14(F₁()) set
c₂ . FF is set
a is Relation-like F₂() . FF -defined F₃() . FF -valued Function-like quasi_total Element of bool [:(F₂() . FF),(F₃() . FF):]
FF is Relation-like F₁() -defined Function-like V14(F₁()) Function-yielding V63() ManySortedFunction of F₂(),F₃()
a is set
b is set
F₂() . a is set
FF . a is Relation-like Function-like set
(FF . a) . b is set
F₃() . a is set
[:(F₂() . a),(F₃() . a):] is Relation-like set
bool [:(F₂() . a),(F₃() . a):] is non empty set
c is Relation-like F₂() . a -defined F₃() . a -valued Function-like quasi_total Element of bool [:(F₂() . a),(F₃() . a):]
A is non empty transitive associative with_units reflexive AltCatStr
(A) is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
the carrier of A is non empty set
FF is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,(A)
a is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,(A)
b is Element of the carrier of A
FF . b is Element of the carrier of (A)
the carrier of (A) is non empty set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
the ObjectMap of FF is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of (A), the carrier of (A):] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is non empty set
the ObjectMap of FF . (b,b) is Element of [: the carrier of (A), the carrier of (A):]
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of FF . [b,b] is set
( the ObjectMap of FF . (b,b)) `1 is set
a . b is Element of the carrier of (A)
the ObjectMap of a is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of (A), the carrier of (A):] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:]
the ObjectMap of a . (b,b) is Element of [: the carrier of (A), the carrier of (A):]
the ObjectMap of a . [b,b] is set
( the ObjectMap of a . (b,b)) `1 is set
b is Element of the carrier of A
c is Element of the carrier of A
<^b,c^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
the Arrows of A . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of A . [b,c] is set
d is Element of <^b,c^>
FF . d is Relation-like Function-like Element of <^(FF . b),(FF . c)^>
FF . b is Element of the carrier of (A)
the ObjectMap of FF . (b,b) is Element of [: the carrier of (A), the carrier of (A):]
[b,b] is V22() set
{b,b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of FF . [b,b] is set
( the ObjectMap of FF . (b,b)) `1 is set
FF . c is Element of the carrier of (A)
the ObjectMap of FF . (c,c) is Element of [: the carrier of (A), the carrier of (A):]
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of FF . [c,c] is set
( the ObjectMap of FF . (c,c)) `1 is set
<^(FF . b),(FF . c)^> is set
the Arrows of (A) is Relation-like [: the carrier of (A), the carrier of (A):] -defined Function-like non empty V14([: the carrier of (A), the carrier of (A):]) set
the Arrows of (A) . ((FF . b),(FF . c)) is set
[(FF . b),(FF . c)] is V22() set
{(FF . b),(FF . c)} is non empty set
{(FF . b)} is non empty set
{{(FF . b),(FF . c)},{(FF . b)}} is non empty set
the Arrows of (A) . [(FF . b),(FF . c)] is set
idm b is retraction coretraction iso mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of A . (b,b) is set
the Arrows of A . [b,b] is set
[(idm b),[b,b]] is V22() set
{(idm b),[b,b]} is non empty set
{(idm b)} is non empty set
{{(idm b),[b,b]},{(idm b)}} is non empty set
(FF . d) . [(idm b),[b,b]] is set
[d,[b,c]] is V22() set
{d,[b,c]} is non empty set
{d} is non empty set
{{d,[b,c]},{d}} is non empty set
a . d is Relation-like Function-like Element of <^(a . b),(a . c)^>
a . b is Element of the carrier of (A)
the ObjectMap of a . (b,b) is Element of [: the carrier of (A), the carrier of (A):]
the ObjectMap of a . [b,b] is set
( the ObjectMap of a . (b,b)) `1 is set
a . c is Element of the carrier of (A)
the ObjectMap of a . (c,c) is Element of [: the carrier of (A), the carrier of (A):]
the ObjectMap of a . [c,c] is set
( the ObjectMap of a . (c,c)) `1 is set
<^(a . b),(a . c)^> is set
the Arrows of (A) . ((a . b),(a . c)) is set
[(a . b),(a . c)] is V22() set
{(a . b),(a . c)} is non empty set
{(a . b)} is non empty set
{{(a . b),(a . c)},{(a . b)}} is non empty set
the Arrows of (A) . [(a . b),(a . c)] is set
(a . d) . [(idm b),[b,b]] is set
the carrier of (A) is non empty set
FF is Element of the carrier of A
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of (A) is Relation-like [: the carrier of (A), the carrier of (A):] -defined Function-like non empty V14([: the carrier of (A), the carrier of (A):]) set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
FF is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
a is set
b is set
the Arrows of A . a is set
FF . a is set
c is set
d is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
f is Element of the carrier of A
fa is Element of the carrier of A
<^f,fa^> is set
the Arrows of A . (f,fa) is set
[f,fa] is V22() set
{f,fa} is non empty set
{f} is non empty set
{{f,fa},{f}} is non empty set
the Arrows of A . [f,fa] is set
((A),f) is non empty set
((A),fa) is non empty set
[:((A),f),((A),fa):] is Relation-like non empty set
bool [:((A),f),((A),fa):] is non empty set
FF . (f,fa) is set
FF . [f,fa] is set
fb is Element of <^f,fa^>
g is Relation-like ((A),f) -defined ((A),fa) -valued Function-like non empty V14(((A),f)) quasi_total Element of bool [:((A),f),((A),fa):]
a is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) Function-yielding V63() ManySortedFunction of the Arrows of A,FF
b is Element of the carrier of A
c is Element of the carrier of A
<^b,c^> is set
the Arrows of A . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of A . [b,c] is set
a . [b,c] is Relation-like Function-like set
the Arrows of (A) . (H₁(b),H₁(c)) is set
the Arrows of (A) . [b,c] is set
d is Element of <^b,c^>
(a . [b,c]) . d is set
b is Element of the carrier of A
c is Element of the carrier of A
<^b,c^> is set
the Arrows of A . (b,c) is set
[b,c] is V22() set
{b,c} is non empty set
{b} is non empty set
{{b,c},{b}} is non empty set
the Arrows of A . [b,c] is set
d is Element of the carrier of A
<^c,d^> is set
the Arrows of A . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
the Arrows of A . [c,d] is set
a . [b,c] is Relation-like Function-like set
a . [c,d] is Relation-like Function-like set
[b,d] is V22() set
{b,d} is non empty set
{{b,d},{b}} is non empty set
a . [b,d] is Relation-like Function-like set
f is Element of <^b,c^>
(a . [b,c]) . f is set
fa is Element of <^c,d^>
(a . [c,d]) . fa is set
fa * f is Element of <^b,d^>
<^b,d^> is set
the Arrows of A . (b,d) is set
the Arrows of A . [b,d] is set
(a . [b,d]) . (fa * f) is set
fb is Element of the carrier of (A)
g is Element of the carrier of (A)
g is Element of the carrier of (A)
<^fb,g^> is set
the Arrows of (A) . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{fb} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of (A) . [fb,g] is set
<^g,g^> is set
the Arrows of (A) . (g,g) is set
[g,g] is V22() set
{g,g} is non empty set
{g} is non empty set
{{g,g},{g}} is non empty set
the Arrows of (A) . [g,g] is set
c₁₃ is Relation-like Function-like Element of <^fb,g^>
g9 is Relation-like Function-like Element of <^g,g^>
g9 * c₁₃ is Relation-like Function-like Element of <^fb,g^>
<^fb,g^> is set
the Arrows of (A) . (fb,g) is set
[fb,g] is V22() set
{fb,g} is non empty set
{{fb,g},{fb}} is non empty set
the Arrows of (A) . [fb,g] is set
a1 is Element of the carrier of A
b1 is Element of the carrier of A
<^a1,b1^> is set
the Arrows of A . (a1,b1) is set
[a1,b1] is V22() set
{a1,b1} is non empty set
{a1} is non empty set
{{a1,b1},{a1}} is non empty set
the Arrows of A . [a1,b1] is set
((A),a1) is non empty set
((A),b1) is non empty set
[:((A),a1),((A),b1):] is Relation-like non empty set
bool [:((A),a1),((A),b1):] is non empty set
f1 is Element of <^a1,b1^>
G1 is Relation-like ((A),a1) -defined ((A),b1) -valued Function-like non empty V14(((A),a1)) quasi_total Element of bool [:((A),a1),((A),b1):]
b2 is Element of the carrier of A
c2 is Element of the carrier of A
<^b2,c2^> is set
the Arrows of A . (b2,c2) is set
[b2,c2] is V22() set
{b2,c2} is non empty set
{b2} is non empty set
{{b2,c2},{b2}} is non empty set
the Arrows of A . [b2,c2] is set
((A),b2) is non empty set
((A),c2) is non empty set
[:((A),b2),((A),c2):] is Relation-like non empty set
bool [:((A),b2),((A),c2):] is non empty set
g2 is Element of <^b2,c2^>
G2 is Relation-like ((A),b2) -defined ((A),c2) -valued Function-like non empty V14(((A),b2)) quasi_total Element of bool [:((A),b2),((A),c2):]
a3 is Element of the carrier of A
c3 is Element of the carrier of A
<^a3,c3^> is set
the Arrows of A . (a3,c3) is set
[a3,c3] is V22() set
{a3,c3} is non empty set
{a3} is non empty set
{{a3,c3},{a3}} is non empty set
the Arrows of A . [a3,c3] is set
((A),a3) is non empty set
((A),c3) is non empty set
[:((A),a3),((A),c3):] is Relation-like non empty set
bool [:((A),a3),((A),c3):] is non empty set
h3 is Element of <^a3,c3^>
G3 is Relation-like ((A),a3) -defined ((A),c3) -valued Function-like non empty V14(((A),a3)) quasi_total Element of bool [:((A),a3),((A),c3):]
((A),b) is non empty set
((A),c) is non empty set
[:((A),b),((A),c):] is Relation-like non empty set
bool [:((A),b),((A),c):] is non empty set
((A),d) is non empty set
[:((A),c),((A),d):] is Relation-like non empty set
bool [:((A),c),((A),d):] is non empty set
[:((A),b),((A),d):] is Relation-like non empty set
bool [:((A),b),((A),d):] is non empty set
x is Element of ((A),b)
bb is Element of the carrier of A
<^bb,b^> is set
the Arrows of A . (bb,b) is set
[bb,b] is V22() set
{bb,b} is non empty set
{bb} is non empty set
{{bb,b},{bb}} is non empty set
the Arrows of A . [bb,b] is set
ff is Element of <^bb,b^>
[ff,[bb,b]] is V22() set
{ff,[bb,b]} is non empty set
{ff} is non empty set
{{ff,[bb,b]},{ff}} is non empty set
<^bb,c^> is set
the Arrows of A . (bb,c) is set
[bb,c] is V22() set
{bb,c} is non empty set
{{bb,c},{bb}} is non empty set
the Arrows of A . [bb,c] is set
G3 is Relation-like ((A),b) -defined ((A),d) -valued Function-like non empty V14(((A),b)) quasi_total Element of bool [:((A),b),((A),d):]
G3 . x is Element of ((A),d)
(fa * f) * ff is Element of <^bb,d^>
<^bb,d^> is set
the Arrows of A . (bb,d) is set
[bb,d] is V22() set
{bb,d} is non empty set
{{bb,d},{bb}} is non empty set
the Arrows of A . [bb,d] is set
[((fa * f) * ff),[bb,d]] is V22() set
{((fa * f) * ff),[bb,d]} is non empty set
{((fa * f) * ff)} is non empty set
{{((fa * f) * ff),[bb,d]},{((fa * f) * ff)}} is non empty set
f * ff is Element of <^bb,c^>
fa * (f * ff) is Element of <^bb,d^>
[(fa * (f * ff)),[bb,d]] is V22() set
{(fa * (f * ff)),[bb,d]} is non empty set
{(fa * (f * ff))} is non empty set
{{(fa * (f * ff)),[bb,d]},{(fa * (f * ff))}} is non empty set
G2 is Relation-like ((A),c) -defined ((A),d) -valued Function-like non empty V14(((A),c)) quasi_total Element of bool [:((A),c),((A),d):]
[(f * ff),[bb,c]] is V22() set
{(f * ff),[bb,c]} is non empty set
{(f * ff)} is non empty set
{{(f * ff),[bb,c]},{(f * ff)}} is non empty set
G2 . [(f * ff),[bb,c]] is set
G1 is Relation-like ((A),b) -defined ((A),c) -valued Function-like non empty V14(((A),b)) quasi_total Element of bool [:((A),b),((A),c):]
G1 . x is Element of ((A),c)
G2 . (G1 . x) is Element of ((A),d)
G2 * G1 is Relation-like ((A),b) -defined ((A),d) -valued Function-like non empty V14(((A),b)) quasi_total Element of bool [:((A),b),((A),d):]
(G2 * G1) . x is Element of ((A),d)
b is Element of the carrier of A
idm b is retraction coretraction iso mono epi Element of <^b,b^>
<^b,b^> is non empty set
the Arrows of A . (b,b) is set
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the Arrows of A . [b,b] is set
a . [b,b] is Relation-like Function-like set
(a . [b,b]) . (idm b) is set
c is Element of the carrier of (A)
idm c is Relation-like Function-like retraction coretraction iso mono epi Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of (A) . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of (A) . [c,c] is set
d is Element of the carrier of A
f is Element of the carrier of A
<^d,f^> is set
the Arrows of A . (d,f) is set
[d,f] is V22() set
{d,f} is non empty set
{d} is non empty set
{{d,f},{d}} is non empty set
the Arrows of A . [d,f] is set
((A),d) is non empty set
((A),f) is non empty set
[:((A),d),((A),f):] is Relation-like non empty set
bool [:((A),d),((A),f):] is non empty set
fa is Element of <^d,f^>
fb is Relation-like ((A),d) -defined ((A),f) -valued Function-like non empty V14(((A),d)) quasi_total Element of bool [:((A),d),((A),f):]
((A),c) is set
proj1 (idm c) is set
id ((A),c) is Relation-like ((A),c) -defined ((A),c) -valued Function-like one-to-one V14(((A),c)) quasi_total Element of bool [:((A),c),((A),c):]
[:((A),c),((A),c):] is Relation-like set
bool [:((A),c),((A),c):] is non empty set
g is Element of ((A),c)
g is Element of the carrier of A
<^g,b^> is set
the Arrows of A . (g,b) is set
[g,b] is V22() set
{g,b} is non empty set
{g} is non empty set
{{g,b},{g}} is non empty set
the Arrows of A . [g,b] is set
c₁₃ is Element of <^g,b^>
[c₁₃,[g,b]] is V22() set
{c₁₃,[g,b]} is non empty set
{c₁₃} is non empty set
{{c₁₃,[g,b]},{c₁₃}} is non empty set
fb . g is set
(idm b) * c₁₃ is Element of <^g,b^>
[((idm b) * c₁₃),[g,b]] is V22() set
{((idm b) * c₁₃),[g,b]} is non empty set
{((idm b) * c₁₃)} is non empty set
{{((idm b) * c₁₃),[g,b]},{((idm b) * c₁₃)}} is non empty set
(id ((A),c)) . g is set
b is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,(A)
c is Element of the carrier of A
b . c is Element of the carrier of (A)
the ObjectMap of b is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of (A), the carrier of (A):] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is non empty set
the ObjectMap of b . (c,c) is Element of [: the carrier of (A), the carrier of (A):]
[c,c] is V22() set
{c,c} is non empty set
{c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of b . [c,c] is set
( the ObjectMap of b . (c,c)) `1 is set
c is Element of the carrier of A
d is Element of the carrier of A
<^c,d^> is set
the Arrows of A . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
the Arrows of A . [c,d] is set
idm c is retraction coretraction iso mono epi Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of A . (c,c) is set
[c,c] is V22() set
{c,c} is non empty set
{{c,c},{c}} is non empty set
the Arrows of A . [c,c] is set
[(idm c),[c,c]] is V22() set
{(idm c),[c,c]} is non empty set
{(idm c)} is non empty set
{{(idm c),[c,c]},{(idm c)}} is non empty set
f is Element of <^c,d^>
b . f is Relation-like Function-like Element of <^(b . c),(b . d)^>
b . c is Element of the carrier of (A)
the ObjectMap of b is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of (A), the carrier of (A):] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is non empty set
the ObjectMap of b . (c,c) is Element of [: the carrier of (A), the carrier of (A):]
the ObjectMap of b . [c,c] is set
( the ObjectMap of b . (c,c)) `1 is set
b . d is Element of the carrier of (A)
the ObjectMap of b . (d,d) is Element of [: the carrier of (A), the carrier of (A):]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of b . [d,d] is set
( the ObjectMap of b . (d,d)) `1 is set
<^(b . c),(b . d)^> is set
the Arrows of (A) . ((b . c),(b . d)) is set
[(b . c),(b . d)] is V22() set
{(b . c),(b . d)} is non empty set
{(b . c)} is non empty set
{{(b . c),(b . d)},{(b . c)}} is non empty set
the Arrows of (A) . [(b . c),(b . d)] is set
(b . f) . [(idm c),[c,c]] is set
[f,[c,d]] is V22() set
{f,[c,d]} is non empty set
{f} is non empty set
{{f,[c,d]},{f}} is non empty set
a . [c,d] is Relation-like Function-like set
(a . [c,d]) . f is set
fa is Element of the carrier of A
fb is Element of the carrier of A
<^fa,fb^> is set
the Arrows of A . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of A . [fa,fb] is set
((A),fa) is non empty set
((A),fb) is non empty set
[:((A),fa),((A),fb):] is Relation-like non empty set
bool [:((A),fa),((A),fb):] is non empty set
g is Element of <^fa,fb^>
g is Relation-like ((A),fa) -defined ((A),fb) -valued Function-like non empty V14(((A),fa)) quasi_total Element of bool [:((A),fa),((A),fb):]
f * (idm c) is Element of <^c,d^>
[(f * (idm c)),[c,d]] is V22() set
{(f * (idm c)),[c,d]} is non empty set
{(f * (idm c))} is non empty set
{{(f * (idm c)),[c,d]},{(f * (idm c))}} is non empty set
A is non empty transitive associative with_units reflexive AltCatStr
(A) is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
(A) is reflexive feasible strict Covariant id-preserving comp-preserving covariant Functor of A,(A)
the carrier of A is non empty set
a is Element of the carrier of A
(A) . a is Element of the carrier of (A)
the carrier of (A) is non empty set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
the ObjectMap of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of (A), the carrier of (A):] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:]
[: the carrier of A, the carrier of A:] is Relation-like non empty set
[:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is non empty set
the ObjectMap of (A) . (a,a) is Element of [: the carrier of (A), the carrier of (A):]
[a,a] is V22() set
{a,a} is non empty set
{a} is non empty set
{{a,a},{a}} is non empty set
the ObjectMap of (A) . [a,a] is set
( the ObjectMap of (A) . (a,a)) `1 is set
a is Element of the carrier of A
b is Element of the carrier of A
<^a,b^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
c is Element of <^a,b^>
(A) . c is Relation-like Function-like Element of <^((A) . a),((A) . b)^>
(A) . a is Element of the carrier of (A)
the carrier of (A) is non empty set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
the ObjectMap of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of (A), the carrier of (A):] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is non empty set
the ObjectMap of (A) . (a,a) is Element of [: the carrier of (A), the carrier of (A):]
[a,a] is V22() set
{a,a} is non empty set
{{a,a},{a}} is non empty set
the ObjectMap of (A) . [a,a] is set
( the ObjectMap of (A) . (a,a)) `1 is set
(A) . b is Element of the carrier of (A)
the ObjectMap of (A) . (b,b) is Element of [: the carrier of (A), the carrier of (A):]
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of (A) . [b,b] is set
( the ObjectMap of (A) . (b,b)) `1 is set
<^((A) . a),((A) . b)^> is set
the Arrows of (A) is Relation-like [: the carrier of (A), the carrier of (A):] -defined Function-like non empty V14([: the carrier of (A), the carrier of (A):]) set
the Arrows of (A) . (((A) . a),((A) . b)) is set
[((A) . a),((A) . b)] is V22() set
{((A) . a),((A) . b)} is non empty set
{((A) . a)} is non empty set
{{((A) . a),((A) . b)},{((A) . a)}} is non empty set
the Arrows of (A) . [((A) . a),((A) . b)] is set
a is Element of the carrier of A
b is Element of the carrier of A
a is Element of the carrier of A
b is Element of the carrier of A
<^a,b^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of A . [a,b] is set
c is Element of <^a,b^>
(A) . c is Relation-like Function-like Element of <^((A) . a),((A) . b)^>
(A) . a is Element of the carrier of (A)
the carrier of (A) is non empty set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
the ObjectMap of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of (A), the carrier of (A):] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is non empty set
the ObjectMap of (A) . (a,a) is Element of [: the carrier of (A), the carrier of (A):]
[a,a] is V22() set
{a,a} is non empty set
{{a,a},{a}} is non empty set
the ObjectMap of (A) . [a,a] is set
( the ObjectMap of (A) . (a,a)) `1 is set
(A) . b is Element of the carrier of (A)
the ObjectMap of (A) . (b,b) is Element of [: the carrier of (A), the carrier of (A):]
[b,b] is V22() set
{b,b} is non empty set
{b} is non empty set
{{b,b},{b}} is non empty set
the ObjectMap of (A) . [b,b] is set
( the ObjectMap of (A) . (b,b)) `1 is set
<^((A) . a),((A) . b)^> is set
the Arrows of (A) is Relation-like [: the carrier of (A), the carrier of (A):] -defined Function-like non empty V14([: the carrier of (A), the carrier of (A):]) set
the Arrows of (A) . (((A) . a),((A) . b)) is set
[((A) . a),((A) . b)] is V22() set
{((A) . a),((A) . b)} is non empty set
{((A) . a)} is non empty set
{{((A) . a),((A) . b)},{((A) . a)}} is non empty set
the Arrows of (A) . [((A) . a),((A) . b)] is set
d is Element of <^a,b^>
(A) . d is Relation-like Function-like Element of <^((A) . a),((A) . b)^>
idm a is retraction coretraction iso mono epi Element of <^a,a^>
<^a,a^> is non empty set
the Arrows of A . (a,a) is set
the Arrows of A . [a,a] is set
[(idm a),[a,a]] is V22() set
{(idm a),[a,a]} is non empty set
{(idm a)} is non empty set
{{(idm a),[a,a]},{(idm a)}} is non empty set
((A) . c) . [(idm a),[a,a]] is set
[c,[a,b]] is V22() set
{c,[a,b]} is non empty set
{c} is non empty set
{{c,[a,b]},{c}} is non empty set
((A) . d) . [(idm a),[a,a]] is set
[d,[a,b]] is V22() set
{d,[a,b]} is non empty set
{d} is non empty set
{{d,[a,b]},{d}} is non empty set
the carrier of (A) is non empty set
a is Element of the carrier of (A)
b is Element of the carrier of (A)
<^a,b^> is set
the Arrows of (A) is Relation-like [: the carrier of (A), the carrier of (A):] -defined Function-like non empty V14([: the carrier of (A), the carrier of (A):]) set
[: the carrier of (A), the carrier of (A):] is Relation-like non empty set
the Arrows of (A) . (a,b) is set
[a,b] is V22() set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the Arrows of (A) . [a,b] is set
f is Relation-like Function-like Element of <^a,b^>
c is Element of the carrier of A
d is Element of the carrier of A
<^c,d^> is set
the Arrows of A is Relation-like [: the carrier of A, the carrier of A:] -defined Function-like non empty V14([: the carrier of A, the carrier of A:]) set
[: the carrier of A, the carrier of A:] is Relation-like non empty set
the Arrows of A . (c,d) is set
[c,d] is V22() set
{c,d} is non empty set
{c} is non empty set
{{c,d},{c}} is non empty set
the Arrows of A . [c,d] is set
fa is Element of the carrier of A
fb is Element of the carrier of A
<^fa,fb^> is set
the Arrows of A . (fa,fb) is set
[fa,fb] is V22() set
{fa,fb} is non empty set
{fa} is non empty set
{{fa,fb},{fa}} is non empty set
the Arrows of A . [fa,fb] is set
g is Element of <^fa,fb^>
g is Element of <^c,d^>
(A) . g is Relation-like Function-like Element of <^((A) . c),((A) . d)^>
(A) . c is Element of the carrier of (A)
the ObjectMap of (A) is Relation-like [: the carrier of A, the carrier of A:] -defined [: the carrier of (A), the carrier of (A):] -valued Function-like non empty V14([: the carrier of A, the carrier of A:]) quasi_total Element of bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:]
[:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is Relation-like non empty set
bool [:[: the carrier of A, the carrier of A:],[: the carrier of (A), the carrier of (A):]:] is non empty set
the ObjectMap of (A) . (c,c) is Element of [: the carrier of (A), the carrier of (A):]
[c,c] is V22() set
{c,c} is non empty set
{{c,c},{c}} is non empty set
the ObjectMap of (A) . [c,c] is set
( the ObjectMap of (A) . (c,c)) `1 is set
(A) . d is Element of the carrier of (A)
the ObjectMap of (A) . (d,d) is Element of [: the carrier of (A), the carrier of (A):]
[d,d] is V22() set
{d,d} is non empty set
{d} is non empty set
{{d,d},{d}} is non empty set
the ObjectMap of (A) . [d,d] is set
( the ObjectMap of (A) . (d,d)) `1 is set
<^((A) . c),((A) . d)^> is set
the Arrows of (A) . (((A) . c),((A) . d)) is set
[((A) . c),((A) . d)] is V22() set
{((A) . c),((A) . d)} is non empty set
{((A) . c)} is non empty set
{{((A) . c),((A) . d)},{((A) . c)}} is non empty set
the Arrows of (A) . [((A) . c),((A) . d)] is set
idm c is retraction coretraction iso mono epi Element of <^c,c^>
<^c,c^> is non empty set
the Arrows of A . (c,c) is set
the Arrows of A . [c,c] is set
[(idm c),[c,c]] is V22() set
{(idm c),[c,c]} is non empty set
{(idm c)} is non empty set
{{(idm c),[c,c]},{(idm c)}} is non empty set
((A) . g) . [(idm c),[c,c]] is set
[g,[c,d]] is V22() set
{g,[c,d]} is non empty set
{g} is non empty set
{{g,[c,d]},{g}} is non empty set
g * (idm c) is Element of <^c,d^>
f . [(idm c),[c,c]] is set
A is non empty transitive associative with_units reflexive AltCatStr
(A) is non empty transitive strict semi-functional associative with_units reflexive () () () AltCatStr
(A) is reflexive feasible strict Covariant id-preserving comp-preserving covariant bijective Functor of A,(A)