:: CAT_4 semantic presentation

K93() is set
K97() is non empty non trivial V24() V25() V26() non finite cardinal limit_cardinal Element of bool K93()
bool K93() is set
K92() is non empty non trivial V24() V25() V26() non finite cardinal limit_cardinal set
bool K92() is non trivial non finite set
bool K97() is non trivial non finite set
{} is Function-like functional empty V24() V25() V26() V28() V29() V30() V31() V32() V33() V35() finite V40() cardinal {} -element set
1 is non empty V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K97()
card {} is Function-like functional empty V24() V25() V26() V28() V29() V30() V31() V32() V33() V35() finite V40() cardinal {} -element set
C is non empty non void V57() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
Hom (c,a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = a ) } is set
id c is Morphism of c,c
id a is Morphism of a,a
d is Morphism of c,a
b is Morphism of a,c
b * d is Morphism of c,c
d * b is Morphism of a,a
C is non empty non void V57() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
[:{}, the carrier of C:] is set
bool [:{}, the carrier of C:] is set
a is Relation-like {} -defined the carrier of C -valued Function-like one-to-one constant functional empty total V18( {} , the carrier of C) V24() V25() V26() V28() V29() V30() V31() V32() V33() V35() finite finite-yielding V40() cardinal {} -element Element of bool [:{}, the carrier of C:]
c is Element of the carrier of C
b is Relation-like {} -defined the carrier' of C -valued Function-like one-to-one constant functional empty total V18( {} , the carrier' of C) V24() V25() V26() V28() V29() V30() V31() V32() V33() V35() finite finite-yielding V40() cardinal {} -element Projections_family of c, {}
cods b is Relation-like {} -defined the carrier of C -valued Function-like one-to-one constant functional empty total V18( {} , the carrier of C) V24() V25() V26() V28() V29() V30() V31() V32() V33() V35() finite finite-yielding V40() cardinal {} -element Element of bool [:{}, the carrier of C:]
d is Element of the carrier of C
e is Element of the carrier of C
({},1) --> (d,e) is Relation-like {{},1} -defined the carrier of C -valued Function-like non empty total V18({{},1}, the carrier of C) finite Element of bool [:{{},1}, the carrier of C:]
{{},1} is non empty finite V40() set
[:{{},1}, the carrier of C:] is set
bool [:{{},1}, the carrier of C:] is set
f is Element of the carrier of C
h is Relation-like {{},1} -defined the carrier' of C -valued Function-like non empty total V18({{},1}, the carrier' of C) finite Projections_family of f,{{},1}
cods h is Relation-like {{},1} -defined the carrier of C -valued Function-like non empty total V18({{},1}, the carrier of C) finite Element of bool [:{{},1}, the carrier of C:]
h /. {} is Element of the carrier' of C
g is Element of the carrier' of C
dom g is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . g is Element of the carrier of C
cod g is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . g is Element of the carrier of C
h /. 1 is Element of the carrier' of C
k is Element of the carrier' of C
dom k is Element of the carrier of C
the Source of C . k is Element of the carrier of C
cod k is Element of the carrier of C
the Target of C . k is Element of the carrier of C
h . 1 is set
(({},1) --> (d,e)) /. {} is Element of the carrier of C
(({},1) --> (d,e)) /. 1 is Element of the carrier of C
dom h is finite V40() Element of bool {{},1}
bool {{},1} is finite V40() set
h . {} is set
({},1) --> (g,k) is Relation-like {{},1} -defined the carrier' of C -valued Function-like non empty total V18({{},1}, the carrier' of C) finite Element of bool [:{{},1}, the carrier' of C:]
[:{{},1}, the carrier' of C:] is set
bool [:{{},1}, the carrier' of C:] is set
a is Element of the carrier of C
c is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal set
c + 1 is non empty V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal set
b is finite set
[:b, the carrier of C:] is set
bool [:b, the carrier of C:] is set
card b is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
d is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
the Element of b is Element of b
{ the Element of b} is non empty trivial finite 1 -element set
b \ { the Element of b} is finite Element of bool b
bool b is finite V40() set
[:(b \ { the Element of b}), the carrier of C:] is set
bool [:(b \ { the Element of b}), the carrier of C:] is set
d | (b \ { the Element of b}) is Relation-like b -defined the carrier of C -valued Function-like finite Element of bool [:b, the carrier of C:]
s is finite set
card s is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
f is finite set
card f is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
(card b) - (card f) is V31() V32() V33() set
(card b) - 1 is V31() V32() V33() set
h is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
g is Element of the carrier of C
k is Relation-like b \ { the Element of b} -defined the carrier' of C -valued Function-like total V18(b \ { the Element of b}, the carrier' of C) finite Projections_family of g,b \ { the Element of b}
cods k is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
d /. the Element of b is Element of the carrier of C
c is Element of the carrier' of C
dom c is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . c is Element of the carrier of C
b is Element of the carrier of C
i1 is Element of the carrier' of C
dom i1 is Element of the carrier of C
the Source of C . i1 is Element of the carrier of C
cod c is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . c is Element of the carrier of C
cod i1 is Element of the carrier of C
the Target of C . i1 is Element of the carrier of C
k * c is Relation-like b \ { the Element of b} -defined the carrier' of C -valued Function-like total V18(b \ { the Element of b}, the carrier' of C) finite Element of bool [:(b \ { the Element of b}), the carrier' of C:]
[:(b \ { the Element of b}), the carrier' of C:] is set
bool [:(b \ { the Element of b}), the carrier' of C:] is set
the Element of b .--> i1 is Relation-like { the Element of b} -defined the carrier' of C -valued Function-like non empty total V18({ the Element of b}, the carrier' of C) finite Element of bool [:{ the Element of b}, the carrier' of C:]
[:{ the Element of b}, the carrier' of C:] is set
bool [:{ the Element of b}, the carrier' of C:] is set
{ the Element of b} --> i1 is Relation-like { the Element of b} -defined {i1} -valued Function-like non empty total V18({ the Element of b},{i1}) finite Element of bool [:{ the Element of b},{i1}:]
{i1} is non empty trivial finite 1 -element set
[:{ the Element of b},{i1}:] is finite set
bool [:{ the Element of b},{i1}:] is finite V40() set
(k * c) +* ( the Element of b .--> i1) is Relation-like Function-like finite set
{ the Element of b} --> i1 is Relation-like { the Element of b} -defined the carrier' of C -valued Function-like non empty total V18({ the Element of b}, the carrier' of C) finite Element of bool [:{ the Element of b}, the carrier' of C:]
dom ({ the Element of b} --> i1) is finite Element of bool { the Element of b}
bool { the Element of b} is finite V40() set
rng ((k * c) +* ( the Element of b .--> i1)) is finite set
rng (k * c) is finite Element of bool the carrier' of C
bool the carrier' of C is set
rng ( the Element of b .--> i1) is finite Element of bool the carrier' of C
(rng (k * c)) \/ (rng ( the Element of b .--> i1)) is finite Element of bool the carrier' of C
dom (k * c) is finite Element of bool (b \ { the Element of b})
bool (b \ { the Element of b}) is finite V40() set
dom ( the Element of b .--> i1) is finite Element of bool { the Element of b}
(dom (k * c)) \/ (dom ( the Element of b .--> i1)) is finite set
b \/ { the Element of b} is non empty finite set
dom ((k * c) +* ( the Element of b .--> i1)) is finite set
[:b, the carrier' of C:] is set
bool [:b, the carrier' of C:] is set
doms k is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(b \ { the Element of b}) --> g is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
{g} is non empty trivial finite 1 -element set
[:(b \ { the Element of b}),{g}:] is finite set
F9 is set
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Element of bool [:b, the carrier' of C:]
F9 /. F9 is Element of the carrier' of C
F9 . F9 is set
( the Element of b .--> i1) . F9 is set
b --> b is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
{b} is non empty trivial finite 1 -element set
[:b,{b}:] is finite set
(b --> b) . F9 is set
dom (F9 /. F9) is Element of the carrier of C
the Source of C . (F9 /. F9) is Element of the carrier of C
doms F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
(doms F9) /. F9 is Element of the carrier of C
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Element of bool [:b, the carrier' of C:]
F9 /. F9 is Element of the carrier' of C
F9 . F9 is set
(k * c) . F9 is set
(k * c) /. F9 is Element of the carrier' of C
doms F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
(doms F9) /. F9 is Element of the carrier of C
dom ((k * c) /. F9) is Element of the carrier of C
the Source of C . ((k * c) /. F9) is Element of the carrier of C
doms (k * c) is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(doms (k * c)) /. F9 is Element of the carrier of C
(b \ { the Element of b}) --> b is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
{b} is non empty trivial finite 1 -element set
[:(b \ { the Element of b}),{b}:] is finite set
((b \ { the Element of b}) --> b) /. F9 is Element of the carrier of C
b --> b is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
[:b,{b}:] is finite set
(b --> b) . F9 is set
b --> b is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
{b} is non empty trivial finite 1 -element set
[:b,{b}:] is finite set
(b --> b) . F9 is set
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Element of bool [:b, the carrier' of C:]
doms F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
(doms F9) /. F9 is Element of the carrier of C
b --> b is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
{b} is non empty trivial finite 1 -element set
[:b,{b}:] is finite set
(b --> b) . F9 is set
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Element of bool [:b, the carrier' of C:]
doms F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
(doms F9) /. F9 is Element of the carrier of C
(doms F9) . F9 is set
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Projections_family of b,b
cods F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
F9 is set
F9 /. F9 is Element of the carrier' of C
F9 . F9 is set
( the Element of b .--> i1) . F9 is set
(cods F9) /. F9 is Element of the carrier of C
d /. F9 is Element of the carrier of C
F9 /. F9 is Element of the carrier' of C
F9 . F9 is set
(k * c) . F9 is set
(k * c) /. F9 is Element of the carrier' of C
(cods F9) /. F9 is Element of the carrier of C
cod ((k * c) /. F9) is Element of the carrier of C
the Target of C . ((k * c) /. F9) is Element of the carrier of C
cods (k * c) is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(cods (k * c)) /. F9 is Element of the carrier of C
h /. F9 is Element of the carrier of C
h . F9 is set
d . F9 is set
d /. F9 is Element of the carrier of C
(cods F9) /. F9 is Element of the carrier of C
d /. F9 is Element of the carrier of C
(cods F9) /. F9 is Element of the carrier of C
d /. F9 is Element of the carrier of C
F9 is Element of the carrier of C
Hom (F9,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = F9 & cod b₁ = b ) } is set
d is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Projections_family of F9,b
cods d is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
d | (b \ { the Element of b}) is Relation-like b -defined the carrier' of C -valued Function-like finite Element of bool [:b, the carrier' of C:]
G99 is set
F99 is Relation-like b \ { the Element of b} -defined the carrier' of C -valued Function-like total V18(b \ { the Element of b}, the carrier' of C) finite Element of bool [:(b \ { the Element of b}), the carrier' of C:]
F99 /. G99 is Element of the carrier' of C
F99 . G99 is set
d . G99 is set
d /. G99 is Element of the carrier' of C
doms F99 is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(doms F99) /. G99 is Element of the carrier of C
dom (d /. G99) is Element of the carrier of C
the Source of C . (d /. G99) is Element of the carrier of C
(b \ { the Element of b}) --> F9 is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
{F9} is non empty trivial finite 1 -element set
[:(b \ { the Element of b}),{F9}:] is finite set
((b \ { the Element of b}) --> F9) /. G99 is Element of the carrier of C
G99 is set
h /. G99 is Element of the carrier of C
h . G99 is set
d . G99 is set
d /. G99 is Element of the carrier of C
d /. G99 is Element of the carrier' of C
d . G99 is set
G99 is Relation-like b \ { the Element of b} -defined the carrier' of C -valued Function-like total V18(b \ { the Element of b}, the carrier' of C) finite Projections_family of F9,b \ { the Element of b}
G99 . G99 is set
G99 /. G99 is Element of the carrier' of C
(cods k) /. G99 is Element of the carrier of C
cod (G99 /. G99) is Element of the carrier of C
the Target of C . (G99 /. G99) is Element of the carrier of C
cods G99 is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(cods G99) /. G99 is Element of the carrier of C
Hom (F9,g) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = F9 & cod b₁ = g ) } is set
G99 is Element of the carrier' of C
d /. the Element of b is Element of the carrier' of C
dom (d /. the Element of b) is Element of the carrier of C
the Source of C . (d /. the Element of b) is Element of the carrier of C
F9 /. the Element of b is Element of the carrier' of C
F9 . the Element of b is set
( the Element of b .--> i1) . the Element of b is set
(cods F9) /. the Element of b is Element of the carrier of C
cod (d /. the Element of b) is Element of the carrier of C
the Target of C . (d /. the Element of b) is Element of the carrier of C
Hom (F9,(cod i1)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = F9 & cod b₁ = cod i1 ) } is set
g is Element of the carrier' of C
h is Element of the carrier' of C
cod h is Element of the carrier of C
the Target of C . h is Element of the carrier of C
c (*) h is Element of the carrier' of C
cod (c (*) h) is Element of the carrier of C
the Target of C . (c (*) h) is Element of the carrier of C
k is set
k /. k is Element of the carrier' of C
(k /. k) (*) (c (*) h) is Element of the carrier' of C
G99 /. k is Element of the carrier' of C
F9 /. k is Element of the carrier' of C
F9 . k is set
(k * c) . k is set
(k * c) /. k is Element of the carrier' of C
dom (k /. k) is Element of the carrier of C
the Source of C . (k /. k) is Element of the carrier of C
(k /. k) (*) c is Element of the carrier' of C
((k /. k) (*) c) (*) h is Element of the carrier' of C
((k * c) /. k) (*) h is Element of the carrier' of C
d /. k is Element of the carrier' of C
d . k is set
G99 . k is set
dom h is Element of the carrier of C
the Source of C . h is Element of the carrier of C
dom (c (*) h) is Element of the carrier of C
the Source of C . (c (*) h) is Element of the carrier of C
i1 (*) h is Element of the carrier' of C
k is set
F9 /. k is Element of the carrier' of C
(F9 /. k) (*) h is Element of the carrier' of C
d /. k is Element of the carrier' of C
F9 . k is set
( the Element of b .--> i1) . k is set
cod h is Element of the carrier of C
the Target of C . h is Element of the carrier of C
k /. k is Element of the carrier' of C
dom (k /. k) is Element of the carrier of C
the Source of C . (k /. k) is Element of the carrier of C
F9 . k is set
(k * c) . k is set
(k * c) /. k is Element of the carrier' of C
(k /. k) (*) c is Element of the carrier' of C
c (*) h is Element of the carrier' of C
(k /. k) (*) (c (*) h) is Element of the carrier' of C
(k /. k) (*) G99 is Element of the carrier' of C
G99 /. k is Element of the carrier' of C
G99 . k is set
d . k is set
c is finite set
[:c, the carrier of C:] is set
bool [:c, the carrier of C:] is set
b is Relation-like c -defined the carrier of C -valued Function-like total V18(c, the carrier of C) finite Element of bool [:c, the carrier of C:]
card c is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
d is finite set
[:d, the carrier of C:] is set
bool [:d, the carrier of C:] is set
card d is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
e is Relation-like d -defined the carrier of C -valued Function-like total V18(d, the carrier of C) finite Element of bool [:d, the carrier of C:]
[:{}, the carrier' of C:] is set
bool [:{}, the carrier' of C:] is set
s is Relation-like d -defined the carrier' of C -valued Function-like total V18(d, the carrier' of C) finite Projections_family of a,d
cods s is Relation-like d -defined the carrier of C -valued Function-like total V18(d, the carrier of C) finite Element of bool [:d, the carrier of C:]
f is set
(cods s) /. f is Element of the carrier of C
e /. f is Element of the carrier of C
the set is set
{ the set } is non empty trivial finite 1 -element set
the set :-> the set is Relation-like { the set } -defined { the set } -valued Function-like non empty total V18({ the set },{ the set }) finite Element of bool [:{ the set },{ the set }:]
[:{ the set },{ the set }:] is finite set
bool [:{ the set },{ the set }:] is finite V40() set
{ the set } --> the set is Relation-like { the set } -defined { the set } -valued Function-like non empty total V18({ the set },{ the set }) finite Element of bool [:{ the set },{ the set }:]
( the set , the set ) :-> the set is Relation-like [:{ the set },{ the set }:] -defined { the set } -valued Function-like total V18([:{ the set },{ the set }:],{ the set }) finite Element of bool [:[:{ the set },{ the set }:],{ the set }:]
[:[:{ the set },{ the set }:],{ the set }:] is finite set
bool [:[:{ the set },{ the set }:],{ the set }:] is finite V40() set
[ the set , the set ] is set
{[ the set , the set ]} is Function-like non empty trivial finite 1 -element set
{[ the set , the set ]} --> the set is Relation-like {[ the set , the set ]} -defined { the set } -valued Function-like non empty total V18({[ the set , the set ]},{ the set }) finite Element of bool [:{[ the set , the set ]},{ the set }:]
[:{[ the set , the set ]},{ the set }:] is finite set
bool [:{[ the set , the set ]},{ the set }:] is finite V40() set
Extract the set is Element of { the set }
({ the set },{ the set },( the set :-> the set ),( the set :-> the set ),(( the set , the set ) :-> the set ),(Extract the set ),(( the set , the set ) :-> the set ),(( the set , the set ) :-> the set ),(( the set , the set ) :-> the set )) is () ()
C is non empty non void V57() ()
the of C is Element of the carrier of C
the carrier of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
a is Element of the carrier of C
c is Element of the carrier of C
the of C . (a,c) is Element of the carrier of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
C is set
{C} is non empty trivial finite 1 -element set
a is set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
C is set
a is set
(C,a) is () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
the Source of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Target of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
the Comp of (C,a) is Relation-like [: the carrier' of (C,a), the carrier' of (C,a):] -defined the carrier' of (C,a) -valued Function-like finite Element of bool [:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):]
[: the carrier' of (C,a), the carrier' of (C,a):] is finite set
[:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):] is finite set
bool [:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):] is finite V40() set
CatStr(# the carrier of (C,a), the carrier' of (C,a), the Source of (C,a), the Target of (C,a), the Comp of (C,a) #) is strict CatStr
1Cat (C,a) is non empty trivial finite non void 1 -element V57() trivial' strict Category-like transitive associative reflexive with_identities CatStr
CatStr(# {C},{a},(a :-> C),(a :-> C),((a,a) :-> a) #) is strict CatStr
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the Comp of (C,a) is Relation-like [: the carrier' of (C,a), the carrier' of (C,a):] -defined the carrier' of (C,a) -valued Function-like finite Element of bool [:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):]
the carrier' of (C,a) is non empty trivial finite 1 -element set
[: the carrier' of (C,a), the carrier' of (C,a):] is finite set
[:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):] is finite set
bool [:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):] is finite V40() set
the Source of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
the carrier of (C,a) is non empty trivial finite 1 -element set
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Target of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
dom the Comp of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier' of (C,a) -valued finite Element of bool [: the carrier' of (C,a), the carrier' of (C,a):]
bool [: the carrier' of (C,a), the carrier' of (C,a):] is finite V40() set
f is Element of the carrier' of (C,a)
s is Element of the carrier' of (C,a)
[f,s] is set
dom f is Element of the carrier of (C,a)
the Source of (C,a) . f is Element of the carrier of (C,a)
cod s is Element of the carrier of (C,a)
the Target of (C,a) . s is Element of the carrier of (C,a)
({},1) is non empty trivial finite non void 1 -element V57() trivial' transitive associative reflexive with_identities () ()
{{}} is non empty trivial finite V40() 1 -element set
{1} is non empty trivial finite V40() 1 -element set
1 :-> {} is Relation-like {1} -defined {{}} -valued Function-like non empty total V18({1},{{}}) finite Element of bool [:{1},{{}}:]
[:{1},{{}}:] is finite set
bool [:{1},{{}}:] is finite V40() set
{1} --> {} is Relation-like {1} -defined {{}} -valued Function-like non empty total V18({1},{{}}) finite Element of bool [:{1},{{}}:]
(1,1) :-> 1 is Relation-like [:{1},{1}:] -defined {1} -valued Function-like total V18([:{1},{1}:],{1}) finite Element of bool [:[:{1},{1}:],{1}:]
[:{1},{1}:] is finite set
[:[:{1},{1}:],{1}:] is finite set
bool [:[:{1},{1}:],{1}:] is finite V40() set
[1,1] is set
{[1,1]} is Function-like non empty trivial finite 1 -element set
{[1,1]} --> 1 is Relation-like {[1,1]} -defined {1} -valued Function-like non empty total V18({[1,1]},{1}) finite Element of bool [:{[1,1]},{1}:]
[:{[1,1]},{1}:] is finite set
bool [:{[1,1]},{1}:] is finite V40() set
Extract {} is finite Element of {{}}
({},{}) :-> {} is Relation-like [:{{}},{{}}:] -defined {{}} -valued Function-like total V18([:{{}},{{}}:],{{}}) finite Element of bool [:[:{{}},{{}}:],{{}}:]
[:{{}},{{}}:] is finite set
[:[:{{}},{{}}:],{{}}:] is finite set
bool [:[:{{}},{{}}:],{{}}:] is finite V40() set
[{},{}] is set
{[{},{}]} is Function-like non empty trivial finite 1 -element set
{[{},{}]} --> {} is Relation-like {[{},{}]} -defined {{}} -valued Function-like non empty total V18({[{},{}]},{{}}) finite Element of bool [:{[{},{}]},{{}}:]
[:{[{},{}]},{{}}:] is finite set
bool [:{[{},{}]},{{}}:] is finite V40() set
({},{}) :-> 1 is Relation-like [:{{}},{{}}:] -defined {1} -valued Function-like total V18([:{{}},{{}}:],{1}) finite Element of bool [:[:{{}},{{}}:],{1}:]
[:[:{{}},{{}}:],{1}:] is finite set
bool [:[:{{}},{{}}:],{1}:] is finite V40() set
{[{},{}]} --> 1 is Relation-like {[{},{}]} -defined {1} -valued Function-like non empty total V18({[{},{}]},{1}) finite Element of bool [:{[{},{}]},{1}:]
[:{[{},{}]},{1}:] is finite set
bool [:{[{},{}]},{1}:] is finite V40() set
({{}},{1},(1 :-> {}),(1 :-> {}),((1,1) :-> 1),(Extract {}),(({},{}) :-> {}),(({},{}) :-> 1),(({},{}) :-> 1)) is () ()
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier' of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier' of (C,a)
b is Element of the carrier' of (C,a)
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
Hom (c,b) is finite Element of bool the carrier' of (C,a)
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = c & cod b₁ = b ) } is set
d is Element of the carrier' of (C,a)
cod d is Element of the carrier of (C,a)
the Target of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Target of (C,a) . d is Element of the carrier of (C,a)
dom d is Element of the carrier of (C,a)
the Source of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
the Source of (C,a) . d is Element of the carrier of (C,a)
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
d is Element of the carrier' of (C,a)
Hom (c,b) is finite Element of bool the carrier' of (C,a)
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = c & cod b₁ = b ) } is set
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
Hom (c,b) is finite Element of bool the carrier' of (C,a)
the carrier' of (C,a) is non empty trivial finite 1 -element set
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = c & cod b₁ = b ) } is set
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
Hom (b,c) is finite Element of bool the carrier' of (C,a)
the carrier' of (C,a) is non empty trivial finite 1 -element set
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = b & cod b₁ = c ) } is set
the Morphism of b,c is Morphism of b,c
e is Morphism of b,c
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier' of (C,a)
d is Element of the carrier' of (C,a)
dom b is Element of the carrier of (C,a)
the Source of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Source of (C,a) . b is Element of the carrier of (C,a)
dom d is Element of the carrier of (C,a)
the Source of (C,a) . d is Element of the carrier of (C,a)
cod b is Element of the carrier of (C,a)
the Target of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
the Target of (C,a) . b is Element of the carrier of (C,a)
cod d is Element of the carrier of (C,a)
the Target of (C,a) . d is Element of the carrier of (C,a)
e is Element of the carrier of (C,a)
Hom (e,(cod b)) is finite Element of bool the carrier' of (C,a)
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = e & cod b₁ = cod b ) } is set
Hom (e,(cod d)) is finite Element of bool the carrier' of (C,a)
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = e & cod b₁ = cod d ) } is set
Hom (e,c) is finite Element of bool the carrier' of (C,a)
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = e & cod b₁ = c ) } is set
s is Element of the carrier' of (C,a)
f is Element of the carrier' of (C,a)
h is Element of the carrier' of (C,a)
g is Element of the carrier' of (C,a)
b (*) g is Element of the carrier' of (C,a)
d (*) g is Element of the carrier' of (C,a)
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the of (C,a) is Element of the carrier of (C,a)
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
the of (C,a) is Relation-like [: the carrier of (C,a), the carrier of (C,a):] -defined the carrier' of (C,a) -valued Function-like total V18([: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a)) finite Element of bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a):]
[: the carrier of (C,a), the carrier of (C,a):] is finite set
[:[: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a):] is finite set
bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a):] is finite V40() set
the of (C,a) is Relation-like [: the carrier of (C,a), the carrier of (C,a):] -defined the carrier' of (C,a) -valued Function-like total V18([: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a)) finite Element of bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a):]
the of (C,a) is Relation-like [: the carrier of (C,a), the carrier of (C,a):] -defined the carrier of (C,a) -valued Function-like total V18([: the carrier of (C,a), the carrier of (C,a):], the carrier of (C,a)) finite Element of bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier of (C,a):]
[:[: the carrier of (C,a), the carrier of (C,a):], the carrier of (C,a):] is finite set
bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier of (C,a):] is finite V40() set
b is Element of the carrier of (C,a)
d is Element of the carrier of (C,a)
the of (C,a) . (b,d) is Element of the carrier' of (C,a)
cod ( the of (C,a) . (b,d)) is Element of the carrier of (C,a)
the Target of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Target of (C,a) . ( the of (C,a) . (b,d)) is Element of the carrier of (C,a)
the of (C,a) . (b,d) is Element of the carrier' of (C,a)
cod ( the of (C,a) . (b,d)) is Element of the carrier of (C,a)
the Target of (C,a) . ( the of (C,a) . (b,d)) is Element of the carrier of (C,a)
the of (C,a) . (b,d) is Element of the carrier of (C,a)
({},1) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{{}} is non empty trivial finite V40() 1 -element set
{1} is non empty trivial finite V40() 1 -element set
1 :-> {} is Relation-like {1} -defined {{}} -valued Function-like non empty total V18({1},{{}}) finite Element of bool [:{1},{{}}:]
[:{1},{{}}:] is finite set
bool [:{1},{{}}:] is finite V40() set
{1} --> {} is Relation-like {1} -defined {{}} -valued Function-like non empty total V18({1},{{}}) finite Element of bool [:{1},{{}}:]
(1,1) :-> 1 is Relation-like [:{1},{1}:] -defined {1} -valued Function-like total V18([:{1},{1}:],{1}) finite Element of bool [:[:{1},{1}:],{1}:]
[:{1},{1}:] is finite set
[:[:{1},{1}:],{1}:] is finite set
bool [:[:{1},{1}:],{1}:] is finite V40() set
[1,1] is set
{[1,1]} is Function-like non empty trivial finite 1 -element set
{[1,1]} --> 1 is Relation-like {[1,1]} -defined {1} -valued Function-like non empty total V18({[1,1]},{1}) finite Element of bool [:{[1,1]},{1}:]
[:{[1,1]},{1}:] is finite set
bool [:{[1,1]},{1}:] is finite V40() set
Extract {} is finite Element of {{}}
({},{}) :-> {} is Relation-like [:{{}},{{}}:] -defined {{}} -valued Function-like total V18([:{{}},{{}}:],{{}}) finite Element of bool [:[:{{}},{{}}:],{{}}:]
[:{{}},{{}}:] is finite set
[:[:{{}},{{}}:],{{}}:] is finite set
bool [:[:{{}},{{}}:],{{}}:] is finite V40() set
[{},{}] is set
{[{},{}]} is Function-like non empty trivial finite 1 -element set
{[{},{}]} --> {} is Relation-like {[{},{}]} -defined {{}} -valued Function-like non empty total V18({[{},{}]},{{}}) finite Element of bool [:{[{},{}]},{{}}:]
[:{[{},{}]},{{}}:] is finite set
bool [:{[{},{}]},{{}}:] is finite V40() set
({},{}) :-> 1 is Relation-like [:{{}},{{}}:] -defined {1} -valued Function-like total V18([:{{}},{{}}:],{1}) finite Element of bool [:[:{{}},{{}}:],{1}:]
[:[:{{}},{{}}:],{1}:] is finite set
bool [:[:{{}},{{}}:],{1}:] is finite V40() set
{[{},{}]} --> 1 is Relation-like {[{},{}]} -defined {1} -valued Function-like non empty total V18({[{},{}]},{1}) finite Element of bool [:{[{},{}]},{1}:]
[:{[{},{}]},{1}:] is finite set
bool [:{[{},{}]},{1}:] is finite V40() set
({{}},{1},(1 :-> {}),(1 :-> {}),((1,1) :-> 1),(Extract {}),(({},{}) :-> {}),(({},{}) :-> 1),(({},{}) :-> 1)) is () ()
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
(C) is Element of the carrier of C
the carrier of C is non empty set
the of C is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
c is Morphism of a,(C)
b is Morphism of a,(C)
d is Morphism of a,(C)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
Hom (a,(C)) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C) ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
(C) is Element of the carrier of C
the of C is Element of the carrier of C
c is Morphism of a,(C)
b is Morphism of a,(C)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,a) is Morphism of a,(C)
term (a,(C)) is Morphism of a,(C)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,a) is Morphism of a,(C)
dom (C,a) is Element of the carrier of C
the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a) is Element of the carrier of C
cod (C,a) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a) is Element of the carrier of C
term (a,(C)) is Morphism of a,(C)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
Hom (a,(C)) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C) ) } is set
(C,a) is Morphism of a,(C)
{(C,a)} is non empty trivial finite 1 -element set
c is Morphism of a,(C)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
Hom ((C,a,c),a) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
Hom ((C,a,c),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
dom ( the of C . (a,c)) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . ( the of C . (a,c)) is Element of the carrier of C
dom ( the of C . (a,c)) is Element of the carrier of C
the Source of C . ( the of C . (a,c)) is Element of the carrier of C
cod ( the of C . (a,c)) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . ( the of C . (a,c)) is Element of the carrier of C
cod ( the of C . (a,c)) is Element of the carrier of C
the Target of C . ( the of C . (a,c)) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of (C,a,c),a
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
the carrier' of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of (C,a,c),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C . (C,a,c) is Element of the carrier of C
(C) is Element of the carrier of C
the of C is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
Hom (c,a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = a ) } is set
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of (C,a,c),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
Hom ((C,a,c),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
Hom ((C,a,c),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Target of C . (C,a,c) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
b is Element of the carrier of C
a is Element of the carrier of C
c is Element of the carrier of C
Hom (b,a) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = a ) } is set
Hom (b,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = c ) } is set
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of (C,a,c),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
d is Morphism of b,a
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
e is Morphism of b,c
Hom ((C,a,c),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
Hom ((C,a,c),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
s is Morphism of b,(C,a,c)
(C,a,c) * s is Morphism of b,a
(C,a,c) * s is Morphism of b,c
Hom ((C,a,c),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
Hom ((C,a,c),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
s is Morphism of b,(C,a,c)
f is Morphism of b,(C,a,c)
(C,a,c) * f is Morphism of b,a
(C,a,c) * f is Morphism of b,c
h is Morphism of b,(C,a,c)
(C,a,c) * h is Morphism of b,a
(C,a,c) * h is Morphism of b,c
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (a,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = b ) } is set
(C,c,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (c,b) is Element of the carrier of C
Hom (a,(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,c,b) ) } is set
(C,c,b) is Morphism of (C,c,b),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (c,b) is Element of the carrier' of C
(C,c,b) is Morphism of (C,c,b),b
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (c,b) is Element of the carrier' of C
Hom ((C,c,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = c ) } is set
Hom ((C,c,b),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = b ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of (C,a,c),a
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(C,a,c,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,a,c)
id (C,a,c) is Morphism of (C,a,c),(C,a,c)
Hom ((C,a,c),c) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
(C,a,c) * (id (C,a,c)) is Morphism of (C,a,c),c
Hom ((C,a,c),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
(C,a,c) * (id (C,a,c)) is Morphism of (C,a,c),a
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (a,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = b ) } is set
(C,c,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (c,b) is Element of the carrier of C
d is Element of the carrier of C
Hom (d,a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = d & cod b₁ = a ) } is set
e is Morphism of a,c
s is Morphism of a,b
(C,c,b,a,e,s) is Morphism of a,(C,c,b)
f is Morphism of d,a
e * f is Morphism of d,c
s * f is Morphism of d,b
(C,c,b,d,(e * f),(s * f)) is Morphism of d,(C,c,b)
(C,c,b,a,e,s) * f is Morphism of d,(C,c,b)
Hom (a,(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,c,b) ) } is set
Hom ((C,c,b),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = b ) } is set
(C,c,b) is Morphism of (C,c,b),b
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,c,b,a,e,s) is Morphism of a,b
((C,c,b) * (C,c,b,a,e,s)) * f is Morphism of d,b
(C,c,b) * ((C,c,b,a,e,s) * f) is Morphism of d,b
Hom ((C,c,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = c ) } is set
Hom (d,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = d & cod b₁ = c ) } is set
Hom (d,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = d & cod b₁ = b ) } is set
(C,c,b) is Morphism of (C,c,b),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,c,b,a,e,s) is Morphism of a,c
((C,c,b) * (C,c,b,a,e,s)) * f is Morphism of d,c
(C,c,b) * ((C,c,b,a,e,s) * f) is Morphism of d,c
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (a,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = b ) } is set
d is Morphism of a,c
e is Morphism of a,c
s is Morphism of a,b
(C,c,b,a,d,s) is Morphism of a,(C,c,b)
(C,c,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (c,b) is Element of the carrier of C
f is Morphism of a,b
(C,c,b,a,e,f) is Morphism of a,(C,c,b)
(C,c,b) is Morphism of (C,c,b),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,c,b,a,d,s) is Morphism of a,c
(C,c,b) is Morphism of (C,c,b),b
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,c,b,a,d,s) is Morphism of a,b
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (a,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = b ) } is set
(C,c,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (c,b) is Element of the carrier of C
d is Morphism of a,c
e is Morphism of a,b
(C,c,b,a,d,e) is Morphism of a,(C,c,b)
s is Element of the carrier of C
Hom (s,a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s & cod b₁ = a ) } is set
f is Morphism of s,a
(C,c,b,a,d,e) * f is Morphism of s,(C,c,b)
h is Morphism of s,a
(C,c,b,a,d,e) * h is Morphism of s,(C,c,b)
Hom (s,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s & cod b₁ = c ) } is set
Hom (s,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s & cod b₁ = b ) } is set
d * f is Morphism of s,c
e * f is Morphism of s,b
(C,c,b,s,(d * f),(e * f)) is Morphism of s,(C,c,b)
d * h is Morphism of s,c
e * h is Morphism of s,b
(C,c,b,s,(d * h),(e * h)) is Morphism of s,(C,c,b)
s is Element of the carrier of C
Hom (s,a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s & cod b₁ = a ) } is set
f is Morphism of s,a
(C,c,b,a,d,e) * f is Morphism of s,(C,c,b)
h is Morphism of s,a
(C,c,b,a,d,e) * h is Morphism of s,(C,c,b)
Hom (s,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s & cod b₁ = c ) } is set
Hom (s,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s & cod b₁ = b ) } is set
d * f is Morphism of s,c
e * f is Morphism of s,b
(C,c,b,s,(d * f),(e * f)) is Morphism of s,(C,c,b)
d * h is Morphism of s,c
e * h is Morphism of s,b
(C,c,b,s,(d * h),(e * h)) is Morphism of s,(C,c,b)
Hom (a,(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,c,b) ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,a,(C)) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,(C)) is Element of the carrier of C
Hom (a,(C,a,(C))) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,(C)) ) } is set
(C,(C),a) is Element of the carrier of C
the of C . ((C),a) is Element of the carrier of C
Hom (a,(C,(C),a)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,(C),a) ) } is set
Hom (a,(C)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C) ) } is set
Hom (a,a) is non empty Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = a ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,(C),a) is Morphism of (C,(C),a),a
(C,(C),a) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . ((C),a) is Element of the carrier of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . ((C),a) is Element of the carrier' of C
(C,a) is Morphism of a,(C)
id a is Morphism of a,a
(C,(C),a,a,(C,a),(id a)) is Morphism of a,(C,(C),a)
(C,a,(C)) is Morphism of (C,a,(C)),a
(C,a,(C)) is Element of the carrier of C
the of C . (a,(C)) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,(C)) is Element of the carrier' of C
(C,a,(C),a,(id a),(C,a)) is Morphism of a,(C,a,(C))
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,(C),a) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . ((C),a) is Element of the carrier of C
(C,a) is Morphism of a,(C,(C),a)
(C,a) is Morphism of a,(C)
id a is Morphism of a,a
(C,(C),a,a,(C,a),(id a)) is Morphism of a,(C,(C),a)
(C,a) is Morphism of (C,(C),a),a
(C,(C),a) is Morphism of (C,(C),a),a
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . ((C),a) is Element of the carrier' of C
(C,a) * (C,a) is Morphism of a,a
(C,a) * (C,a) is Morphism of (C,(C),a),(C,(C),a)
id (C,(C),a) is Morphism of (C,(C),a),(C,(C),a)
(C,a,(C)) is Element of the carrier of C
the of C . (a,(C)) is Element of the carrier of C
(C,a) is Morphism of a,(C,a,(C))
(C,a,(C),a,(id a),(C,a)) is Morphism of a,(C,a,(C))
(C,a) is Morphism of (C,a,(C)),a
(C,a,(C)) is Morphism of (C,a,(C)),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,(C)) is Element of the carrier' of C
(C,a) * (C,a) is Morphism of a,a
(C,a) * (C,a) is Morphism of (C,a,(C)),(C,a,(C))
id (C,a,(C)) is Morphism of (C,a,(C)),(C,a,(C))
(C,a) * (C,(C),a) is Morphism of (C,(C),a),(C)
(C,(C),a) is Morphism of (C,(C),a),(C)
the of C . ((C),a) is Element of the carrier' of C
Hom (a,(C)) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C) ) } is set
Hom (a,a) is non empty Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = a ) } is set
Hom ((C,(C),a),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C),a) & cod b₁ = a ) } is set
(id a) * (C,(C),a) is Morphism of (C,(C),a),a
(C,(C),a,a,(C,a),(id a)) * (C,(C),a) is Morphism of (C,(C),a),(C,(C),a)
(C,(C),a,(C,(C),a),(C,(C),a),(C,(C),a)) is Morphism of (C,(C),a),(C,(C),a)
(C,a) * (C,a,(C)) is Morphism of (C,a,(C)),(C)
(C,a,(C)) is Morphism of (C,a,(C)),(C)
the of C . (a,(C)) is Element of the carrier' of C
Hom ((C,a,(C)),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C)) & cod b₁ = a ) } is set
(id a) * (C,a,(C)) is Morphism of (C,a,(C)),a
(C,a,(C),a,(id a),(C,a)) * (C,a,(C)) is Morphism of (C,a,(C)),(C,a,(C))
(C,a,(C),(C,a,(C)),(C,a,(C)),(C,a,(C))) is Morphism of (C,a,(C)),(C,a,(C))
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,a,(C)) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,(C)) is Element of the carrier of C
(C,(C),a) is Element of the carrier of C
the of C . ((C),a) is Element of the carrier of C
Hom (a,(C,a,(C))) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,(C)) ) } is set
Hom ((C,a,(C)),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C)) & cod b₁ = a ) } is set
id (C,a,(C)) is Morphism of (C,a,(C)),(C,a,(C))
id a is Morphism of a,a
(C,a) is Morphism of a,(C,a,(C))
(C,a) is Morphism of a,(C)
(C,a,(C),a,(id a),(C,a)) is Morphism of a,(C,a,(C))
(C,a) is Morphism of (C,a,(C)),a
(C,a,(C)) is Morphism of (C,a,(C)),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,(C)) is Element of the carrier' of C
(C,a) * (C,a) is Morphism of (C,a,(C)),(C,a,(C))
(C,a) * (C,a) is Morphism of a,a
Hom (a,(C,(C),a)) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,(C),a) ) } is set
Hom ((C,(C),a),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C),a) & cod b₁ = a ) } is set
id (C,(C),a) is Morphism of (C,(C),a),(C,(C),a)
id a is Morphism of a,a
(C,a) is Morphism of a,(C,(C),a)
(C,a) is Morphism of a,(C)
(C,(C),a,a,(C,a),(id a)) is Morphism of a,(C,(C),a)
(C,a) is Morphism of (C,(C),a),a
(C,(C),a) is Morphism of (C,(C),a),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . ((C),a) is Element of the carrier' of C
(C,a) * (C,a) is Morphism of (C,(C),a),(C,(C),a)
(C,a) * (C,a) is Morphism of a,a
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
c is Element of the carrier of C
a is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of (C,a,c),c
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(C,c,a,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,c,a)
(C,c,a) is Element of the carrier of C
the of C . (c,a) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,c,a) is Element of the carrier of C
the of C . (c,a) is Element of the carrier of C
Hom ((C,a,c),(C,c,a)) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = (C,c,a) ) } is set
Hom ((C,a,c),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
Hom ((C,a,c),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,c,a) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (c,a) is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C . (a,c) is Element of the carrier of C
(C,c,a) is Morphism of (C,c,a),(C,a,c)
(C,c,a) is Morphism of (C,c,a),a
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (c,a) is Element of the carrier' of C
(C,c,a) is Morphism of (C,c,a),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (c,a) is Element of the carrier' of C
(C,a,c,(C,c,a),(C,c,a),(C,c,a)) is Morphism of (C,c,a),(C,a,c)
(C,a,c) is Morphism of (C,a,c),(C,c,a)
(C,a,c) is Morphism of (C,a,c),c
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),a
the of C . (a,c) is Element of the carrier' of C
(C,c,a,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,c,a)
(C,a,c) * (C,c,a) is Morphism of (C,c,a),(C,c,a)
id (C,c,a) is Morphism of (C,c,a),(C,c,a)
Hom ((C,a,c),a) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
Hom ((C,a,c),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
Hom ((C,c,a),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,a) & cod b₁ = c ) } is set
Hom ((C,c,a),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,a) & cod b₁ = a ) } is set
Hom ((C,c,a),(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,a) & cod b₁ = (C,a,c) ) } is set
(C,a,c) * (C,a,c,(C,c,a),(C,c,a),(C,c,a)) is Morphism of (C,c,a),c
(C,a,c) * (C,a,c,(C,c,a),(C,c,a),(C,c,a)) is Morphism of (C,c,a),a
(C,c,a,(C,c,a),((C,a,c) * (C,a,c,(C,c,a),(C,c,a),(C,c,a))),((C,a,c) * (C,a,c,(C,c,a),(C,c,a),(C,c,a)))) is Morphism of (C,c,a),(C,c,a)
(C,c,a,(C,c,a),(C,c,a),((C,a,c) * (C,a,c,(C,c,a),(C,c,a),(C,c,a)))) is Morphism of (C,c,a),(C,c,a)
(C,c,a,(C,c,a),(C,c,a),(C,c,a)) is Morphism of (C,c,a),(C,c,a)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,c,a) is Element of the carrier of C
the of C . (c,a) is Element of the carrier of C
Hom ((C,a,c),(C,c,a)) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = (C,c,a) ) } is set
Hom ((C,c,a),(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,a) & cod b₁ = (C,a,c) ) } is set
id (C,c,a) is Morphism of (C,c,a),(C,c,a)
id (C,a,c) is Morphism of (C,a,c),(C,a,c)
(C,a,c) is Morphism of (C,a,c),(C,c,a)
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(C,c,a,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,c,a)
(C,c,a) is Morphism of (C,c,a),(C,a,c)
(C,c,a) is Morphism of (C,c,a),a
the of C . (c,a) is Element of the carrier' of C
(C,c,a) is Morphism of (C,c,a),c
the of C . (c,a) is Element of the carrier' of C
(C,a,c,(C,c,a),(C,c,a),(C,c,a)) is Morphism of (C,c,a),(C,a,c)
(C,a,c) * (C,c,a) is Morphism of (C,c,a),(C,c,a)
(C,c,a) * (C,a,c) is Morphism of (C,a,c),(C,a,c)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
id a is Morphism of a,a
(C,a,a,a,(id a),(id a)) is Morphism of a,(C,a,a)
(C,a,a) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,a) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
(C,a,a) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,a) is Element of the carrier of C
Hom (a,(C,a,a)) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,a) ) } is set
Hom (a,a) is non empty Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = a ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
(C,c,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (c,c) is Element of the carrier of C
(C,c) is Morphism of c,(C,c,c)
id c is Morphism of c,c
(C,c,c,c,(id c),(id c)) is Morphism of c,(C,c,c)
b is Morphism of a,c
(C,c,c,a,b,b) is Morphism of a,(C,c,c)
(C,c) * b is Morphism of a,(C,c,c)
Hom (c,c) is non empty Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = c ) } is set
(id c) * b is Morphism of a,c
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
b is Element of the carrier of C
(C,c,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (c,b) is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C . (a,c) is Element of the carrier of C
(C,(C,a,c),b) is Element of the carrier of C
the of C . ((C,a,c),b) is Element of the carrier of C
(C,(C,a,c),b) is Morphism of (C,(C,a,c),b),(C,a,c)
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . ((C,a,c),b) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),a
the of C . (a,c) is Element of the carrier' of C
(C,a,c) * (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),a
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(C,a,c) * (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),c
(C,(C,a,c),b) is Morphism of (C,(C,a,c),b),b
the of C . ((C,a,c),b) is Element of the carrier' of C
(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)) is Morphism of (C,(C,a,c),b),(C,c,b)
(C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),(C,a,(C,c,b))
(C,a,(C,c,b)) is Element of the carrier of C
the of C . (a,(C,c,b)) is Element of the carrier of C
(C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),a
the of C . (a,(C,c,b)) is Element of the carrier' of C
(C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),(C,c,b)
the of C . (a,(C,c,b)) is Element of the carrier' of C
(C,c,b) is Morphism of (C,c,b),c
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),c
(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,a,c)
(C,c,b) is Morphism of (C,c,b),b
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),b
(C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,(C,a,c),b)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
b is Element of the carrier of C
(C,(C,a,c),b) is Element of the carrier of C
the of C . ((C,a,c),b) is Element of the carrier of C
(C,c,b) is Element of the carrier of C
the of C . (c,b) is Element of the carrier of C
(C,a,(C,c,b)) is Element of the carrier of C
the of C . (a,(C,c,b)) is Element of the carrier of C
Hom ((C,(C,a,c),b),(C,a,(C,c,b))) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = (C,a,(C,c,b)) ) } is set
Hom ((C,a,(C,c,b)),(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = (C,(C,a,c),b) ) } is set
Hom ((C,(C,a,c),b),(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = (C,a,c) ) } is set
Hom ((C,a,c),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
Hom ((C,(C,a,c),b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = c ) } is set
Hom ((C,a,c),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
Hom ((C,(C,a,c),b),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = a ) } is set
Hom ((C,(C,a,c),b),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = b ) } is set
Hom ((C,(C,a,c),b),(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = (C,c,b) ) } is set
Hom ((C,a,(C,c,b)),(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = (C,c,b) ) } is set
Hom ((C,c,b),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = b ) } is set
Hom ((C,a,(C,c,b)),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = b ) } is set
Hom ((C,c,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = c ) } is set
Hom ((C,a,(C,c,b)),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = c ) } is set
Hom ((C,a,(C,c,b)),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = a ) } is set
Hom ((C,a,(C,c,b)),(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = (C,a,c) ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
b is Element of the carrier of C
(C,c,b) is Element of the carrier of C
the of C . (c,b) is Element of the carrier of C
(C,a,(C,c,b)) is Element of the carrier of C
the of C . (a,(C,c,b)) is Element of the carrier of C
(C,(C,a,c),b) is Element of the carrier of C
the of C . ((C,a,c),b) is Element of the carrier of C
(C,a,c,b) is Morphism of (C,a,(C,c,b)),(C,(C,a,c),b)
(C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),a
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,(C,c,b)) is Element of the carrier' of C
(C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),(C,c,b)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,(C,c,b)) is Element of the carrier' of C
(C,c,b) is Morphism of (C,c,b),c
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),c
(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,a,c)
(C,c,b) is Morphism of (C,c,b),b
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),b
(C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,(C,a,c),b)
(C,a,c,b) is Morphism of (C,(C,a,c),b),(C,a,(C,c,b))
(C,(C,a,c),b) is Morphism of (C,(C,a,c),b),(C,a,c)
the of C . ((C,a,c),b) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),a
the of C . (a,c) is Element of the carrier' of C
(C,a,c) * (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),a
(C,a,c) is Morphism of (C,a,c),c
the of C . (a,c) is Element of the carrier' of C
(C,a,c) * (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),c
(C,(C,a,c),b) is Morphism of (C,(C,a,c),b),b
the of C . ((C,a,c),b) is Element of the carrier' of C
(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)) is Morphism of (C,(C,a,c),b),(C,c,b)
(C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),(C,a,(C,c,b))
(C,a,c,b) * (C,a,c,b) is Morphism of (C,a,(C,c,b)),(C,a,(C,c,b))
id (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),(C,a,(C,c,b))
(C,a,c,b) * (C,a,c,b) is Morphism of (C,(C,a,c),b),(C,(C,a,c),b)
id (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),(C,(C,a,c),b)
Hom ((C,(C,a,c),b),(C,a,c)) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = (C,a,c) ) } is set
Hom ((C,a,c),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
Hom ((C,(C,a,c),b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = c ) } is set
Hom ((C,(C,a,c),b),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = b ) } is set
Hom ((C,(C,a,c),b),(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = (C,c,b) ) } is set
Hom ((C,a,c),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
Hom ((C,(C,a,c),b),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = a ) } is set
Hom ((C,a,(C,c,b)),(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = (C,c,b) ) } is set
Hom ((C,c,b),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = b ) } is set
Hom ((C,a,(C,c,b)),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = b ) } is set
Hom ((C,c,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = c ) } is set
Hom ((C,a,(C,c,b)),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = c ) } is set
Hom ((C,a,(C,c,b)),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = a ) } is set
Hom ((C,a,(C,c,b)),(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = (C,a,c) ) } is set
Hom ((C,a,(C,c,b)),(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = (C,(C,a,c),b) ) } is set
((C,a,c) * (C,(C,a,c),b)) * (C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),c
(C,(C,a,c),b) * (C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,a,c)
(C,a,c) * ((C,(C,a,c),b) * (C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b))))) is Morphism of (C,a,(C,c,b)),c
(C,a,c) * (C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),c
(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)) * (C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,c,b)
(C,(C,a,c),b) * (C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),b
(C,c,b,(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b))),((C,(C,a,c),b) * (C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))))) is Morphism of (C,a,(C,c,b)),(C,c,b)
(C,c,b,(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,c,b)
(C,c,b,(C,c,b),(C,c,b),(C,c,b)) is Morphism of (C,c,b),(C,c,b)
(C,c,b,(C,c,b),(C,c,b),(C,c,b)) * (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),(C,c,b)
id (C,c,b) is Morphism of (C,c,b),(C,c,b)
(id (C,c,b)) * (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),(C,c,b)
Hom ((C,(C,a,c),b),(C,a,(C,c,b))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = (C,a,(C,c,b)) ) } is set
((C,c,b) * (C,a,(C,c,b))) * (C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),c
(C,a,(C,c,b)) * (C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),(C,c,b)
(C,c,b) * ((C,a,(C,c,b)) * (C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)))) is Morphism of (C,(C,a,c),b),c
(C,c,b) * (C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)) is Morphism of (C,(C,a,c),b),c
(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))) * (C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),(C,a,c)
(C,a,(C,c,b)) * (C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),a
(C,a,c,(C,(C,a,c),b),((C,a,(C,c,b)) * (C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)))),((C,a,c) * (C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),(C,a,c)
(C,a,c,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),((C,a,c) * (C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),(C,a,c)
(C,a,c,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,a,c)
(C,a,c,(C,a,c),(C,a,c),(C,a,c)) * (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),(C,a,c)
id (C,a,c) is Morphism of (C,a,c),(C,a,c)
(id (C,a,c)) * (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),(C,a,c)
((C,a,c) * (C,(C,a,c),b)) * (C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),a
(C,a,c) * ((C,(C,a,c),b) * (C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b))))) is Morphism of (C,a,(C,c,b)),a
(C,a,c) * (C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),a
(C,a,(C,c,b),(C,a,(C,c,b)),(C,a,(C,c,b)),(C,a,(C,c,b))) is Morphism of (C,a,(C,c,b)),(C,a,(C,c,b))
((C,c,b) * (C,a,(C,c,b))) * (C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),b
(C,c,b) * ((C,a,(C,c,b)) * (C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)))) is Morphism of (C,(C,a,c),b),b
(C,c,b) * (C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)) is Morphism of (C,(C,a,c),b),b
(C,(C,a,c),b,(C,(C,a,c),b),(C,(C,a,c),b),(C,(C,a,c),b)) is Morphism of (C,(C,a,c),b),(C,(C,a,c),b)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
b is Element of the carrier of C
(C,(C,a,c),b) is Element of the carrier of C
the of C . ((C,a,c),b) is Element of the carrier of C
(C,c,b) is Element of the carrier of C
the of C . (c,b) is Element of the carrier of C
(C,a,(C,c,b)) is Element of the carrier of C
the of C . (a,(C,c,b)) is Element of the carrier of C
Hom ((C,(C,a,c),b),(C,a,(C,c,b))) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = (C,a,(C,c,b)) ) } is set
Hom ((C,a,(C,c,b)),(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = (C,(C,a,c),b) ) } is set
id (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),(C,a,(C,c,b))
id (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),(C,(C,a,c),b)
(C,a,c,b) is Morphism of (C,(C,a,c),b),(C,a,(C,c,b))
(C,(C,a,c),b) is Morphism of (C,(C,a,c),b),(C,a,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . ((C,a,c),b) is Element of the carrier' of C
(C,a,c) is Morphism of (C,a,c),a
the of C . (a,c) is Element of the carrier' of C
(C,a,c) * (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),a
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(C,a,c) * (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),c
(C,(C,a,c),b) is Morphism of (C,(C,a,c),b),b
the of C . ((C,a,c),b) is Element of the carrier' of C
(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b)) is Morphism of (C,(C,a,c),b),(C,c,b)
(C,a,(C,c,b),(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,c,b,(C,(C,a,c),b),((C,a,c) * (C,(C,a,c),b)),(C,(C,a,c),b))) is Morphism of (C,(C,a,c),b),(C,a,(C,c,b))
(C,a,c,b) is Morphism of (C,a,(C,c,b)),(C,(C,a,c),b)
(C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),a
the of C . (a,(C,c,b)) is Element of the carrier' of C
(C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),(C,c,b)
the of C . (a,(C,c,b)) is Element of the carrier' of C
(C,c,b) is Morphism of (C,c,b),c
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),c
(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,a,c)
(C,c,b) is Morphism of (C,c,b),b
the of C . (c,b) is Element of the carrier' of C
(C,c,b) * (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),b
(C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,c,b) * (C,a,(C,c,b)))),((C,c,b) * (C,a,(C,c,b)))) is Morphism of (C,a,(C,c,b)),(C,(C,a,c),b)
(C,a,c,b) * (C,a,c,b) is Morphism of (C,a,(C,c,b)),(C,a,(C,c,b))
(C,a,c,b) * (C,a,c,b) is Morphism of (C,(C,a,c),b),(C,(C,a,c),b)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
b is Element of the carrier of C
d is Element of the carrier of C
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
(C,a,b) is Morphism of (C,a,b),a
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,b) is Element of the carrier' of C
e is Morphism of a,c
e * (C,a,b) is Morphism of (C,a,b),c
(C,a,b) is Morphism of (C,a,b),b
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,b) is Element of the carrier' of C
s is Morphism of b,d
s * (C,a,b) is Morphism of (C,a,b),d
(C,c,d,(C,a,b),(e * (C,a,b)),(s * (C,a,b))) is Morphism of (C,a,b),(C,c,d)
(C,c,d) is Element of the carrier of C
the of C . (c,d) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
d is Element of the carrier of C
Hom (b,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = d ) } is set
(C,c,d) is Element of the carrier of C
the of C . (c,d) is Element of the carrier of C
Hom ((C,a,b),(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = (C,c,d) ) } is set
Hom ((C,a,b),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = b ) } is set
Hom ((C,a,b),d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = d ) } is set
Hom ((C,a,b),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = a ) } is set
Hom ((C,a,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = c ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
id a is Morphism of a,a
c is Element of the carrier of C
id c is Morphism of c,c
(C,a,a,c,c,(id a),(id c)) is Morphism of (C,a,c),(C,a,c)
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of (C,a,c),a
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(id a) * (C,a,c) is Morphism of (C,a,c),a
(C,a,c) is Morphism of (C,a,c),c
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(id c) * (C,a,c) is Morphism of (C,a,c),c
(C,a,c,(C,a,c),((id a) * (C,a,c)),((id c) * (C,a,c))) is Morphism of (C,a,c),(C,a,c)
id (C,a,c) is Morphism of (C,a,c),(C,a,c)
Hom ((C,a,c),c) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = c ) } is set
Hom ((C,a,c),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = a ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
d is Element of the carrier of C
Hom (b,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = d ) } is set
(C,c,d) is Element of the carrier of C
the of C . (c,d) is Element of the carrier of C
e is Element of the carrier of C
Hom (e,a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = e & cod b₁ = a ) } is set
Hom (e,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = e & cod b₁ = b ) } is set
s is Morphism of a,c
f is Morphism of b,d
(C,a,c,b,d,s,f) is Morphism of (C,a,b),(C,c,d)
(C,a,b) is Morphism of (C,a,b),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,b) is Element of the carrier' of C
s * (C,a,b) is Morphism of (C,a,b),c
(C,a,b) is Morphism of (C,a,b),b
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,b) is Element of the carrier' of C
f * (C,a,b) is Morphism of (C,a,b),d
(C,c,d,(C,a,b),(s * (C,a,b)),(f * (C,a,b))) is Morphism of (C,a,b),(C,c,d)
h is Morphism of e,a
s * h is Morphism of e,c
g is Morphism of e,b
(C,a,b,e,h,g) is Morphism of e,(C,a,b)
(C,a,c,b,d,s,f) * (C,a,b,e,h,g) is Morphism of e,(C,c,d)
f * g is Morphism of e,d
(C,c,d,e,(s * h),(f * g)) is Morphism of e,(C,c,d)
Hom (e,(C,a,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = e & cod b₁ = (C,a,b) ) } is set
Hom ((C,a,b),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = b ) } is set
Hom ((C,a,b),d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = d ) } is set
Hom ((C,a,b),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = a ) } is set
Hom ((C,a,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = c ) } is set
(C,a,b) * (C,a,b,e,h,g) is Morphism of e,b
(f * (C,a,b)) * (C,a,b,e,h,g) is Morphism of e,d
(C,a,b) * (C,a,b,e,h,g) is Morphism of e,a
(s * (C,a,b)) * (C,a,b,e,h,g) is Morphism of e,c
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
(C,a,a) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,a) is Element of the carrier of C
(C,a) is Morphism of a,(C,a,a)
id a is Morphism of a,a
(C,a,a,a,(id a),(id a)) is Morphism of a,(C,a,a)
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (a,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = b ) } is set
(C,c,b) is Element of the carrier of C
the of C . (c,b) is Element of the carrier of C
d is Morphism of a,c
e is Morphism of a,b
(C,c,b,a,d,e) is Morphism of a,(C,c,b)
(C,a,c,a,b,d,e) is Morphism of (C,a,a),(C,c,b)
(C,a,a) is Morphism of (C,a,a),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,a) is Element of the carrier' of C
d * (C,a,a) is Morphism of (C,a,a),c
(C,a,a) is Morphism of (C,a,a),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,a) is Element of the carrier' of C
e * (C,a,a) is Morphism of (C,a,a),b
(C,c,b,(C,a,a),(d * (C,a,a)),(e * (C,a,a))) is Morphism of (C,a,a),(C,c,b)
(C,a,c,a,b,d,e) * (C,a) is Morphism of a,(C,c,b)
Hom (a,a) is non empty Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = a ) } is set
d * (id a) is Morphism of a,c
e * (id a) is Morphism of a,b
(C,c,b,a,(d * (id a)),(e * (id a))) is Morphism of a,(C,c,b)
(C,c,b,a,d,(e * (id a))) is Morphism of a,(C,c,b)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
d is Element of the carrier of C
Hom (b,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = d ) } is set
(C,c,d) is Element of the carrier of C
the of C . (c,d) is Element of the carrier of C
e is Element of the carrier of C
Hom (e,a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = e & cod b₁ = a ) } is set
s is Element of the carrier of C
Hom (s,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s & cod b₁ = b ) } is set
(C,e,s) is Element of the carrier of C
the of C . (e,s) is Element of the carrier of C
f is Morphism of a,c
h is Morphism of b,d
(C,a,c,b,d,f,h) is Morphism of (C,a,b),(C,c,d)
(C,a,b) is Morphism of (C,a,b),a
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,b) is Element of the carrier' of C
f * (C,a,b) is Morphism of (C,a,b),c
(C,a,b) is Morphism of (C,a,b),b
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,b) is Element of the carrier' of C
h * (C,a,b) is Morphism of (C,a,b),d
(C,c,d,(C,a,b),(f * (C,a,b)),(h * (C,a,b))) is Morphism of (C,a,b),(C,c,d)
g is Morphism of e,a
f * g is Morphism of e,c
k is Morphism of s,b
(C,e,a,s,b,g,k) is Morphism of (C,e,s),(C,a,b)
(C,e,s) is Morphism of (C,e,s),e
the of C . (e,s) is Element of the carrier' of C
g * (C,e,s) is Morphism of (C,e,s),a
(C,e,s) is Morphism of (C,e,s),s
the of C . (e,s) is Element of the carrier' of C
k * (C,e,s) is Morphism of (C,e,s),b
(C,a,b,(C,e,s),(g * (C,e,s)),(k * (C,e,s))) is Morphism of (C,e,s),(C,a,b)
(C,a,c,b,d,f,h) * (C,e,a,s,b,g,k) is Morphism of (C,e,s),(C,c,d)
h * k is Morphism of s,d
(C,e,c,s,d,(f * g),(h * k)) is Morphism of (C,e,s),(C,c,d)
(f * g) * (C,e,s) is Morphism of (C,e,s),c
(h * k) * (C,e,s) is Morphism of (C,e,s),d
(C,c,d,(C,e,s),((f * g) * (C,e,s)),((h * k) * (C,e,s))) is Morphism of (C,e,s),(C,c,d)
Hom ((C,e,s),s) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,e,s) & cod b₁ = s ) } is set
Hom ((C,e,s),b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,e,s) & cod b₁ = b ) } is set
Hom ((C,e,s),e) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,e,s) & cod b₁ = e ) } is set
f * (g * (C,e,s)) is Morphism of (C,e,s),c
h * (k * (C,e,s)) is Morphism of (C,e,s),d
(C,c,d,(C,e,s),(f * (g * (C,e,s))),(h * (k * (C,e,s)))) is Morphism of (C,e,s),(C,c,d)
Hom ((C,e,s),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,e,s) & cod b₁ = a ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities CatStr
the carrier of C is non empty set
the carrier' of C is non empty set
[:{}, the carrier of C:] is set
bool [:{}, the carrier of C:] is set
{{},1} is non empty finite V40() set
a is Relation-like {} -defined the carrier of C -valued Function-like one-to-one constant functional empty total V18( {} , the carrier of C) V24() V25() V26() V28() V29() V30() V31() V32() V33() V35() finite finite-yielding V40() cardinal {} -element Element of bool [:{}, the carrier of C:]
c is Element of the carrier of C
b is Relation-like {} -defined the carrier' of C -valued Function-like one-to-one constant functional empty total V18( {} , the carrier' of C) V24() V25() V26() V28() V29() V30() V31() V32() V33() V35() finite finite-yielding V40() cardinal {} -element Injections_family of c, {}
doms b is Relation-like {} -defined the carrier of C -valued Function-like one-to-one constant functional empty total V18( {} , the carrier of C) V24() V25() V26() V28() V29() V30() V31() V32() V33() V35() finite finite-yielding V40() cardinal {} -element Element of bool [:{}, the carrier of C:]
d is Element of the carrier of C
e is Element of the carrier of C
({},1) --> (d,e) is Relation-like {{},1} -defined the carrier of C -valued Function-like non empty total V18({{},1}, the carrier of C) finite Element of bool [:{{},1}, the carrier of C:]
[:{{},1}, the carrier of C:] is set
bool [:{{},1}, the carrier of C:] is set
f is Element of the carrier of C
h is Relation-like {{},1} -defined the carrier' of C -valued Function-like non empty total V18({{},1}, the carrier' of C) finite Injections_family of f,{{},1}
doms h is Relation-like {{},1} -defined the carrier of C -valued Function-like non empty total V18({{},1}, the carrier of C) finite Element of bool [:{{},1}, the carrier of C:]
h /. {} is Element of the carrier' of C
g is Element of the carrier' of C
dom g is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . g is Element of the carrier of C
cod g is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . g is Element of the carrier of C
h /. 1 is Element of the carrier' of C
k is Element of the carrier' of C
dom k is Element of the carrier of C
the Source of C . k is Element of the carrier of C
cod k is Element of the carrier of C
the Target of C . k is Element of the carrier of C
h . 1 is set
(({},1) --> (d,e)) /. {} is Element of the carrier of C
(({},1) --> (d,e)) /. 1 is Element of the carrier of C
dom h is finite V40() Element of bool {{},1}
bool {{},1} is finite V40() set
h . {} is set
({},1) --> (g,k) is Relation-like {{},1} -defined the carrier' of C -valued Function-like non empty total V18({{},1}, the carrier' of C) finite Element of bool [:{{},1}, the carrier' of C:]
[:{{},1}, the carrier' of C:] is set
bool [:{{},1}, the carrier' of C:] is set
a is Element of the carrier of C
c is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal set
c + 1 is non empty V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal set
b is finite set
[:b, the carrier of C:] is set
bool [:b, the carrier of C:] is set
card b is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
d is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
the Element of b is Element of b
{ the Element of b} is non empty trivial finite 1 -element set
b \ { the Element of b} is finite Element of bool b
bool b is finite V40() set
[:(b \ { the Element of b}), the carrier of C:] is set
bool [:(b \ { the Element of b}), the carrier of C:] is set
d | (b \ { the Element of b}) is Relation-like b -defined the carrier of C -valued Function-like finite Element of bool [:b, the carrier of C:]
s is finite set
card s is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
f is finite set
card f is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
(card b) - (card f) is V31() V32() V33() set
(card b) - 1 is V31() V32() V33() set
h is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
g is Element of the carrier of C
k is Relation-like b \ { the Element of b} -defined the carrier' of C -valued Function-like total V18(b \ { the Element of b}, the carrier' of C) finite Injections_family of g,b \ { the Element of b}
doms k is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
d /. the Element of b is Element of the carrier of C
i1 is Element of the carrier' of C
dom i1 is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . i1 is Element of the carrier of C
i2 is Element of the carrier' of C
dom i2 is Element of the carrier of C
the Source of C . i2 is Element of the carrier of C
cod i1 is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . i1 is Element of the carrier of C
c is Element of the carrier of C
cod i2 is Element of the carrier of C
the Target of C . i2 is Element of the carrier of C
i1 * k is Relation-like b \ { the Element of b} -defined the carrier' of C -valued Function-like total V18(b \ { the Element of b}, the carrier' of C) finite Element of bool [:(b \ { the Element of b}), the carrier' of C:]
[:(b \ { the Element of b}), the carrier' of C:] is set
bool [:(b \ { the Element of b}), the carrier' of C:] is set
the Element of b .--> i2 is Relation-like { the Element of b} -defined the carrier' of C -valued Function-like non empty total V18({ the Element of b}, the carrier' of C) finite Element of bool [:{ the Element of b}, the carrier' of C:]
[:{ the Element of b}, the carrier' of C:] is set
bool [:{ the Element of b}, the carrier' of C:] is set
{ the Element of b} --> i2 is Relation-like { the Element of b} -defined {i2} -valued Function-like non empty total V18({ the Element of b},{i2}) finite Element of bool [:{ the Element of b},{i2}:]
{i2} is non empty trivial finite 1 -element set
[:{ the Element of b},{i2}:] is finite set
bool [:{ the Element of b},{i2}:] is finite V40() set
(i1 * k) +* ( the Element of b .--> i2) is Relation-like Function-like finite set
{ the Element of b} --> i2 is Relation-like { the Element of b} -defined the carrier' of C -valued Function-like non empty total V18({ the Element of b}, the carrier' of C) finite Element of bool [:{ the Element of b}, the carrier' of C:]
dom ({ the Element of b} --> i2) is finite Element of bool { the Element of b}
bool { the Element of b} is finite V40() set
rng ((i1 * k) +* ( the Element of b .--> i2)) is finite set
rng (i1 * k) is finite Element of bool the carrier' of C
bool the carrier' of C is set
rng ( the Element of b .--> i2) is finite Element of bool the carrier' of C
(rng (i1 * k)) \/ (rng ( the Element of b .--> i2)) is finite Element of bool the carrier' of C
dom (i1 * k) is finite Element of bool (b \ { the Element of b})
bool (b \ { the Element of b}) is finite V40() set
dom ( the Element of b .--> i2) is finite Element of bool { the Element of b}
(dom (i1 * k)) \/ (dom ( the Element of b .--> i2)) is finite set
b \/ { the Element of b} is non empty finite set
dom ((i1 * k) +* ( the Element of b .--> i2)) is finite set
[:b, the carrier' of C:] is set
bool [:b, the carrier' of C:] is set
cods k is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(b \ { the Element of b}) --> g is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
{g} is non empty trivial finite 1 -element set
[:(b \ { the Element of b}),{g}:] is finite set
F9 is set
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Element of bool [:b, the carrier' of C:]
F9 /. F9 is Element of the carrier' of C
F9 . F9 is set
( the Element of b .--> i2) . F9 is set
b --> c is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
{c} is non empty trivial finite 1 -element set
[:b,{c}:] is finite set
(b --> c) . F9 is set
cod (F9 /. F9) is Element of the carrier of C
the Target of C . (F9 /. F9) is Element of the carrier of C
cods F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
(cods F9) /. F9 is Element of the carrier of C
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Element of bool [:b, the carrier' of C:]
F9 /. F9 is Element of the carrier' of C
F9 . F9 is set
(i1 * k) . F9 is set
(i1 * k) /. F9 is Element of the carrier' of C
cods F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
(cods F9) /. F9 is Element of the carrier of C
cod ((i1 * k) /. F9) is Element of the carrier of C
the Target of C . ((i1 * k) /. F9) is Element of the carrier of C
cods (i1 * k) is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(cods (i1 * k)) /. F9 is Element of the carrier of C
(b \ { the Element of b}) --> c is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
{c} is non empty trivial finite 1 -element set
[:(b \ { the Element of b}),{c}:] is finite set
((b \ { the Element of b}) --> c) /. F9 is Element of the carrier of C
b --> c is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
[:b,{c}:] is finite set
(b --> c) . F9 is set
b --> c is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
{c} is non empty trivial finite 1 -element set
[:b,{c}:] is finite set
(b --> c) . F9 is set
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Element of bool [:b, the carrier' of C:]
cods F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
(cods F9) /. F9 is Element of the carrier of C
b --> c is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
{c} is non empty trivial finite 1 -element set
[:b,{c}:] is finite set
(b --> c) . F9 is set
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Element of bool [:b, the carrier' of C:]
cods F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
(cods F9) /. F9 is Element of the carrier of C
(cods F9) . F9 is set
F9 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Injections_family of c,b
doms F9 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
d is set
F9 /. d is Element of the carrier' of C
F9 . d is set
( the Element of b .--> i2) . d is set
(doms F9) /. d is Element of the carrier of C
d /. d is Element of the carrier of C
F9 /. d is Element of the carrier' of C
F9 . d is set
(i1 * k) . d is set
(i1 * k) /. d is Element of the carrier' of C
(doms F9) /. d is Element of the carrier of C
dom ((i1 * k) /. d) is Element of the carrier of C
the Source of C . ((i1 * k) /. d) is Element of the carrier of C
doms (i1 * k) is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(doms (i1 * k)) /. d is Element of the carrier of C
h /. d is Element of the carrier of C
h . d is set
d . d is set
d /. d is Element of the carrier of C
(doms F9) /. d is Element of the carrier of C
d /. d is Element of the carrier of C
(doms F9) /. d is Element of the carrier of C
d /. d is Element of the carrier of C
d is Element of the carrier of C
Hom (c,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = d ) } is set
F99 is Relation-like b -defined the carrier' of C -valued Function-like total V18(b, the carrier' of C) finite Injections_family of d,b
doms F99 is Relation-like b -defined the carrier of C -valued Function-like total V18(b, the carrier of C) finite Element of bool [:b, the carrier of C:]
F99 | (b \ { the Element of b}) is Relation-like b -defined the carrier' of C -valued Function-like finite Element of bool [:b, the carrier' of C:]
G99 is set
G99 is Relation-like b \ { the Element of b} -defined the carrier' of C -valued Function-like total V18(b \ { the Element of b}, the carrier' of C) finite Element of bool [:(b \ { the Element of b}), the carrier' of C:]
G99 /. G99 is Element of the carrier' of C
G99 . G99 is set
F99 . G99 is set
F99 /. G99 is Element of the carrier' of C
cods G99 is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(cods G99) /. G99 is Element of the carrier of C
cod (F99 /. G99) is Element of the carrier of C
the Target of C . (F99 /. G99) is Element of the carrier of C
(b \ { the Element of b}) --> d is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
{d} is non empty trivial finite 1 -element set
[:(b \ { the Element of b}),{d}:] is finite set
((b \ { the Element of b}) --> d) /. G99 is Element of the carrier of C
h9 is set
h /. h9 is Element of the carrier of C
h . h9 is set
d . h9 is set
d /. h9 is Element of the carrier of C
F99 /. h9 is Element of the carrier' of C
F99 . h9 is set
G99 is Relation-like b \ { the Element of b} -defined the carrier' of C -valued Function-like total V18(b \ { the Element of b}, the carrier' of C) finite Injections_family of d,b \ { the Element of b}
G99 . h9 is set
G99 /. h9 is Element of the carrier' of C
(doms k) /. h9 is Element of the carrier of C
dom (G99 /. h9) is Element of the carrier of C
the Source of C . (G99 /. h9) is Element of the carrier of C
doms G99 is Relation-like b \ { the Element of b} -defined the carrier of C -valued Function-like total V18(b \ { the Element of b}, the carrier of C) finite Element of bool [:(b \ { the Element of b}), the carrier of C:]
(doms G99) /. h9 is Element of the carrier of C
Hom (g,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = g & cod b₁ = d ) } is set
h9 is Element of the carrier' of C
F99 /. the Element of b is Element of the carrier' of C
cod (F99 /. the Element of b) is Element of the carrier of C
the Target of C . (F99 /. the Element of b) is Element of the carrier of C
F9 /. the Element of b is Element of the carrier' of C
F9 . the Element of b is set
( the Element of b .--> i2) . the Element of b is set
(doms F9) /. the Element of b is Element of the carrier of C
dom (F99 /. the Element of b) is Element of the carrier of C
the Source of C . (F99 /. the Element of b) is Element of the carrier of C
Hom ((dom i2),d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = dom i2 & cod b₁ = d ) } is set
h is Element of the carrier' of C
k is Element of the carrier' of C
dom k is Element of the carrier of C
the Source of C . k is Element of the carrier of C
k (*) i1 is Element of the carrier' of C
dom (k (*) i1) is Element of the carrier of C
the Source of C . (k (*) i1) is Element of the carrier of C
y is set
k /. y is Element of the carrier' of C
(k (*) i1) (*) (k /. y) is Element of the carrier' of C
G99 /. y is Element of the carrier' of C
F9 /. y is Element of the carrier' of C
F9 . y is set
(i1 * k) . y is set
(i1 * k) /. y is Element of the carrier' of C
cod (k /. y) is Element of the carrier of C
the Target of C . (k /. y) is Element of the carrier of C
i1 (*) (k /. y) is Element of the carrier' of C
k (*) (i1 (*) (k /. y)) is Element of the carrier' of C
k (*) ((i1 * k) /. y) is Element of the carrier' of C
F99 /. y is Element of the carrier' of C
F99 . y is set
G99 . y is set
cod k is Element of the carrier of C
the Target of C . k is Element of the carrier of C
cod (k (*) i1) is Element of the carrier of C
the Target of C . (k (*) i1) is Element of the carrier of C
k (*) i2 is Element of the carrier' of C
y is set
F9 /. y is Element of the carrier' of C
k (*) (F9 /. y) is Element of the carrier' of C
F99 /. y is Element of the carrier' of C
F9 . y is set
( the Element of b .--> i2) . y is set
dom k is Element of the carrier of C
the Source of C . k is Element of the carrier of C
k /. y is Element of the carrier' of C
cod (k /. y) is Element of the carrier of C
the Target of C . (k /. y) is Element of the carrier of C
F9 . y is set
(i1 * k) . y is set
(i1 * k) /. y is Element of the carrier' of C
i1 (*) (k /. y) is Element of the carrier' of C
k (*) i1 is Element of the carrier' of C
(k (*) i1) (*) (k /. y) is Element of the carrier' of C
h9 (*) (k /. y) is Element of the carrier' of C
G99 /. y is Element of the carrier' of C
G99 . y is set
F99 . y is set
c is finite set
[:c, the carrier of C:] is set
bool [:c, the carrier of C:] is set
b is Relation-like c -defined the carrier of C -valued Function-like total V18(c, the carrier of C) finite Element of bool [:c, the carrier of C:]
card c is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
d is finite set
[:d, the carrier of C:] is set
bool [:d, the carrier of C:] is set
card d is V24() V25() V26() V30() V31() V32() V33() V35() finite cardinal Element of K92()
e is Relation-like d -defined the carrier of C -valued Function-like total V18(d, the carrier of C) finite Element of bool [:d, the carrier of C:]
[:{}, the carrier' of C:] is set
bool [:{}, the carrier' of C:] is set
s is Relation-like d -defined the carrier' of C -valued Function-like total V18(d, the carrier' of C) finite Injections_family of a,d
doms s is Relation-like d -defined the carrier of C -valued Function-like total V18(d, the carrier of C) finite Element of bool [:d, the carrier of C:]
f is set
(doms s) /. f is Element of the carrier of C
e /. f is Element of the carrier of C
the set is set
{ the set } is non empty trivial finite 1 -element set
the set :-> the set is Relation-like { the set } -defined { the set } -valued Function-like non empty total V18({ the set },{ the set }) finite Element of bool [:{ the set },{ the set }:]
[:{ the set },{ the set }:] is finite set
bool [:{ the set },{ the set }:] is finite V40() set
{ the set } --> the set is Relation-like { the set } -defined { the set } -valued Function-like non empty total V18({ the set },{ the set }) finite Element of bool [:{ the set },{ the set }:]
( the set , the set ) :-> the set is Relation-like [:{ the set },{ the set }:] -defined { the set } -valued Function-like total V18([:{ the set },{ the set }:],{ the set }) finite Element of bool [:[:{ the set },{ the set }:],{ the set }:]
[:[:{ the set },{ the set }:],{ the set }:] is finite set
bool [:[:{ the set },{ the set }:],{ the set }:] is finite V40() set
[ the set , the set ] is set
{[ the set , the set ]} is Function-like non empty trivial finite 1 -element set
{[ the set , the set ]} --> the set is Relation-like {[ the set , the set ]} -defined { the set } -valued Function-like non empty total V18({[ the set , the set ]},{ the set }) finite Element of bool [:{[ the set , the set ]},{ the set }:]
[:{[ the set , the set ]},{ the set }:] is finite set
bool [:{[ the set , the set ]},{ the set }:] is finite V40() set
Extract the set is Element of { the set }
({ the set },{ the set },( the set :-> the set ),( the set :-> the set ),(( the set , the set ) :-> the set ),(Extract the set ),(( the set , the set ) :-> the set ),(( the set , the set ) :-> the set ),(( the set , the set ) :-> the set )) is () ()
C is non empty non void V57() ()
the of C is Element of the carrier of C
the carrier of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
a is Element of the carrier of C
c is Element of the carrier of C
the of C . (a,c) is Element of the carrier of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
C is set
{C} is non empty trivial finite 1 -element set
a is set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
C is set
a is set
(C,a) is () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the Comp of (C,a) is Relation-like [: the carrier' of (C,a), the carrier' of (C,a):] -defined the carrier' of (C,a) -valued Function-like finite Element of bool [:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):]
the carrier' of (C,a) is non empty trivial finite 1 -element set
[: the carrier' of (C,a), the carrier' of (C,a):] is finite set
[:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):] is finite set
bool [:[: the carrier' of (C,a), the carrier' of (C,a):], the carrier' of (C,a):] is finite V40() set
the Source of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
the carrier of (C,a) is non empty trivial finite 1 -element set
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Target of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
dom the Comp of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier' of (C,a) -valued finite Element of bool [: the carrier' of (C,a), the carrier' of (C,a):]
bool [: the carrier' of (C,a), the carrier' of (C,a):] is finite V40() set
f is Element of the carrier' of (C,a)
s is Element of the carrier' of (C,a)
[f,s] is set
dom f is Element of the carrier of (C,a)
the Source of (C,a) . f is Element of the carrier of (C,a)
cod s is Element of the carrier of (C,a)
the Target of (C,a) . s is Element of the carrier of (C,a)
({},1) is non empty trivial finite non void 1 -element V57() trivial' transitive associative reflexive with_identities () ()
{{}} is non empty trivial finite V40() 1 -element set
{1} is non empty trivial finite V40() 1 -element set
1 :-> {} is Relation-like {1} -defined {{}} -valued Function-like non empty total V18({1},{{}}) finite Element of bool [:{1},{{}}:]
[:{1},{{}}:] is finite set
bool [:{1},{{}}:] is finite V40() set
{1} --> {} is Relation-like {1} -defined {{}} -valued Function-like non empty total V18({1},{{}}) finite Element of bool [:{1},{{}}:]
(1,1) :-> 1 is Relation-like [:{1},{1}:] -defined {1} -valued Function-like total V18([:{1},{1}:],{1}) finite Element of bool [:[:{1},{1}:],{1}:]
[:{1},{1}:] is finite set
[:[:{1},{1}:],{1}:] is finite set
bool [:[:{1},{1}:],{1}:] is finite V40() set
[1,1] is set
{[1,1]} is Function-like non empty trivial finite 1 -element set
{[1,1]} --> 1 is Relation-like {[1,1]} -defined {1} -valued Function-like non empty total V18({[1,1]},{1}) finite Element of bool [:{[1,1]},{1}:]
[:{[1,1]},{1}:] is finite set
bool [:{[1,1]},{1}:] is finite V40() set
Extract {} is finite Element of {{}}
({},{}) :-> {} is Relation-like [:{{}},{{}}:] -defined {{}} -valued Function-like total V18([:{{}},{{}}:],{{}}) finite Element of bool [:[:{{}},{{}}:],{{}}:]
[:{{}},{{}}:] is finite set
[:[:{{}},{{}}:],{{}}:] is finite set
bool [:[:{{}},{{}}:],{{}}:] is finite V40() set
[{},{}] is set
{[{},{}]} is Function-like non empty trivial finite 1 -element set
{[{},{}]} --> {} is Relation-like {[{},{}]} -defined {{}} -valued Function-like non empty total V18({[{},{}]},{{}}) finite Element of bool [:{[{},{}]},{{}}:]
[:{[{},{}]},{{}}:] is finite set
bool [:{[{},{}]},{{}}:] is finite V40() set
({},{}) :-> 1 is Relation-like [:{{}},{{}}:] -defined {1} -valued Function-like total V18([:{{}},{{}}:],{1}) finite Element of bool [:[:{{}},{{}}:],{1}:]
[:[:{{}},{{}}:],{1}:] is finite set
bool [:[:{{}},{{}}:],{1}:] is finite V40() set
{[{},{}]} --> 1 is Relation-like {[{},{}]} -defined {1} -valued Function-like non empty total V18({[{},{}]},{1}) finite Element of bool [:{[{},{}]},{1}:]
[:{[{},{}]},{1}:] is finite set
bool [:{[{},{}]},{1}:] is finite V40() set
({{}},{1},(1 :-> {}),(1 :-> {}),((1,1) :-> 1),(Extract {}),(({},{}) :-> {}),(({},{}) :-> 1),(({},{}) :-> 1)) is () ()
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier' of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier' of (C,a)
b is Element of the carrier' of (C,a)
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
Hom (c,b) is finite Element of bool the carrier' of (C,a)
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = c & cod b₁ = b ) } is set
d is Element of the carrier' of (C,a)
cod d is Element of the carrier of (C,a)
the Target of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Target of (C,a) . d is Element of the carrier of (C,a)
dom d is Element of the carrier of (C,a)
the Source of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
the Source of (C,a) . d is Element of the carrier of (C,a)
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
d is Element of the carrier' of (C,a)
Hom (c,b) is finite Element of bool the carrier' of (C,a)
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = c & cod b₁ = b ) } is set
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
Hom (c,b) is finite Element of bool the carrier' of (C,a)
the carrier' of (C,a) is non empty trivial finite 1 -element set
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = c & cod b₁ = b ) } is set
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier of (C,a)
Hom (c,b) is finite Element of bool the carrier' of (C,a)
the carrier' of (C,a) is non empty trivial finite 1 -element set
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = c & cod b₁ = b ) } is set
the Morphism of c,b is Morphism of c,b
e is Morphism of c,b
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
c is Element of the carrier of (C,a)
b is Element of the carrier' of (C,a)
d is Element of the carrier' of (C,a)
cod b is Element of the carrier of (C,a)
the Target of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Target of (C,a) . b is Element of the carrier of (C,a)
cod d is Element of the carrier of (C,a)
the Target of (C,a) . d is Element of the carrier of (C,a)
dom b is Element of the carrier of (C,a)
the Source of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
the Source of (C,a) . b is Element of the carrier of (C,a)
dom d is Element of the carrier of (C,a)
the Source of (C,a) . d is Element of the carrier of (C,a)
e is Element of the carrier of (C,a)
Hom ((dom b),e) is finite Element of bool the carrier' of (C,a)
bool the carrier' of (C,a) is finite V40() set
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = dom b & cod b₁ = e ) } is set
Hom ((dom d),e) is finite Element of bool the carrier' of (C,a)
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = dom d & cod b₁ = e ) } is set
Hom (c,e) is finite Element of bool the carrier' of (C,a)
{ b₁ where b₁ is Element of the carrier' of (C,a) : ( dom b₁ = c & cod b₁ = e ) } is set
s is Element of the carrier' of (C,a)
f is Element of the carrier' of (C,a)
h is Element of the carrier' of (C,a)
g is Element of the carrier' of (C,a)
g (*) b is Element of the carrier' of (C,a)
g (*) d is Element of the carrier' of (C,a)
C is set
a is set
(C,a) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{C} is non empty trivial finite 1 -element set
{a} is non empty trivial finite 1 -element set
a :-> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
[:{a},{C}:] is finite set
bool [:{a},{C}:] is finite V40() set
{a} --> C is Relation-like {a} -defined {C} -valued Function-like non empty total V18({a},{C}) finite Element of bool [:{a},{C}:]
(a,a) :-> a is Relation-like [:{a},{a}:] -defined {a} -valued Function-like total V18([:{a},{a}:],{a}) finite Element of bool [:[:{a},{a}:],{a}:]
[:{a},{a}:] is finite set
[:[:{a},{a}:],{a}:] is finite set
bool [:[:{a},{a}:],{a}:] is finite V40() set
[a,a] is set
{[a,a]} is Function-like non empty trivial finite 1 -element set
{[a,a]} --> a is Relation-like {[a,a]} -defined {a} -valued Function-like non empty total V18({[a,a]},{a}) finite Element of bool [:{[a,a]},{a}:]
[:{[a,a]},{a}:] is finite set
bool [:{[a,a]},{a}:] is finite V40() set
Extract C is Element of {C}
(C,C) :-> C is Relation-like [:{C},{C}:] -defined {C} -valued Function-like total V18([:{C},{C}:],{C}) finite Element of bool [:[:{C},{C}:],{C}:]
[:{C},{C}:] is finite set
[:[:{C},{C}:],{C}:] is finite set
bool [:[:{C},{C}:],{C}:] is finite V40() set
[C,C] is set
{[C,C]} is Function-like non empty trivial finite 1 -element set
{[C,C]} --> C is Relation-like {[C,C]} -defined {C} -valued Function-like non empty total V18({[C,C]},{C}) finite Element of bool [:{[C,C]},{C}:]
[:{[C,C]},{C}:] is finite set
bool [:{[C,C]},{C}:] is finite V40() set
(C,C) :-> a is Relation-like [:{C},{C}:] -defined {a} -valued Function-like total V18([:{C},{C}:],{a}) finite Element of bool [:[:{C},{C}:],{a}:]
[:[:{C},{C}:],{a}:] is finite set
bool [:[:{C},{C}:],{a}:] is finite V40() set
{[C,C]} --> a is Relation-like {[C,C]} -defined {a} -valued Function-like non empty total V18({[C,C]},{a}) finite Element of bool [:{[C,C]},{a}:]
[:{[C,C]},{a}:] is finite set
bool [:{[C,C]},{a}:] is finite V40() set
({C},{a},(a :-> C),(a :-> C),((a,a) :-> a),(Extract C),((C,C) :-> C),((C,C) :-> a),((C,C) :-> a)) is () ()
the of (C,a) is Element of the carrier of (C,a)
the carrier of (C,a) is non empty trivial finite 1 -element set
the carrier' of (C,a) is non empty trivial finite 1 -element set
the of (C,a) is Relation-like [: the carrier of (C,a), the carrier of (C,a):] -defined the carrier' of (C,a) -valued Function-like total V18([: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a)) finite Element of bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a):]
[: the carrier of (C,a), the carrier of (C,a):] is finite set
[:[: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a):] is finite set
bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a):] is finite V40() set
the of (C,a) is Relation-like [: the carrier of (C,a), the carrier of (C,a):] -defined the carrier' of (C,a) -valued Function-like total V18([: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a)) finite Element of bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier' of (C,a):]
the of (C,a) is Relation-like [: the carrier of (C,a), the carrier of (C,a):] -defined the carrier of (C,a) -valued Function-like total V18([: the carrier of (C,a), the carrier of (C,a):], the carrier of (C,a)) finite Element of bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier of (C,a):]
[:[: the carrier of (C,a), the carrier of (C,a):], the carrier of (C,a):] is finite set
bool [:[: the carrier of (C,a), the carrier of (C,a):], the carrier of (C,a):] is finite V40() set
b is Element of the carrier of (C,a)
d is Element of the carrier of (C,a)
the of (C,a) . (b,d) is Element of the carrier' of (C,a)
dom ( the of (C,a) . (b,d)) is Element of the carrier of (C,a)
the Source of (C,a) is Relation-like the carrier' of (C,a) -defined the carrier of (C,a) -valued Function-like non empty total V18( the carrier' of (C,a), the carrier of (C,a)) finite Element of bool [: the carrier' of (C,a), the carrier of (C,a):]
[: the carrier' of (C,a), the carrier of (C,a):] is finite set
bool [: the carrier' of (C,a), the carrier of (C,a):] is finite V40() set
the Source of (C,a) . ( the of (C,a) . (b,d)) is Element of the carrier of (C,a)
the of (C,a) . (b,d) is Element of the carrier' of (C,a)
dom ( the of (C,a) . (b,d)) is Element of the carrier of (C,a)
the Source of (C,a) . ( the of (C,a) . (b,d)) is Element of the carrier of (C,a)
the of (C,a) . (b,d) is Element of the carrier of (C,a)
({},1) is non empty trivial finite non void 1 -element V57() trivial' Category-like transitive associative reflexive with_identities () ()
{{}} is non empty trivial finite V40() 1 -element set
{1} is non empty trivial finite V40() 1 -element set
1 :-> {} is Relation-like {1} -defined {{}} -valued Function-like non empty total V18({1},{{}}) finite Element of bool [:{1},{{}}:]
[:{1},{{}}:] is finite set
bool [:{1},{{}}:] is finite V40() set
{1} --> {} is Relation-like {1} -defined {{}} -valued Function-like non empty total V18({1},{{}}) finite Element of bool [:{1},{{}}:]
(1,1) :-> 1 is Relation-like [:{1},{1}:] -defined {1} -valued Function-like total V18([:{1},{1}:],{1}) finite Element of bool [:[:{1},{1}:],{1}:]
[:{1},{1}:] is finite set
[:[:{1},{1}:],{1}:] is finite set
bool [:[:{1},{1}:],{1}:] is finite V40() set
[1,1] is set
{[1,1]} is Function-like non empty trivial finite 1 -element set
{[1,1]} --> 1 is Relation-like {[1,1]} -defined {1} -valued Function-like non empty total V18({[1,1]},{1}) finite Element of bool [:{[1,1]},{1}:]
[:{[1,1]},{1}:] is finite set
bool [:{[1,1]},{1}:] is finite V40() set
Extract {} is finite Element of {{}}
({},{}) :-> {} is Relation-like [:{{}},{{}}:] -defined {{}} -valued Function-like total V18([:{{}},{{}}:],{{}}) finite Element of bool [:[:{{}},{{}}:],{{}}:]
[:{{}},{{}}:] is finite set
[:[:{{}},{{}}:],{{}}:] is finite set
bool [:[:{{}},{{}}:],{{}}:] is finite V40() set
[{},{}] is set
{[{},{}]} is Function-like non empty trivial finite 1 -element set
{[{},{}]} --> {} is Relation-like {[{},{}]} -defined {{}} -valued Function-like non empty total V18({[{},{}]},{{}}) finite Element of bool [:{[{},{}]},{{}}:]
[:{[{},{}]},{{}}:] is finite set
bool [:{[{},{}]},{{}}:] is finite V40() set
({},{}) :-> 1 is Relation-like [:{{}},{{}}:] -defined {1} -valued Function-like total V18([:{{}},{{}}:],{1}) finite Element of bool [:[:{{}},{{}}:],{1}:]
[:[:{{}},{{}}:],{1}:] is finite set
bool [:[:{{}},{{}}:],{1}:] is finite V40() set
{[{},{}]} --> 1 is Relation-like {[{},{}]} -defined {1} -valued Function-like non empty total V18({[{},{}]},{1}) finite Element of bool [:{[{},{}]},{1}:]
[:{[{},{}]},{1}:] is finite set
bool [:{[{},{}]},{1}:] is finite V40() set
({{}},{1},(1 :-> {}),(1 :-> {}),((1,1) :-> 1),(Extract {}),(({},{}) :-> {}),(({},{}) :-> 1),(({},{}) :-> 1)) is () ()
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
(C) is Element of the carrier of C
the carrier of C is non empty set
the of C is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
c is Morphism of (C),a
b is Morphism of (C),a
d is Morphism of (C),a
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
c is Morphism of (C),a
b is Morphism of (C),a
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
Hom ((C),a) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C) & cod b₁ = a ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,a) is Morphism of (C),a
init ((C),a) is Morphism of (C),a
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,a) is Morphism of (C),a
dom (C,a) is Element of the carrier of C
the carrier' of C is non empty set
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a) is Element of the carrier of C
cod (C,a) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a) is Element of the carrier of C
init ((C),a) is Morphism of (C),a
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
Hom ((C),a) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C) & cod b₁ = a ) } is set
(C,a) is Morphism of (C),a
{(C,a)} is non empty trivial finite 1 -element set
c is Morphism of (C),a
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
Hom (a,(C,a,c)) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,c) ) } is set
Hom (c,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,c) ) } is set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
cod ( the of C . (a,c)) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Target of C . ( the of C . (a,c)) is Element of the carrier of C
cod ( the of C . (a,c)) is Element of the carrier of C
the Target of C . ( the of C . (a,c)) is Element of the carrier of C
dom ( the of C . (a,c)) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C . ( the of C . (a,c)) is Element of the carrier of C
dom ( the of C . (a,c)) is Element of the carrier of C
the Source of C . ( the of C . (a,c)) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
the carrier' of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C . (C,a,c) is Element of the carrier of C
(C) is Element of the carrier of C
the of C is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Target of C . (C,a,c) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
Hom (c,a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = a ) } is set
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of a,(C,a,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of c,(C,a,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
Hom (a,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,c) ) } is set
Hom (c,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,c) ) } is set
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Source of C . (C,a,c) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of a,(C,a,c)
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Target of C . (C,a,c) is Element of the carrier of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C . (C,a,c) is Element of the carrier of C
(C,a,c) is Element of the carrier' of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of c,(C,a,c)
cod (C,a,c) is Element of the carrier of C
the Target of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
[: the carrier' of C, the carrier of C:] is set
bool [: the carrier' of C, the carrier of C:] is set
the Target of C . (C,a,c) is Element of the carrier of C
dom (C,a,c) is Element of the carrier of C
the Source of C is Relation-like the carrier' of C -defined the carrier of C -valued Function-like non empty total V18( the carrier' of C, the carrier of C) Element of bool [: the carrier' of C, the carrier of C:]
the Source of C . (C,a,c) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
b is Element of the carrier of C
c is Element of the carrier of C
Hom (a,b) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = b ) } is set
Hom (c,b) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = b ) } is set
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of a,(C,a,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
d is Morphism of a,b
(C,a,c) is Morphism of c,(C,a,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
e is Morphism of c,b
Hom (a,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,c) ) } is set
Hom (c,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,c) ) } is set
s is Morphism of (C,a,c),b
s * (C,a,c) is Morphism of a,b
s * (C,a,c) is Morphism of c,b
Hom (c,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,c) ) } is set
Hom (a,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,c) ) } is set
s is Morphism of (C,a,c),b
f is Morphism of (C,a,c),b
f * (C,a,c) is Morphism of a,b
f * (C,a,c) is Morphism of c,b
h is Morphism of (C,a,c),b
h * (C,a,c) is Morphism of a,b
h * (C,a,c) is Morphism of c,b
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (b,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = c ) } is set
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
Hom ((C,a,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = c ) } is set
(C,a,b) is Morphism of a,(C,a,b)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,b) is Element of the carrier' of C
(C,a,b) is Morphism of b,(C,a,b)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,b) is Element of the carrier' of C
Hom (a,(C,a,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,b) ) } is set
Hom (b,(C,a,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = (C,a,b) ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of a,(C,a,c)
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of c,(C,a,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(C,a,c,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,a,c)
id (C,a,c) is Morphism of (C,a,c),(C,a,c)
Hom (c,(C,a,c)) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,c) ) } is set
(id (C,a,c)) * (C,a,c) is Morphism of c,(C,a,c)
Hom (a,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,c) ) } is set
(id (C,a,c)) * (C,a,c) is Morphism of a,(C,a,c)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (b,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = c ) } is set
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
d is Element of the carrier of C
Hom (c,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = d ) } is set
e is Morphism of a,c
s is Morphism of b,c
(C,a,b,c,e,s) is Morphism of (C,a,b),c
f is Morphism of c,d
f * e is Morphism of a,d
f * s is Morphism of b,d
(C,a,b,d,(f * e),(f * s)) is Morphism of (C,a,b),d
f * (C,a,b,c,e,s) is Morphism of (C,a,b),d
Hom ((C,a,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = c ) } is set
Hom (b,(C,a,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = (C,a,b) ) } is set
(C,a,b) is Morphism of b,(C,a,b)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,b) is Element of the carrier' of C
(C,a,b,c,e,s) * (C,a,b) is Morphism of b,c
f * ((C,a,b,c,e,s) * (C,a,b)) is Morphism of b,d
(f * (C,a,b,c,e,s)) * (C,a,b) is Morphism of b,d
Hom (a,(C,a,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,b) ) } is set
Hom (a,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = d ) } is set
Hom (b,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = d ) } is set
(C,a,b) is Morphism of a,(C,a,b)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,b) is Element of the carrier' of C
(C,a,b,c,e,s) * (C,a,b) is Morphism of a,c
f * ((C,a,b,c,e,s) * (C,a,b)) is Morphism of a,d
(f * (C,a,b,c,e,s)) * (C,a,b) is Morphism of a,d
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (b,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = c ) } is set
d is Morphism of a,c
e is Morphism of a,c
s is Morphism of b,c
(C,a,b,c,d,s) is Morphism of (C,a,b),c
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
f is Morphism of b,c
(C,a,b,c,e,f) is Morphism of (C,a,b),c
(C,a,b) is Morphism of a,(C,a,b)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,b) is Element of the carrier' of C
(C,a,b,c,d,s) * (C,a,b) is Morphism of a,c
(C,a,b) is Morphism of b,(C,a,b)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,b) is Element of the carrier' of C
(C,a,b,c,d,s) * (C,a,b) is Morphism of b,c
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
Hom (b,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = c ) } is set
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
d is Morphism of a,c
e is Morphism of b,c
(C,a,b,c,d,e) is Morphism of (C,a,b),c
s is Element of the carrier of C
Hom (c,s) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = s ) } is set
f is Morphism of c,s
f * (C,a,b,c,d,e) is Morphism of (C,a,b),s
h is Morphism of c,s
h * (C,a,b,c,d,e) is Morphism of (C,a,b),s
Hom (a,s) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = s ) } is set
Hom (b,s) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = s ) } is set
f * d is Morphism of a,s
f * e is Morphism of b,s
(C,a,b,s,(f * d),(f * e)) is Morphism of (C,a,b),s
h * d is Morphism of a,s
h * e is Morphism of b,s
(C,a,b,s,(h * d),(h * e)) is Morphism of (C,a,b),s
s is Element of the carrier of C
Hom (c,s) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = s ) } is set
f is Morphism of c,s
f * (C,a,b,c,d,e) is Morphism of (C,a,b),s
h is Morphism of c,s
h * (C,a,b,c,d,e) is Morphism of (C,a,b),s
Hom (a,s) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = s ) } is set
Hom (b,s) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = s ) } is set
f * d is Morphism of a,s
f * e is Morphism of b,s
(C,a,b,s,(f * d),(f * e)) is Morphism of (C,a,b),s
h * d is Morphism of a,s
h * e is Morphism of b,s
(C,a,b,s,(h * d),(h * e)) is Morphism of (C,a,b),s
Hom ((C,a,b),c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = c ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
(C) is Element of the carrier of C
the of C is Element of the carrier of C
a is Element of the carrier of C
(C,a,(C)) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,(C)) is Element of the carrier of C
(C,(C),a) is Element of the carrier of C
the of C . ((C),a) is Element of the carrier of C
(C,a) is Morphism of (C),a
(C,(C),a) is Morphism of a,(C,(C),a)
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . ((C),a) is Element of the carrier' of C
(C,(C),a) * (C,a) is Morphism of (C),(C,(C),a)
(C,(C),a) is Morphism of (C),(C,(C),a)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . ((C),a) is Element of the carrier' of C
Hom ((C),a) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C) & cod b₁ = a ) } is set
Hom (a,a) is non empty Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = a ) } is set
Hom (a,(C,a,(C))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,(C)) ) } is set
Hom ((C,a,(C)),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C)) & cod b₁ = a ) } is set
id (C,a,(C)) is Morphism of (C,a,(C)),(C,a,(C))
id a is Morphism of a,a
(C,a,(C)) is Morphism of a,(C,a,(C))
the of C . (a,(C)) is Element of the carrier' of C
c is Morphism of a,(C,a,(C))
(C,a,(C),a,(id a),(C,a)) is Morphism of (C,a,(C)),a
b is Morphism of (C,a,(C)),a
c * b is Morphism of (C,a,(C)),(C,a,(C))
b * c is Morphism of a,a
(C,a,(C)) * (C,a) is Morphism of (C),(C,a,(C))
(C,a,(C)) is Morphism of (C),(C,a,(C))
the of C . (a,(C)) is Element of the carrier' of C
(C,a,(C)) * (id a) is Morphism of a,(C,a,(C))
(C,a,(C),(C,a,(C)),(C,a,(C)),(C,a,(C))) is Morphism of (C,a,(C)),(C,a,(C))
Hom (a,(C,(C),a)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,(C),a) ) } is set
Hom ((C,(C),a),a) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C),a) & cod b₁ = a ) } is set
id (C,(C),a) is Morphism of (C,(C),a),(C,(C),a)
id a is Morphism of a,a
c is Morphism of a,(C,(C),a)
(C,(C),a,a,(C,a),(id a)) is Morphism of (C,(C),a),a
b is Morphism of (C,(C),a),a
c * b is Morphism of (C,(C),a),(C,(C),a)
b * c is Morphism of a,a
(C,(C),a) * (id a) is Morphism of a,(C,(C),a)
(C,(C),a,(C,(C),a),(C,(C),a),(C,(C),a)) is Morphism of (C,(C),a),(C,(C),a)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,c,a) is Element of the carrier of C
the of C . (c,a) is Element of the carrier of C
Hom (a,(C,c,a)) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,c,a) ) } is set
Hom (c,(C,c,a)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,c,a) ) } is set
Hom ((C,a,c),(C,c,a)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = (C,c,a) ) } is set
Hom ((C,c,a),(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,a) & cod b₁ = (C,a,c) ) } is set
id (C,c,a) is Morphism of (C,c,a),(C,c,a)
id (C,a,c) is Morphism of (C,a,c),(C,a,c)
Hom (a,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,c) ) } is set
Hom (c,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,c) ) } is set
(C,c,a) is Morphism of a,(C,c,a)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (c,a) is Element of the carrier' of C
(C,c,a) is Morphism of c,(C,c,a)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (c,a) is Element of the carrier' of C
(C,a,c,(C,c,a),(C,c,a),(C,c,a)) is Morphism of (C,a,c),(C,c,a)
b is Morphism of (C,a,c),(C,c,a)
(C,a,c) is Morphism of c,(C,a,c)
the of C . (a,c) is Element of the carrier' of C
(C,a,c) is Morphism of a,(C,a,c)
the of C . (a,c) is Element of the carrier' of C
(C,c,a,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,c,a),(C,a,c)
d is Morphism of (C,c,a),(C,a,c)
b * d is Morphism of (C,c,a),(C,c,a)
d * b is Morphism of (C,a,c),(C,a,c)
b * (C,a,c) is Morphism of c,(C,c,a)
b * (C,a,c) is Morphism of a,(C,c,a)
(C,c,a,(C,c,a),(b * (C,a,c)),(b * (C,a,c))) is Morphism of (C,c,a),(C,c,a)
(C,c,a,(C,c,a),(C,c,a),(b * (C,a,c))) is Morphism of (C,c,a),(C,c,a)
(C,c,a,(C,c,a),(C,c,a),(C,c,a)) is Morphism of (C,c,a),(C,c,a)
d * (C,c,a) is Morphism of a,(C,a,c)
d * (C,c,a) is Morphism of c,(C,a,c)
(C,a,c,(C,a,c),(d * (C,c,a)),(d * (C,c,a))) is Morphism of (C,a,c),(C,a,c)
(C,a,c,(C,a,c),(C,a,c),(d * (C,c,a))) is Morphism of (C,a,c),(C,a,c)
(C,a,c,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,a,c)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
b is Element of the carrier of C
(C,(C,a,c),b) is Element of the carrier of C
the of C . ((C,a,c),b) is Element of the carrier of C
(C,c,b) is Element of the carrier of C
the of C . (c,b) is Element of the carrier of C
(C,a,(C,c,b)) is Element of the carrier of C
the of C . (a,(C,c,b)) is Element of the carrier of C
(C,a,c) is Morphism of c,(C,a,c)
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,(C,a,c),b) is Morphism of (C,a,c),(C,(C,a,c),b)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . ((C,a,c),b) is Element of the carrier' of C
(C,(C,a,c),b) * (C,a,c) is Morphism of c,(C,(C,a,c),b)
(C,(C,a,c),b) is Morphism of b,(C,(C,a,c),b)
the of C . ((C,a,c),b) is Element of the carrier' of C
(C,c,b,(C,(C,a,c),b),((C,(C,a,c),b) * (C,a,c)),(C,(C,a,c),b)) is Morphism of (C,c,b),(C,(C,a,c),b)
(C,a,(C,c,b)) is Morphism of a,(C,a,(C,c,b))
the of C . (a,(C,c,b)) is Element of the carrier' of C
(C,c,b) is Morphism of c,(C,c,b)
the of C . (c,b) is Element of the carrier' of C
(C,a,(C,c,b)) is Morphism of (C,c,b),(C,a,(C,c,b))
the of C . (a,(C,c,b)) is Element of the carrier' of C
(C,a,(C,c,b)) * (C,c,b) is Morphism of c,(C,a,(C,c,b))
(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,a,(C,c,b)) * (C,c,b))) is Morphism of (C,a,c),(C,a,(C,c,b))
Hom ((C,c,b),(C,a,(C,c,b))) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = (C,a,(C,c,b)) ) } is set
Hom (c,(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,c,b) ) } is set
Hom (c,(C,a,(C,c,b))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,(C,c,b)) ) } is set
Hom (a,(C,a,(C,c,b))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,(C,c,b)) ) } is set
Hom ((C,a,c),(C,a,(C,c,b))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = (C,a,(C,c,b)) ) } is set
Hom (b,(C,c,b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = (C,c,b) ) } is set
Hom (b,(C,a,(C,c,b))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = (C,a,(C,c,b)) ) } is set
Hom ((C,(C,a,c),b),(C,a,(C,c,b))) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,(C,a,c),b) & cod b₁ = (C,a,(C,c,b)) ) } is set
Hom ((C,a,(C,c,b)),(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,(C,c,b)) & cod b₁ = (C,(C,a,c),b) ) } is set
id (C,a,(C,c,b)) is Morphism of (C,a,(C,c,b)),(C,a,(C,c,b))
id (C,(C,a,c),b) is Morphism of (C,(C,a,c),b),(C,(C,a,c),b)
Hom ((C,a,c),(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,c) & cod b₁ = (C,(C,a,c),b) ) } is set
Hom (c,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,c) ) } is set
Hom (c,(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,(C,a,c),b) ) } is set
Hom (b,(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = (C,(C,a,c),b) ) } is set
Hom ((C,c,b),(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,b) & cod b₁ = (C,(C,a,c),b) ) } is set
Hom (a,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,c) ) } is set
Hom (a,(C,(C,a,c),b)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,(C,a,c),b) ) } is set
(C,c,b) is Morphism of b,(C,c,b)
the of C . (c,b) is Element of the carrier' of C
(C,a,(C,c,b)) * (C,c,b) is Morphism of b,(C,a,(C,c,b))
(C,(C,a,c),b,(C,a,(C,c,b)),(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,a,(C,c,b)) * (C,c,b))),((C,a,(C,c,b)) * (C,c,b))) is Morphism of (C,(C,a,c),b),(C,a,(C,c,b))
s is Morphism of (C,(C,a,c),b),(C,a,(C,c,b))
s * ((C,(C,a,c),b) * (C,a,c)) is Morphism of c,(C,a,(C,c,b))
s * (C,(C,a,c),b) is Morphism of (C,a,c),(C,a,(C,c,b))
(s * (C,(C,a,c),b)) * (C,a,c) is Morphism of c,(C,a,(C,c,b))
(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,a,(C,c,b)) * (C,c,b))) * (C,a,c) is Morphism of c,(C,a,(C,c,b))
s * (C,c,b,(C,(C,a,c),b),((C,(C,a,c),b) * (C,a,c)),(C,(C,a,c),b)) is Morphism of (C,c,b),(C,a,(C,c,b))
s * (C,(C,a,c),b) is Morphism of b,(C,a,(C,c,b))
(C,c,b,(C,a,(C,c,b)),((C,a,(C,c,b)) * (C,c,b)),(s * (C,(C,a,c),b))) is Morphism of (C,c,b),(C,a,(C,c,b))
(C,c,b,(C,a,(C,c,b)),((C,a,(C,c,b)) * (C,c,b)),((C,a,(C,c,b)) * (C,c,b))) is Morphism of (C,c,b),(C,a,(C,c,b))
(C,c,b,(C,c,b),(C,c,b),(C,c,b)) is Morphism of (C,c,b),(C,c,b)
(C,a,(C,c,b)) * (C,c,b,(C,c,b),(C,c,b),(C,c,b)) is Morphism of (C,c,b),(C,a,(C,c,b))
id (C,c,b) is Morphism of (C,c,b),(C,c,b)
(C,a,(C,c,b)) * (id (C,c,b)) is Morphism of (C,c,b),(C,a,(C,c,b))
(C,a,c) is Morphism of a,(C,a,c)
the of C . (a,c) is Element of the carrier' of C
(C,(C,a,c),b) * (C,a,c) is Morphism of a,(C,(C,a,c),b)
(C,a,(C,c,b),(C,(C,a,c),b),((C,(C,a,c),b) * (C,a,c)),(C,c,b,(C,(C,a,c),b),((C,(C,a,c),b) * (C,a,c)),(C,(C,a,c),b))) is Morphism of (C,a,(C,c,b)),(C,(C,a,c),b)
f is Morphism of (C,a,(C,c,b)),(C,(C,a,c),b)
s * f is Morphism of (C,a,(C,c,b)),(C,a,(C,c,b))
f * s is Morphism of (C,(C,a,c),b),(C,(C,a,c),b)
f * ((C,a,(C,c,b)) * (C,c,b)) is Morphism of c,(C,(C,a,c),b)
f * (C,a,(C,c,b)) is Morphism of (C,c,b),(C,(C,a,c),b)
(f * (C,a,(C,c,b))) * (C,c,b) is Morphism of c,(C,(C,a,c),b)
(C,c,b,(C,(C,a,c),b),((C,(C,a,c),b) * (C,a,c)),(C,(C,a,c),b)) * (C,c,b) is Morphism of c,(C,(C,a,c),b)
f * (C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,a,(C,c,b)) * (C,c,b))) is Morphism of (C,a,c),(C,(C,a,c),b)
f * (C,a,(C,c,b)) is Morphism of a,(C,(C,a,c),b)
(C,a,c,(C,(C,a,c),b),(f * (C,a,(C,c,b))),((C,(C,a,c),b) * (C,a,c))) is Morphism of (C,a,c),(C,(C,a,c),b)
(C,a,c,(C,(C,a,c),b),((C,(C,a,c),b) * (C,a,c)),((C,(C,a,c),b) * (C,a,c))) is Morphism of (C,a,c),(C,(C,a,c),b)
(C,a,c,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,a,c)
(C,(C,a,c),b) * (C,a,c,(C,a,c),(C,a,c),(C,a,c)) is Morphism of (C,a,c),(C,(C,a,c),b)
id (C,a,c) is Morphism of (C,a,c),(C,a,c)
(C,(C,a,c),b) * (id (C,a,c)) is Morphism of (C,a,c),(C,(C,a,c),b)
s * ((C,(C,a,c),b) * (C,a,c)) is Morphism of a,(C,a,(C,c,b))
(s * (C,(C,a,c),b)) * (C,a,c) is Morphism of a,(C,a,(C,c,b))
(C,a,c,(C,a,(C,c,b)),(C,a,(C,c,b)),((C,a,(C,c,b)) * (C,c,b))) * (C,a,c) is Morphism of a,(C,a,(C,c,b))
(C,a,(C,c,b),(C,a,(C,c,b)),(C,a,(C,c,b)),(C,a,(C,c,b))) is Morphism of (C,a,(C,c,b)),(C,a,(C,c,b))
f * ((C,a,(C,c,b)) * (C,c,b)) is Morphism of b,(C,(C,a,c),b)
(f * (C,a,(C,c,b))) * (C,c,b) is Morphism of b,(C,(C,a,c),b)
(C,c,b,(C,(C,a,c),b),((C,(C,a,c),b) * (C,a,c)),(C,(C,a,c),b)) * (C,c,b) is Morphism of b,(C,(C,a,c),b)
(C,(C,a,c),b,(C,(C,a,c),b),(C,(C,a,c),b),(C,(C,a,c),b)) is Morphism of (C,(C,a,c),b),(C,(C,a,c),b)
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
id a is Morphism of a,a
(C,a,a,a,(id a),(id a)) is Morphism of (C,a,a),a
(C,a,a) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,a) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
b is Element of the carrier of C
c is Element of the carrier of C
d is Element of the carrier of C
(C,b,d) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (b,d) is Element of the carrier of C
e is Morphism of a,b
(C,b,d) is Morphism of b,(C,b,d)
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (b,d) is Element of the carrier' of C
(C,b,d) * e is Morphism of a,(C,b,d)
s is Morphism of c,d
(C,b,d) is Morphism of d,(C,b,d)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (b,d) is Element of the carrier' of C
(C,b,d) * s is Morphism of c,(C,b,d)
(C,a,c,(C,b,d),((C,b,d) * e),((C,b,d) * s)) is Morphism of (C,a,c),(C,b,d)
(C,a,c) is Element of the carrier of C
the of C . (a,c) is Element of the carrier of C
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
d is Element of the carrier of C
Hom (b,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = d ) } is set
(C,c,d) is Element of the carrier of C
the of C . (c,d) is Element of the carrier of C
Hom ((C,a,b),(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,a,b) & cod b₁ = (C,c,d) ) } is set
Hom (d,(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = d & cod b₁ = (C,c,d) ) } is set
Hom (b,(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = (C,c,d) ) } is set
Hom (c,(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,c,d) ) } is set
Hom (a,(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,c,d) ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
id a is Morphism of a,a
c is Element of the carrier of C
id c is Morphism of c,c
(C,a,c,a,c,(id a),(id c)) is Morphism of (C,a,c),(C,a,c)
(C,a,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,c) is Element of the carrier of C
(C,a,c) is Morphism of a,(C,a,c)
the carrier' of C is non empty set
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (a,c) is Element of the carrier' of C
(C,a,c) * (id a) is Morphism of a,(C,a,c)
(C,a,c) is Morphism of c,(C,a,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (a,c) is Element of the carrier' of C
(C,a,c) * (id c) is Morphism of c,(C,a,c)
(C,a,c,(C,a,c),((C,a,c) * (id a)),((C,a,c) * (id c))) is Morphism of (C,a,c),(C,a,c)
id (C,a,c) is Morphism of (C,a,c),(C,a,c)
Hom (c,(C,a,c)) is Element of bool the carrier' of C
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,a,c) ) } is set
Hom (a,(C,a,c)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,a,c) ) } is set
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
d is Element of the carrier of C
Hom (b,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = d ) } is set
(C,c,d) is Element of the carrier of C
the of C . (c,d) is Element of the carrier of C
e is Element of the carrier of C
Hom (c,e) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = e ) } is set
Hom (d,e) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = d & cod b₁ = e ) } is set
s is Morphism of a,c
f is Morphism of b,d
(C,a,b,c,d,s,f) is Morphism of (C,a,b),(C,c,d)
(C,c,d) is Morphism of c,(C,c,d)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (c,d) is Element of the carrier' of C
(C,c,d) * s is Morphism of a,(C,c,d)
(C,c,d) is Morphism of d,(C,c,d)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (c,d) is Element of the carrier' of C
(C,c,d) * f is Morphism of b,(C,c,d)
(C,a,b,(C,c,d),((C,c,d) * s),((C,c,d) * f)) is Morphism of (C,a,b),(C,c,d)
h is Morphism of c,e
h * s is Morphism of a,e
g is Morphism of d,e
(C,c,d,e,h,g) is Morphism of (C,c,d),e
(C,c,d,e,h,g) * (C,a,b,c,d,s,f) is Morphism of (C,a,b),e
g * f is Morphism of b,e
(C,a,b,e,(h * s),(g * f)) is Morphism of (C,a,b),e
Hom ((C,c,d),e) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = (C,c,d) & cod b₁ = e ) } is set
Hom (d,(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = d & cod b₁ = (C,c,d) ) } is set
Hom (b,(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = (C,c,d) ) } is set
Hom (c,(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,c,d) ) } is set
Hom (a,(C,c,d)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = (C,c,d) ) } is set
(C,c,d,e,h,g) * (C,c,d) is Morphism of d,e
(C,c,d,e,h,g) * ((C,c,d) * f) is Morphism of b,e
(C,c,d,e,h,g) * (C,c,d) is Morphism of c,e
(C,c,d,e,h,g) * ((C,c,d) * s) is Morphism of a,e
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
(C,c,c) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (c,c) is Element of the carrier of C
(C,c) is Morphism of (C,c,c),c
id c is Morphism of c,c
(C,c,c,c,(id c),(id c)) is Morphism of (C,c,c),c
b is Element of the carrier of C
Hom (b,c) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = c ) } is set
(C,a,b) is Element of the carrier of C
the of C . (a,b) is Element of the carrier of C
d is Morphism of a,c
e is Morphism of b,c
(C,a,b,c,c,d,e) is Morphism of (C,a,b),(C,c,c)
(C,c,c) is Morphism of c,(C,c,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (c,c) is Element of the carrier' of C
(C,c,c) * d is Morphism of a,(C,c,c)
(C,c,c) is Morphism of c,(C,c,c)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (c,c) is Element of the carrier' of C
(C,c,c) * e is Morphism of b,(C,c,c)
(C,a,b,(C,c,c),((C,c,c) * d),((C,c,c) * e)) is Morphism of (C,a,b),(C,c,c)
(C,c) * (C,a,b,c,c,d,e) is Morphism of (C,a,b),c
(C,a,b,c,d,e) is Morphism of (C,a,b),c
Hom (c,c) is non empty Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = c ) } is set
(id c) * d is Morphism of a,c
(id c) * e is Morphism of b,c
(C,a,b,c,((id c) * d),((id c) * e)) is Morphism of (C,a,b),c
(C,a,b,c,d,((id c) * e)) is Morphism of (C,a,b),c
C is non empty non void V57() Category-like transitive associative reflexive with_identities () ()
the carrier of C is non empty set
a is Element of the carrier of C
c is Element of the carrier of C
Hom (a,c) is Element of bool the carrier' of C
the carrier' of C is non empty set
bool the carrier' of C is set
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = a & cod b₁ = c ) } is set
b is Element of the carrier of C
(C,a,b) is Element of the carrier of C
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is set
the of C . (a,b) is Element of the carrier of C
d is Element of the carrier of C
Hom (b,d) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = b & cod b₁ = d ) } is set
(C,c,d) is Element of the carrier of C
the of C . (c,d) is Element of the carrier of C
e is Element of the carrier of C
Hom (c,e) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = e ) } is set
s is Element of the carrier of C
Hom (d,s) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = d & cod b₁ = s ) } is set
(C,e,s) is Element of the carrier of C
the of C . (e,s) is Element of the carrier of C
f is Morphism of a,c
h is Morphism of b,d
(C,a,b,c,d,f,h) is Morphism of (C,a,b),(C,c,d)
(C,c,d) is Morphism of c,(C,c,d)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
[:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
bool [:[: the carrier of C, the carrier of C:], the carrier' of C:] is set
the of C . (c,d) is Element of the carrier' of C
(C,c,d) * f is Morphism of a,(C,c,d)
(C,c,d) is Morphism of d,(C,c,d)
the of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier' of C -valued Function-like total V18([: the carrier of C, the carrier of C:], the carrier' of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier' of C:]
the of C . (c,d) is Element of the carrier' of C
(C,c,d) * h is Morphism of b,(C,c,d)
(C,a,b,(C,c,d),((C,c,d) * f),((C,c,d) * h)) is Morphism of (C,a,b),(C,c,d)
g is Morphism of c,e
g * f is Morphism of a,e
k is Morphism of d,s
(C,c,d,e,s,g,k) is Morphism of (C,c,d),(C,e,s)
(C,e,s) is Morphism of e,(C,e,s)
the of C . (e,s) is Element of the carrier' of C
(C,e,s) * g is Morphism of c,(C,e,s)
(C,e,s) is Morphism of s,(C,e,s)
the of C . (e,s) is Element of the carrier' of C
(C,e,s) * k is Morphism of d,(C,e,s)
(C,c,d,(C,e,s),((C,e,s) * g),((C,e,s) * k)) is Morphism of (C,c,d),(C,e,s)
(C,c,d,e,s,g,k) * (C,a,b,c,d,f,h) is Morphism of (C,a,b),(C,e,s)
k * h is Morphism of b,s
(C,a,b,e,s,(g * f),(k * h)) is Morphism of (C,a,b),(C,e,s)
(C,e,s) * (g * f) is Morphism of a,(C,e,s)
(C,e,s) * (k * h) is Morphism of b,(C,e,s)
(C,a,b,(C,e,s),((C,e,s) * (g * f)),((C,e,s) * (k * h))) is Morphism of (C,a,b),(C,e,s)
Hom (s,(C,e,s)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = s & cod b₁ = (C,e,s) ) } is set
Hom (d,(C,e,s)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = d & cod b₁ = (C,e,s) ) } is set
Hom (e,(C,e,s)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = e & cod b₁ = (C,e,s) ) } is set
((C,e,s) * g) * f is Morphism of a,(C,e,s)
((C,e,s) * k) * h is Morphism of b,(C,e,s)
(C,a,b,(C,e,s),(((C,e,s) * g) * f),(((C,e,s) * k) * h)) is Morphism of (C,a,b),(C,e,s)
Hom (c,(C,e,s)) is Element of bool the carrier' of C
{ b₁ where b₁ is Element of the carrier' of C : ( dom b₁ = c & cod b₁ = (C,e,s) ) } is set