REAL is set
NAT is non empty non trivial V4() V5() V6() non finite cardinal limit_cardinal Element of bool REAL
bool REAL is non empty set
NAT is non empty non trivial V4() V5() V6() non finite cardinal limit_cardinal set
bool NAT is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
2 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
[:2,2:] is non empty Relation-like finite set
[:[:2,2:],2:] is non empty Relation-like finite set
bool [:[:2,2:],2:] is non empty finite V54() set
[:NAT,NAT:] is non empty non trivial Relation-like non finite set
[:[:NAT,NAT:],NAT:] is non empty non trivial Relation-like non finite set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite set
K287() is non empty V155() L16()
the carrier of K287() is non empty set
K290() is Element of bool NAT
[:K290(),K290():] is Relation-like set
[:[:K290(),K290():],K290():] is Relation-like set
bool [:[:K290(),K290():],K290():] is non empty set
{} is empty trivial V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() set
the empty trivial V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() set is empty trivial V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() set
1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
{{},1} is non empty finite V54() set
fin_RelStr is non empty set
bool fin_RelStr is non empty set
3 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
4 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
0 is empty trivial V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() Element of NAT
{0,1,2,3} is non empty finite set
Necklace 4 is non empty strict symmetric irreflexive RelStr
4 -SuccRelStr is strict RelStr
SymRelStr (4 -SuccRelStr) is strict symmetric RelStr
ComplRelStr (Necklace 4) is non empty strict RelStr
FinSETS is non empty universal set
K139({}) is set
the InternalRel of (Necklace 4) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued symmetric finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
the carrier of (Necklace 4) is non empty finite set
[: the carrier of (Necklace 4), the carrier of (Necklace 4):] is non empty Relation-like finite set
bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):] is non empty finite V54() set
[0,1] is non empty set
{0,1} is non empty finite V54() set
{0} is non empty trivial functional finite V54() 1 -element set
{{0,1},{0}} is non empty finite V54() set
[1,0] is non empty set
{1,0} is non empty finite V54() set
{1} is non empty trivial finite V54() 1 -element set
{{1,0},{1}} is non empty finite V54() set
[1,2] is non empty set
{1,2} is non empty finite V54() set
{{1,2},{1}} is non empty finite V54() set
[2,1] is non empty set
{2,1} is non empty finite V54() set
{2} is non empty trivial finite V54() 1 -element set
{{2,1},{2}} is non empty finite V54() set
[2,3] is non empty set
{2,3} is non empty finite V54() set
{{2,3},{2}} is non empty finite V54() set
[3,2] is non empty set
{3,2} is non empty finite V54() set
{3} is non empty trivial finite V54() 1 -element set
{{3,2},{3}} is non empty finite V54() set
{[0,1],[1,0],[1,2],[2,1],[2,3],[3,2]} is non empty finite set
fin_RelStr_sp is non empty Element of bool fin_RelStr
field {} is finite set
card {} is empty trivial V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() set
R is set
id R is Relation-like R -defined R -valued Function-like one-to-one V25(R) V29(R,R) V30(R) V31(R,R) reflexive symmetric antisymmetric transitive Element of bool [:R,R:]
[:R,R:] is Relation-like set
bool [:R,R:] is non empty set
n is set
(id R) | n is Relation-like R -defined n -defined R -defined R -valued Function-like Element of bool [:R,R:]
[:n,n:] is Relation-like set
(id R) /\ [:n,n:] is Relation-like R -defined R -valued Element of bool [:R,R:]
G is set
[:n,R:] is Relation-like set
bool [:n,R:] is non empty set
CG is set
x is set
[CG,x] is non empty set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
G is set
CG is set
x is set
[CG,x] is non empty set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
R is set
[R,R] is non empty set
{R,R} is non empty finite set
{R} is non empty trivial finite 1 -element set
{{R,R},{R}} is non empty finite V54() set
n is set
[n,n] is non empty set
{n,n} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,n},{n}} is non empty finite V54() set
G is set
[G,G] is non empty set
{G,G} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,G},{G}} is non empty finite V54() set
CG is set
{R,n,G,CG} is non empty finite set
id {R,n,G,CG} is non empty Relation-like {R,n,G,CG} -defined {R,n,G,CG} -valued Function-like one-to-one V25({R,n,G,CG}) V29({R,n,G,CG},{R,n,G,CG}) V30({R,n,G,CG}) V31({R,n,G,CG},{R,n,G,CG}) reflexive symmetric antisymmetric transitive finite Element of bool [:{R,n,G,CG},{R,n,G,CG}:]
[:{R,n,G,CG},{R,n,G,CG}:] is non empty Relation-like finite set
bool [:{R,n,G,CG},{R,n,G,CG}:] is non empty finite V54() set
[CG,CG] is non empty set
{CG,CG} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,CG},{CG}} is non empty finite V54() set
{[R,R],[n,n],[G,G],[CG,CG]} is non empty finite set
x is set
A is set
A is set
[A,A] is non empty set
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V54() set
x is set
R is set
n is set
G is set
CG is set
{R,n,G,CG} is non empty finite set
x is set
[R,x] is non empty set
{R,x} is non empty finite set
{R} is non empty trivial finite 1 -element set
{{R,x},{R}} is non empty finite V54() set
[n,x] is non empty set
{n,x} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,x},{n}} is non empty finite V54() set
[G,x] is non empty set
{G,x} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,x},{G}} is non empty finite V54() set
[CG,x] is non empty set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
x is set
[R,x] is non empty set
{R,x} is non empty finite set
{{R,x},{R}} is non empty finite V54() set
[n,x] is non empty set
{n,x} is non empty finite set
{{n,x},{n}} is non empty finite V54() set
[G,x] is non empty set
{G,x} is non empty finite set
{{G,x},{G}} is non empty finite V54() set
[CG,x] is non empty set
{CG,x} is non empty finite set
{{CG,x},{CG}} is non empty finite V54() set
A is set
[R,A] is non empty set
{R,A} is non empty finite set
{{R,A},{R}} is non empty finite V54() set
[n,A] is non empty set
{n,A} is non empty finite set
{{n,A},{n}} is non empty finite V54() set
[G,A] is non empty set
{G,A} is non empty finite set
{{G,A},{G}} is non empty finite V54() set
[CG,A] is non empty set
{CG,A} is non empty finite set
{{CG,A},{CG}} is non empty finite V54() set
A is set
{x,x,A,A} is non empty finite set
[:{R,n,G,CG},{x,x,A,A}:] is non empty Relation-like finite set
[R,A] is non empty set
{R,A} is non empty finite set
{{R,A},{R}} is non empty finite V54() set
[n,A] is non empty set
{n,A} is non empty finite set
{{n,A},{n}} is non empty finite V54() set
{[R,x],[R,x],[n,x],[n,x],[R,A],[R,A],[n,A],[n,A]} is non empty finite set
[G,A] is non empty set
{G,A} is non empty finite set
{{G,A},{G}} is non empty finite V54() set
[CG,A] is non empty set
{CG,A} is non empty finite set
{{CG,A},{CG}} is non empty finite V54() set
{[G,x],[G,x],[CG,x],[CG,x],[G,A],[G,A],[CG,A],[CG,A]} is non empty finite set
{[R,x],[R,x],[n,x],[n,x],[R,A],[R,A],[n,A],[n,A]} \/ {[G,x],[G,x],[CG,x],[CG,x],[G,A],[G,A],[CG,A],[CG,A]} is non empty finite set
{R,n} is non empty finite set
{G,CG} is non empty finite set
{x,x} is non empty finite set
{A,A} is non empty finite set
[:{G,CG},{x,x}:] is non empty Relation-like finite set
{[G,x],[G,x],[CG,x],[CG,x]} is non empty finite set
[:{G,CG},{A,A}:] is non empty Relation-like finite set
{[G,A],[G,A],[CG,A],[CG,A]} is non empty finite set
{R,n} \/ {G,CG} is non empty finite set
{x,x} \/ {A,A} is non empty finite set
[:{R,n},{x,x}:] is non empty Relation-like finite set
[:{R,n},{A,A}:] is non empty Relation-like finite set
[:{R,n},{x,x}:] \/ [:{R,n},{A,A}:] is non empty Relation-like finite set
([:{R,n},{x,x}:] \/ [:{R,n},{A,A}:]) \/ [:{G,CG},{x,x}:] is non empty Relation-like finite set
(([:{R,n},{x,x}:] \/ [:{R,n},{A,A}:]) \/ [:{G,CG},{x,x}:]) \/ [:{G,CG},{A,A}:] is non empty Relation-like finite set
{[R,x],[R,x],[n,x],[n,x]} is non empty finite set
{[R,A],[R,A],[n,A],[n,A]} is non empty finite set
{[R,x],[R,x],[n,x],[n,x],[R,A],[R,A],[n,A],[n,A]} \/ {[G,x],[G,x],[CG,x],[CG,x]} is non empty finite set
({[R,x],[R,x],[n,x],[n,x],[R,A],[R,A],[n,A],[n,A]} \/ {[G,x],[G,x],[CG,x],[CG,x]}) \/ {[G,A],[G,A],[CG,A],[CG,A]} is non empty finite set
{[G,x],[G,x],[CG,x],[CG,x]} \/ {[G,A],[G,A],[CG,A],[CG,A]} is non empty finite set
{[R,x],[R,x],[n,x],[n,x],[R,A],[R,A],[n,A],[n,A]} \/ ({[G,x],[G,x],[CG,x],[CG,x]} \/ {[G,A],[G,A],[CG,A],[CG,A]}) is non empty finite set
R is trivial finite set
n is trivial finite set
[:R,n:] is Relation-like finite set
bool [:R,n:] is non empty finite V54() set
G is Relation-like R -defined n -valued finite Element of bool [:R,n:]
CG is set
x is set
x is set
{x} is non empty trivial finite 1 -element set
x is set
{x} is non empty trivial finite 1 -element set
x is set
{x} is non empty trivial finite 1 -element set
A is set
{A} is non empty trivial finite 1 -element set
x is set
{x} is non empty trivial finite 1 -element set
A is set
A is set
[A,A] is non empty set
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V54() set
R is set
{R} is non empty trivial finite 1 -element set
R is set
{R} is non empty trivial finite 1 -element set
R is set
{R} is non empty trivial finite 1 -element set
R is set
R1 is set
[R,R1] is non empty set
{R,R1} is non empty finite set
{R} is non empty trivial finite 1 -element set
{{R,R1},{R}} is non empty finite V54() set
x is set
{x} is non empty trivial finite 1 -element set
A is set
{A} is non empty trivial finite 1 -element set
R is trivial finite set
[:R,R:] is Relation-like finite set
bool [:R,R:] is non empty finite V54() set
n is trivial Relation-like R -defined R -valued finite Element of bool [:R,R:]
G is set
CG is set
x is set
[CG,x] is non empty set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
x is set
{x} is non empty trivial finite 1 -element set
[x,x] is non empty set
{x,x} is non empty finite set
{{x,x},{x}} is non empty finite V54() set
{[x,x]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
A is set
A is set
R is set
[A,R] is non empty set
{A,R} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,R},{A}} is non empty finite V54() set
A is set
R is trivial finite set
[:R,R:] is Relation-like finite set
bool [:R,R:] is non empty finite V54() set
n is trivial Relation-like R -defined R -valued finite Element of bool [:R,R:]
field n is finite set
G is set
[G,G] is non empty set
{G,G} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,G},{G}} is non empty finite V54() set
G is set
[G,G] is non empty set
{G,G} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,G},{G}} is non empty finite V54() set
{[G,G]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
CG is set
[CG,CG] is non empty set
{CG,CG} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,CG},{CG}} is non empty finite V54() set
dom n is trivial finite Element of bool R
bool R is non empty finite V54() set
rng n is trivial finite Element of bool R
(dom n) \/ (rng n) is trivial finite Element of bool R
G is set
CG is set
x is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,x] is non empty set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
[G,x] is non empty set
{G,x} is non empty finite set
{{G,x},{G}} is non empty finite V54() set
G is set
CG is set
x is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,x] is non empty set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
[G,x] is non empty set
{G,x} is non empty finite set
{{G,x},{G}} is non empty finite V54() set
x is set
[x,x] is non empty set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V54() set
{[x,x]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
G is set
CG is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,G] is non empty set
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
G is set
CG is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,G] is non empty set
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
x is set
[x,x] is non empty set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V54() set
{[x,x]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
dom n is trivial finite Element of bool R
bool R is non empty finite V54() set
rng n is trivial finite Element of bool R
(dom n) \/ (rng n) is trivial finite Element of bool R
G is set
CG is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,G] is non empty set
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
G is set
CG is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,G] is non empty set
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
x is set
[x,x] is non empty set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V54() set
{[x,x]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
R is non empty trivial finite 1 -element set
[:R,R:] is non empty Relation-like finite set
bool [:R,R:] is non empty finite V54() set
n is trivial Relation-like R -defined R -valued reflexive symmetric strongly_connected transitive finite Element of bool [:R,R:]
G is set
{G} is non empty trivial finite 1 -element set
CG is set
x is set
[CG,x] is non empty set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
[x,CG] is non empty set
{x,CG} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,CG},{x}} is non empty finite V54() set
{0,1} is non empty finite V54() Element of bool NAT
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
{[0,1],[1,0]} is non empty Relation-like NAT -defined NAT -valued finite Element of bool [:NAT,NAT:]
bool [:NAT,NAT:] is non empty non trivial non finite set
[:{0,1},{0,1}:] is non empty Relation-like finite set
G is set
bool [:{0,1},{0,1}:] is non empty finite V54() set
G is Relation-like {0,1} -defined {0,1} -valued finite Element of bool [:{0,1},{0,1}:]
RelStr(# {0,1},G #) is non empty strict RelStr
CG is non empty strict RelStr
the carrier of CG is non empty set
the InternalRel of CG is Relation-like the carrier of CG -defined the carrier of CG -valued Element of bool [: the carrier of CG, the carrier of CG:]
[: the carrier of CG, the carrier of CG:] is non empty Relation-like set
bool [: the carrier of CG, the carrier of CG:] is non empty set
x is set
[x,x] is non empty set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V54() set
[0,0] is non empty Element of [:NAT,NAT:]
{0,0} is non empty functional finite V54() set
{{0,0},{0}} is non empty finite V54() set
[1,1] is non empty Element of [:NAT,NAT:]
{1,1} is non empty finite V54() set
{{1,1},{1}} is non empty finite V54() set
x is set
x is set
[x,x] is non empty set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V54() set
[x,x] is non empty set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V54() set
R is irreflexive RelStr
n is full SubRelStr of R
G is set
the carrier of n is set
[G,G] is non empty set
{G,G} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,G},{G}} is non empty finite V54() set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R |_2 the carrier of n is Relation-like set
the InternalRel of R /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued set
R is symmetric RelStr
n is full SubRelStr of R
G is set
the carrier of n is set
CG is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
[CG,G] is non empty set
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R |_2 the carrier of n is Relation-like set
the InternalRel of R /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued set
R is symmetric irreflexive RelStr
the carrier of R is set
card the carrier of R is V4() V5() V6() cardinal set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
G is finite set
CG is set
x is set
{CG,x} is non empty finite set
[CG,x] is non empty set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
[x,CG] is non empty set
{x,CG} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,CG},{x}} is non empty finite V54() set
{[CG,x],[x,CG]} is non empty Relation-like finite set
x is set
A is set
A is set
[A,A] is non empty set
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V54() set
[CG,CG] is non empty set
{CG,CG} is non empty finite set
{{CG,CG},{CG}} is non empty finite V54() set
[x,x] is non empty set
{x,x} is non empty finite set
{{x,x},{x}} is non empty finite V54() set
[CG,CG] is non empty set
{CG,CG} is non empty finite set
{{CG,CG},{CG}} is non empty finite V54() set
[x,x] is non empty set
{x,x} is non empty finite set
{{x,x},{x}} is non empty finite V54() set
{[CG,x]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
{[x,CG]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
{[CG,x]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
{[x,CG]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
R is non empty RelStr
n is RelStr
union_of (R,n) is strict RelStr
the carrier of R is non empty set
the carrier of n is set
the carrier of R \/ the carrier of n is non empty set
sum_of (R,n) is strict RelStr
the carrier of R is non empty set
the carrier of n is set
the carrier of R \/ the carrier of n is non empty set
R is RelStr
n is non empty RelStr
union_of (R,n) is strict RelStr
the carrier of R is set
the carrier of n is non empty set
the carrier of R \/ the carrier of n is non empty set
sum_of (R,n) is strict RelStr
the carrier of R is set
the carrier of n is non empty set
the carrier of R \/ the carrier of n is non empty set
R is finite RelStr
n is finite RelStr
union_of (R,n) is strict RelStr
the carrier of R is finite set
the carrier of n is finite set
the carrier of R \/ the carrier of n is finite set
sum_of (R,n) is strict RelStr
the carrier of R is finite set
the carrier of n is finite set
the carrier of R \/ the carrier of n is finite set
R is symmetric RelStr
n is symmetric RelStr
union_of (R,n) is strict RelStr
G is set
the carrier of (union_of (R,n)) is set
CG is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is Relation-like set
bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is non empty set
[CG,G] is non empty set
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
the carrier of R is set
the carrier of n is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued symmetric Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
sum_of (R,n) is strict RelStr
the carrier of (sum_of (R,n)) is set
the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
[: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is Relation-like set
bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is non empty set
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the carrier of n is set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued symmetric Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
R is set
R1 is set
[R,R1] is non empty set
{R,R1} is non empty finite set
{R} is non empty trivial finite 1 -element set
{{R,R1},{R}} is non empty finite V54() set
[R1,R] is non empty set
{R1,R} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R},{R1}} is non empty finite V54() set
the InternalRel of R \/ the InternalRel of n is Relation-like set
[: the carrier of R, the carrier of n:] is Relation-like set
( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:] is Relation-like set
[: the carrier of n, the carrier of R:] is Relation-like set
(( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
[: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:] is Relation-like set
the InternalRel of n \/ ([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) is Relation-like set
the InternalRel of n \/ [: the carrier of R, the carrier of n:] is Relation-like set
( the InternalRel of n \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
the InternalRel of R \/ (( the InternalRel of n \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:]) is Relation-like set
the InternalRel of R \/ ( the InternalRel of n \/ ([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:])) is Relation-like set
( the InternalRel of R \/ the InternalRel of n) \/ ([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) is Relation-like set
[: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:] is Relation-like set
the InternalRel of n \/ ([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) is Relation-like set
the InternalRel of n \/ [: the carrier of R, the carrier of n:] is Relation-like set
( the InternalRel of n \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
the InternalRel of R \/ (( the InternalRel of n \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:]) is Relation-like set
the InternalRel of R \/ ( the InternalRel of n \/ ([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:])) is Relation-like set
( the InternalRel of R \/ the InternalRel of n) \/ ([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) is Relation-like set
R is irreflexive RelStr
n is irreflexive RelStr
union_of (R,n) is strict RelStr
the carrier of (union_of (R,n)) is set
the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is Relation-like set
bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is non empty set
the carrier of R is set
the carrier of n is set
A is set
[A,A] is non empty set
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V54() set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
R is irreflexive RelStr
the carrier of R is set
n is irreflexive RelStr
the carrier of n is set
sum_of (R,n) is strict RelStr
the carrier of (sum_of (R,n)) is set
the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
[: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is Relation-like set
bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
[: the carrier of R, the carrier of n:] is Relation-like set
[: the carrier of n, the carrier of R:] is Relation-like set
A is set
[A,A] is non empty set
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V54() set
the InternalRel of R \/ the InternalRel of n is Relation-like set
( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:] is Relation-like set
(( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
R is RelStr
n is RelStr
union_of (R,n) is strict RelStr
union_of (n,R) is strict RelStr
sum_of (R,n) is strict RelStr
sum_of (n,R) is strict RelStr
the carrier of (sum_of (R,n)) is set
the carrier of n is set
the carrier of R is set
the carrier of n \/ the carrier of R is set
the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
[: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is Relation-like set
bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
[: the carrier of R, the carrier of n:] is Relation-like set
( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:] is Relation-like set
[: the carrier of n, the carrier of R:] is Relation-like set
(( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
the InternalRel of n \/ the InternalRel of R is Relation-like set
( the InternalRel of n \/ the InternalRel of R) \/ [: the carrier of n, the carrier of R:] is Relation-like set
(( the InternalRel of n \/ the InternalRel of R) \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of R, the carrier of n:] is Relation-like set
the carrier of (union_of (R,n)) is set
the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is Relation-like set
bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is non empty set
R is irreflexive RelStr
n is RelStr
G is RelStr
union_of (n,G) is strict RelStr
sum_of (n,G) is strict RelStr
the carrier of n is set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
CG is set
[CG,CG] is non empty set
{CG,CG} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,CG},{CG}} is non empty finite V54() set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
the carrier of G is set
[: the carrier of G, the carrier of G:] is Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
the InternalRel of n \/ the InternalRel of G is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the carrier of n \/ the carrier of G is set
the carrier of G is set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
CG is set
[CG,CG] is non empty set
{CG,CG} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,CG},{CG}} is non empty finite V54() set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the carrier of n is set
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of n \/ the InternalRel of G is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the carrier of n \/ the carrier of G is set
the carrier of n is set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
CG is set
[CG,CG] is non empty set
{CG,CG} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,CG},{CG}} is non empty finite V54() set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
the carrier of G is set
[: the carrier of G, the carrier of G:] is Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
the InternalRel of n \/ the InternalRel of G is Relation-like set
[: the carrier of n, the carrier of G:] is Relation-like set
( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:] is Relation-like set
[: the carrier of G, the carrier of n:] is Relation-like set
(( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the carrier of n \/ the carrier of G is set
the carrier of G is set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
CG is set
[CG,CG] is non empty set
{CG,CG} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,CG},{CG}} is non empty finite V54() set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the carrier of n is set
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of n \/ the InternalRel of G is Relation-like set
[: the carrier of n, the carrier of G:] is Relation-like set
( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:] is Relation-like set
[: the carrier of G, the carrier of n:] is Relation-like set
(( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the carrier of n \/ the carrier of G is set
R is non empty RelStr
the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
RelStr(# the carrier of R, the InternalRel of R #) is non empty strict RelStr
n is RelStr
the carrier of n is set
G is RelStr
the carrier of G is set
union_of (n,G) is strict RelStr
sum_of (n,G) is strict RelStr
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
[: the carrier of n, the carrier of G:] is Relation-like set
[: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of R |_2 the carrier of G is Relation-like set
the InternalRel of R /\ [: the carrier of G, the carrier of G:] is Relation-like the carrier of R -defined the carrier of R -valued set
R is set
the InternalRel of n \/ the InternalRel of G is Relation-like set
R is set
the InternalRel of n \/ the InternalRel of G is Relation-like set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of n /\ the carrier of G is set
the InternalRel of R |_2 the carrier of n is Relation-like set
the InternalRel of R /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued set
R is set
the InternalRel of n \/ the InternalRel of G is Relation-like set
R is set
the InternalRel of n \/ the InternalRel of G is Relation-like set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of n \/ the carrier of G is set
the InternalRel of n \/ the InternalRel of G is Relation-like set
the InternalRel of R |_2 the carrier of G is Relation-like set
the InternalRel of R /\ [: the carrier of G, the carrier of G:] is Relation-like the carrier of R -defined the carrier of R -valued set
R is set
the InternalRel of n \/ the InternalRel of G is Relation-like set
( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:] is Relation-like set
(( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of n \/ [: the carrier of n, the carrier of G:] is Relation-like set
( the InternalRel of n \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of G \/ (( the InternalRel of n \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:]) is Relation-like set
R is set
the InternalRel of n \/ the InternalRel of G is Relation-like set
( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:] is Relation-like set
(( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of G \/ [: the carrier of n, the carrier of G:] is Relation-like set
( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of n \/ (( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:]) is Relation-like set
[: the carrier of n, the carrier of G:] \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of G \/ ([: the carrier of n, the carrier of G:] \/ [: the carrier of G, the carrier of n:]) is Relation-like set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of n /\ the carrier of G is set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of n /\ the carrier of G is set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of n /\ the carrier of G is set
the InternalRel of n \/ the InternalRel of G is Relation-like set
( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:] is Relation-like set
(( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of R |_2 the carrier of n is Relation-like set
the InternalRel of R /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued set
R is set
the InternalRel of G \/ [: the carrier of n, the carrier of G:] is Relation-like set
( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of n \/ (( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:]) is Relation-like set
R is set
the InternalRel of G \/ [: the carrier of n, the carrier of G:] is Relation-like set
( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of n \/ (( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:]) is Relation-like set
[: the carrier of n, the carrier of G:] \/ [: the carrier of G, the carrier of n:] is Relation-like set
the InternalRel of G \/ ([: the carrier of n, the carrier of G:] \/ [: the carrier of G, the carrier of n:]) is Relation-like set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of n /\ the carrier of G is set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of n /\ the carrier of G is set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of n /\ the carrier of G is set
the InternalRel of G \/ [: the carrier of n, the carrier of G:] is Relation-like set
the InternalRel of n \/ ( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) is Relation-like set
the carrier of n \/ the carrier of G is set
the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (ComplRelStr (Necklace 4)) -valued Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
the carrier of (ComplRelStr (Necklace 4)) is non empty set
[: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):] is non empty Relation-like set
bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):] is non empty set
[0,2] is non empty Element of [:NAT,NAT:]
{0,2} is non empty finite V54() set
{{0,2},{0}} is non empty finite V54() set
[2,0] is non empty Element of [:NAT,NAT:]
{2,0} is non empty finite V54() set
{{2,0},{2}} is non empty finite V54() set
[0,3] is non empty Element of [:NAT,NAT:]
{0,3} is non empty finite V54() set
{{0,3},{0}} is non empty finite V54() set
[3,0] is non empty Element of [:NAT,NAT:]
{3,0} is non empty finite V54() set
{{3,0},{3}} is non empty finite V54() set
[1,3] is non empty Element of [:NAT,NAT:]
{1,3} is non empty finite V54() set
{{1,3},{1}} is non empty finite V54() set
[3,1] is non empty Element of [:NAT,NAT:]
{3,1} is non empty finite V54() set
{{3,1},{3}} is non empty finite V54() set
{[0,2],[2,0],[0,3],[3,0],[1,3],[3,1]} is non empty Relation-like NAT -defined NAT -valued finite Element of bool [:NAT,NAT:]
bool [:NAT,NAT:] is non empty non trivial non finite set
{0,1,2,3} is non empty finite Element of bool NAT
CG is set
the InternalRel of (Necklace 4) ` is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
id the carrier of (Necklace 4) is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued Function-like one-to-one V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (Necklace 4)) V30( the carrier of (Necklace 4)) V31( the carrier of (Necklace 4), the carrier of (Necklace 4)) reflexive symmetric antisymmetric transitive finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
( the InternalRel of (Necklace 4) `) \ (id the carrier of (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
[: the carrier of (Necklace 4), the carrier of (Necklace 4):] \ the InternalRel of (Necklace 4) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
x is set
x is set
[x,x] is non empty set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V54() set
CG is set
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[: the carrier of (Necklace 4), the carrier of (Necklace 4):] \ the InternalRel of (Necklace 4) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
the InternalRel of (Necklace 4) ` is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
id the carrier of (Necklace 4) is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued Function-like one-to-one V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (Necklace 4)) V30( the carrier of (Necklace 4)) V31( the carrier of (Necklace 4), the carrier of (Necklace 4)) reflexive symmetric antisymmetric transitive finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
( the InternalRel of (Necklace 4) `) \ (id the carrier of (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[: the carrier of (Necklace 4), the carrier of (Necklace 4):] \ the InternalRel of (Necklace 4) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
the InternalRel of (Necklace 4) ` is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
id the carrier of (Necklace 4) is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued Function-like one-to-one V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (Necklace 4)) V30( the carrier of (Necklace 4)) V31( the carrier of (Necklace 4), the carrier of (Necklace 4)) reflexive symmetric antisymmetric transitive finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
( the InternalRel of (Necklace 4) `) \ (id the carrier of (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[: the carrier of (Necklace 4), the carrier of (Necklace 4):] \ the InternalRel of (Necklace 4) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
the InternalRel of (Necklace 4) ` is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
id the carrier of (Necklace 4) is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued Function-like one-to-one V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (Necklace 4)) V30( the carrier of (Necklace 4)) V31( the carrier of (Necklace 4), the carrier of (Necklace 4)) reflexive symmetric antisymmetric transitive finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
( the InternalRel of (Necklace 4) `) \ (id the carrier of (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[: the carrier of (Necklace 4), the carrier of (Necklace 4):] \ the InternalRel of (Necklace 4) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
the InternalRel of (Necklace 4) ` is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
id the carrier of (Necklace 4) is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued Function-like one-to-one V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (Necklace 4)) V30( the carrier of (Necklace 4)) V31( the carrier of (Necklace 4), the carrier of (Necklace 4)) reflexive symmetric antisymmetric transitive finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
( the InternalRel of (Necklace 4) `) \ (id the carrier of (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[: the carrier of (Necklace 4), the carrier of (Necklace 4):] \ the InternalRel of (Necklace 4) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
the InternalRel of (Necklace 4) ` is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
id the carrier of (Necklace 4) is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued Function-like one-to-one V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (Necklace 4)) V30( the carrier of (Necklace 4)) V31( the carrier of (Necklace 4), the carrier of (Necklace 4)) reflexive symmetric antisymmetric transitive finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
( the InternalRel of (Necklace 4) `) \ (id the carrier of (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[: the carrier of (Necklace 4), the carrier of (Necklace 4):] \ the InternalRel of (Necklace 4) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
the InternalRel of (Necklace 4) ` is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
id the carrier of (Necklace 4) is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued Function-like one-to-one V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (Necklace 4)) V30( the carrier of (Necklace 4)) V31( the carrier of (Necklace 4), the carrier of (Necklace 4)) reflexive symmetric antisymmetric transitive finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
( the InternalRel of (Necklace 4) `) \ (id the carrier of (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (Necklace 4) -valued finite Element of bool [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
R is RelStr
ComplRelStr R is strict RelStr
the carrier of (ComplRelStr R) is set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
G is set
[G,G] is non empty set
{G,G} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,G},{G}} is non empty finite V54() set
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
R is symmetric RelStr
ComplRelStr R is strict irreflexive RelStr
n is set
the carrier of (ComplRelStr R) is set
G is set
[n,G] is non empty set
{n,G} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,G},{n}} is non empty finite V54() set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
[G,n] is non empty set
{G,n} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,n},{G}} is non empty finite V54() set
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
R is RelStr
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
ComplRelStr R is strict irreflexive RelStr
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of R -defined the carrier of (ComplRelStr R) -defined the carrier of R -valued the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
n is set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
R is RelStr
the carrier of R is set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
ComplRelStr R is strict irreflexive RelStr
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
(id the carrier of R) /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of R -defined the carrier of (ComplRelStr R) -defined the carrier of R -valued the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
n is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
R is RelStr
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
ComplRelStr R is strict irreflexive RelStr
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is Relation-like set
x is set
A is set
A is set
[A,A] is non empty set
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V54() set
[A,A] is non empty set
{A,A} is non empty finite set
{{A,A},{A}} is non empty finite V54() set
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R \/ the InternalRel of (ComplRelStr R) is Relation-like set
(id the carrier of R) \/ ( the InternalRel of R \/ the InternalRel of (ComplRelStr R)) is Relation-like set
x is set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
R is strict irreflexive RelStr
ComplRelStr R is strict irreflexive RelStr
the carrier of R is set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
[: the carrier of R, the carrier of R:] is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
{} \ {} is empty trivial non proper V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() Element of bool {}
bool {} is non empty finite V54() set
id {} is empty trivial non proper V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding {} -defined {} -valued Function-like one-to-one constant functional V25( {} ) V29( {} , {} ) V30( {} ) V31( {} , {} ) reflexive symmetric antisymmetric strongly_connected transitive finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() Element of bool [:{},{}:]
[:{},{}:] is empty trivial V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() set
bool [:{},{}:] is non empty finite V54() set
({} \ {}) \ (id {}) is empty trivial non proper V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional finite finite-yielding V54() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V71() Function-yielding V175() Element of bool {}
the carrier of R is set
G is set
{G} is non empty trivial finite 1 -element set
G is set
{G} is non empty trivial finite 1 -element set
the carrier of (ComplRelStr R) is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
[:{G},{G}:] is non empty Relation-like finite set
[G,G] is non empty set
{G,G} is non empty finite set
{{G,G},{G}} is non empty finite V54() set
{[G,G]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[:{G},{G}:] \ {} is trivial Relation-like {G} -defined {G} -valued reflexive symmetric strongly_connected transitive finite Element of bool [:{G},{G}:]
bool [:{G},{G}:] is non empty finite V54() set
id {G} is non empty trivial Relation-like {G} -defined {G} -valued Function-like one-to-one constant V25({G}) V29({G},{G}) V30({G}) V31({G},{G}) reflexive symmetric antisymmetric strongly_connected transitive finite 1 -element Element of bool [:{G},{G}:]
([:{G},{G}:] \ {}) \ (id {G}) is trivial Relation-like {G} -defined {G} -valued reflexive symmetric strongly_connected transitive finite Element of bool [:{G},{G}:]
{[G,G]} \ (id {G}) is trivial Relation-like Function-like one-to-one constant finite Element of bool {[G,G]}
bool {[G,G]} is non empty finite V54() set
{[G,G]} \ {[G,G]} is trivial Relation-like Function-like one-to-one constant finite Element of bool {[G,G]}
the carrier of R is set
R is strict irreflexive RelStr
ComplRelStr R is strict irreflexive RelStr
ComplRelStr (ComplRelStr R) is strict irreflexive RelStr
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
the InternalRel of (ComplRelStr (ComplRelStr R)) is Relation-like the carrier of (ComplRelStr (ComplRelStr R)) -defined the carrier of (ComplRelStr (ComplRelStr R)) -valued Element of bool [: the carrier of (ComplRelStr (ComplRelStr R)), the carrier of (ComplRelStr (ComplRelStr R)):]
the carrier of (ComplRelStr (ComplRelStr R)) is set
[: the carrier of (ComplRelStr (ComplRelStr R)), the carrier of (ComplRelStr (ComplRelStr R)):] is Relation-like set
bool [: the carrier of (ComplRelStr (ComplRelStr R)), the carrier of (ComplRelStr (ComplRelStr R)):] is non empty set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) /\ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
A is set
R is set
R is set
[R,R] is non empty set
{R,R} is non empty finite set
{R} is non empty trivial finite 1 -element set
{{R,R},{R}} is non empty finite V54() set
the InternalRel of (ComplRelStr R) ` is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
id the carrier of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Function-like one-to-one V25( the carrier of (ComplRelStr R)) V29( the carrier of (ComplRelStr R), the carrier of (ComplRelStr R)) V30( the carrier of (ComplRelStr R)) V31( the carrier of (ComplRelStr R), the carrier of (ComplRelStr R)) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
( the InternalRel of (ComplRelStr R) `) \ (id the carrier of (ComplRelStr R)) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] \ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
([: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] \ the InternalRel of (ComplRelStr R)) \ (id the carrier of (ComplRelStr R)) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ (( the InternalRel of R `) \ (id the carrier of R)) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ (( the InternalRel of R `) \ (id the carrier of R))) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ ( the InternalRel of R `) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] /\ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ ( the InternalRel of R `)) \/ ([: the carrier of R, the carrier of R:] /\ (id the carrier of R)) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
(([: the carrier of R, the carrier of R:] \ ( the InternalRel of R `)) \/ ([: the carrier of R, the carrier of R:] /\ (id the carrier of R))) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ ( the InternalRel of R `)) \/ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
(([: the carrier of R, the carrier of R:] \ ( the InternalRel of R `)) \/ (id the carrier of R)) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ ( the InternalRel of R `)) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ ([: the carrier of R, the carrier of R:] \ the InternalRel of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ ([: the carrier of R, the carrier of R:] \ the InternalRel of R)) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] /\ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] /\ the InternalRel of R) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
R is RelStr
the carrier of R is set
n is RelStr
the carrier of n is set
union_of (R,n) is strict RelStr
ComplRelStr (union_of (R,n)) is strict irreflexive RelStr
ComplRelStr R is strict irreflexive RelStr
ComplRelStr n is strict irreflexive RelStr
sum_of ((ComplRelStr R),(ComplRelStr n)) is strict RelStr
the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))) is set
the carrier of (ComplRelStr R) is set
the carrier of (ComplRelStr n) is set
the carrier of (ComplRelStr R) \/ the carrier of (ComplRelStr n) is set
the carrier of R \/ the carrier of (ComplRelStr n) is set
the carrier of R \/ the carrier of n is set
the InternalRel of (ComplRelStr (union_of (R,n))) is Relation-like the carrier of (ComplRelStr (union_of (R,n))) -defined the carrier of (ComplRelStr (union_of (R,n))) -valued Element of bool [: the carrier of (ComplRelStr (union_of (R,n))), the carrier of (ComplRelStr (union_of (R,n))):]
the carrier of (ComplRelStr (union_of (R,n))) is set
[: the carrier of (ComplRelStr (union_of (R,n))), the carrier of (ComplRelStr (union_of (R,n))):] is Relation-like set
bool [: the carrier of (ComplRelStr (union_of (R,n))), the carrier of (ComplRelStr (union_of (R,n))):] is non empty set
the InternalRel of (sum_of ((ComplRelStr R),(ComplRelStr n))) is Relation-like the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))) -defined the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))) -valued Element of bool [: the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))), the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))):]
[: the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))), the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))):] is Relation-like set
bool [: the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))), the carrier of (sum_of ((ComplRelStr R),(ComplRelStr n))):] is non empty set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
the InternalRel of (ComplRelStr n) is Relation-like the carrier of (ComplRelStr n) -defined the carrier of (ComplRelStr n) -valued Element of bool [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):]
[: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):] is Relation-like set
bool [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):] is non empty set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
[: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
[: the carrier of R, the carrier of R:] is Relation-like set
[: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of R, the carrier of n:] is Relation-like set
[: the carrier of n, the carrier of R:] is Relation-like set
R22 is set
R11 is set
[R22,R11] is non empty set
{R22,R11} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,R11},{R22}} is non empty finite V54() set
the carrier of (union_of (R,n)) is set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is Relation-like set
the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is non empty set
the InternalRel of (union_of (R,n)) ` is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
id the carrier of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Function-like one-to-one V25( the carrier of (union_of (R,n))) V29( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) V30( the carrier of (union_of (R,n))) V31( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
( the InternalRel of (union_of (R,n)) `) \ (id the carrier of (union_of (R,n))) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
[:( the carrier of R \/ the carrier of n), the carrier of (union_of (R,n)):] is Relation-like set
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
id ( the carrier of R \/ the carrier of n) is Relation-like the carrier of R \/ the carrier of n -defined the carrier of R \/ the carrier of n -valued Function-like one-to-one V25( the carrier of R \/ the carrier of n) V29( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) V30( the carrier of R \/ the carrier of n) V31( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):]
bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is non empty set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
(id the carrier of R) \/ (id the carrier of n) is Relation-like set
[: the carrier of R, the carrier of R:] \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
([: the carrier of R, the carrier of R:] \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
(([: the carrier of R, the carrier of R:] \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
([: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of R, the carrier of R:] \/ (([: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):]) \/ [: the carrier of n, the carrier of n:]) is Relation-like set
[: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] \/ [: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] \/ ([: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] \/ [: the carrier of n, the carrier of n:]) is Relation-like set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] \ the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the InternalRel of R \/ the InternalRel of n is Relation-like set
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
( the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
the InternalRel of (ComplRelStr R) \/ (( the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):]) is Relation-like set
the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n) is Relation-like set
( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
(( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
( the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
the InternalRel of (ComplRelStr R) \/ (( the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):]) is Relation-like set
the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n) is Relation-like set
( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
(( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
the InternalRel of (ComplRelStr n) \/ ([: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):]) is Relation-like set
the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
( the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
the InternalRel of (ComplRelStr R) \/ (( the InternalRel of (ComplRelStr n) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):]) is Relation-like set
the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n) is Relation-like set
( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
(( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
[: the carrier of n, the carrier of n:] \ the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the InternalRel of n ` is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
( the InternalRel of n `) \ (id the carrier of n) is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n) is Relation-like set
( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
(( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n) is Relation-like set
( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):] is Relation-like set
(( the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n)) \/ [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr n):]) \/ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr R):] is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the carrier of (union_of (R,n)) is set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is Relation-like set
bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
[: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:] is Relation-like set
id the carrier of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Function-like one-to-one V25( the carrier of (union_of (R,n))) V29( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) V30( the carrier of (union_of (R,n))) V31( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
id ( the carrier of R \/ the carrier of n) is Relation-like the carrier of R \/ the carrier of n -defined the carrier of R \/ the carrier of n -valued Function-like one-to-one V25( the carrier of R \/ the carrier of n) V29( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) V30( the carrier of R \/ the carrier of n) V31( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):]
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is non empty set
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
(id the carrier of R) \/ (id the carrier of n) is Relation-like set
[: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:] is Relation-like set
([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
(([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
[:( the carrier of R \/ the carrier of n), the carrier of (union_of (R,n)):] is Relation-like set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] \ the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the InternalRel of (union_of (R,n)) ` is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
( the InternalRel of (union_of (R,n)) `) \ (id the carrier of (union_of (R,n))) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of n ` is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
( the InternalRel of n `) \ (id the carrier of n) is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] \ the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the carrier of (union_of (R,n)) is set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is Relation-like set
bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
[: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:] is Relation-like set
id the carrier of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Function-like one-to-one V25( the carrier of (union_of (R,n))) V29( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) V30( the carrier of (union_of (R,n))) V31( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
id ( the carrier of R \/ the carrier of n) is Relation-like the carrier of R \/ the carrier of n -defined the carrier of R \/ the carrier of n -valued Function-like one-to-one V25( the carrier of R \/ the carrier of n) V29( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) V30( the carrier of R \/ the carrier of n) V31( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):]
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is non empty set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
(id the carrier of R) \/ (id the carrier of n) is Relation-like set
[: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of n, the carrier of R:] \/ [: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of R, the carrier of n:] \/ ([: the carrier of n, the carrier of R:] \/ [: the carrier of n, the carrier of n:]) is Relation-like set
[: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:] is Relation-like set
([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of R, the carrier of R:] \/ (([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:]) is Relation-like set
[: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:] is Relation-like set
([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
(([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
[:( the carrier of R \/ the carrier of n), the carrier of (union_of (R,n)):] is Relation-like set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] \ the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the InternalRel of (union_of (R,n)) ` is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
( the InternalRel of (union_of (R,n)) `) \ (id the carrier of (union_of (R,n))) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
[: the carrier of R, the carrier of (ComplRelStr n):] is Relation-like set
the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the carrier of (union_of (R,n)) is set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is Relation-like set
bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
the carrier of R /\ the carrier of n is set
the carrier of R /\ the carrier of n is set
id the carrier of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Function-like one-to-one V25( the carrier of (union_of (R,n))) V29( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) V30( the carrier of (union_of (R,n))) V31( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
id ( the carrier of R \/ the carrier of n) is Relation-like the carrier of R \/ the carrier of n -defined the carrier of R \/ the carrier of n -valued Function-like one-to-one V25( the carrier of R \/ the carrier of n) V29( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) V30( the carrier of R \/ the carrier of n) V31( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):]
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is non empty set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
(id the carrier of R) \/ (id the carrier of n) is Relation-like set
the carrier of R /\ the carrier of n is set
the carrier of R /\ the carrier of n is set
[: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:] is Relation-like set
[: the carrier of R, the carrier of R:] \/ ([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) is Relation-like set
[: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:] is Relation-like set
([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
(([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
[:( the carrier of R \/ the carrier of n), the carrier of (union_of (R,n)):] is Relation-like set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] \ the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the InternalRel of (union_of (R,n)) ` is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
( the InternalRel of (union_of (R,n)) `) \ (id the carrier of (union_of (R,n))) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
[: the carrier of n, the carrier of (ComplRelStr R):] is Relation-like set
the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the carrier of (union_of (R,n)) is set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is Relation-like set
bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
the carrier of R /\ the carrier of n is set
the carrier of R /\ the carrier of n is set
id the carrier of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Function-like one-to-one V25( the carrier of (union_of (R,n))) V29( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) V30( the carrier of (union_of (R,n))) V31( the carrier of (union_of (R,n)), the carrier of (union_of (R,n))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
id ( the carrier of R \/ the carrier of n) is Relation-like the carrier of R \/ the carrier of n -defined the carrier of R \/ the carrier of n -valued Function-like one-to-one V25( the carrier of R \/ the carrier of n) V29( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) V30( the carrier of R \/ the carrier of n) V31( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):]
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is non empty set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
(id the carrier of R) \/ (id the carrier of n) is Relation-like set
the carrier of R /\ the carrier of n is set
the carrier of R /\ the carrier of n is set
[: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:] is Relation-like set
[: the carrier of R, the carrier of R:] \/ ([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) is Relation-like set
[: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:] is Relation-like set
([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
(([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
[:( the carrier of R \/ the carrier of n), the carrier of (union_of (R,n)):] is Relation-like set
[: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):] \ the InternalRel of (union_of (R,n)) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the InternalRel of (union_of (R,n)) ` is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
( the InternalRel of (union_of (R,n)) `) \ (id the carrier of (union_of (R,n))) is Relation-like the carrier of (union_of (R,n)) -defined the carrier of (union_of (R,n)) -valued Element of bool [: the carrier of (union_of (R,n)), the carrier of (union_of (R,n)):]
the carrier of (union_of (R,n)) is set
R is RelStr
the carrier of R is set
n is RelStr
the carrier of n is set
sum_of (R,n) is strict RelStr
ComplRelStr (sum_of (R,n)) is strict irreflexive RelStr
ComplRelStr R is strict irreflexive RelStr
ComplRelStr n is strict irreflexive RelStr
union_of ((ComplRelStr R),(ComplRelStr n)) is strict irreflexive RelStr
the InternalRel of (ComplRelStr (sum_of (R,n))) is Relation-like the carrier of (ComplRelStr (sum_of (R,n))) -defined the carrier of (ComplRelStr (sum_of (R,n))) -valued Element of bool [: the carrier of (ComplRelStr (sum_of (R,n))), the carrier of (ComplRelStr (sum_of (R,n))):]
the carrier of (ComplRelStr (sum_of (R,n))) is set
[: the carrier of (ComplRelStr (sum_of (R,n))), the carrier of (ComplRelStr (sum_of (R,n))):] is Relation-like set
bool [: the carrier of (ComplRelStr (sum_of (R,n))), the carrier of (ComplRelStr (sum_of (R,n))):] is non empty set
the InternalRel of (union_of ((ComplRelStr R),(ComplRelStr n))) is Relation-like the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))) -defined the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))) -valued Element of bool [: the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))), the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))):]
the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))) is set
[: the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))), the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))):] is Relation-like set
bool [: the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))), the carrier of (union_of ((ComplRelStr R),(ComplRelStr n))):] is non empty set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
the InternalRel of (ComplRelStr n) is Relation-like the carrier of (ComplRelStr n) -defined the carrier of (ComplRelStr n) -valued Element of bool [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):]
the carrier of (ComplRelStr n) is set
[: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):] is Relation-like set
bool [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):] is non empty set
[: the carrier of R, the carrier of R:] is Relation-like set
[: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of R, the carrier of n:] is Relation-like set
[: the carrier of n, the carrier of R:] is Relation-like set
the carrier of (sum_of (R,n)) is set
[: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is Relation-like set
the carrier of R \/ the carrier of n is set
[:( the carrier of R \/ the carrier of n), the carrier of (sum_of (R,n)):] is Relation-like set
[:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is Relation-like set
[: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:] is Relation-like set
([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
(([: the carrier of R, the carrier of R:] \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
R1 is set
R2 is set
[R1,R2] is non empty set
{R1,R2} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,R2},{R1}} is non empty finite V54() set
the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is non empty set
the InternalRel of (sum_of (R,n)) ` is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
id the carrier of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Function-like one-to-one V25( the carrier of (sum_of (R,n))) V29( the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n))) V30( the carrier of (sum_of (R,n))) V31( the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
( the InternalRel of (sum_of (R,n)) `) \ (id the carrier of (sum_of (R,n))) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
[: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] \ the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:] is Relation-like set
(( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
id ( the carrier of R \/ the carrier of n) is Relation-like the carrier of R \/ the carrier of n -defined the carrier of R \/ the carrier of n -valued Function-like one-to-one V25( the carrier of R \/ the carrier of n) V29( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) V30( the carrier of R \/ the carrier of n) V31( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):]
bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is non empty set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
(id the carrier of R) \/ (id the carrier of n) is Relation-like set
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n) is Relation-like set
[: the carrier of n, the carrier of n:] \ the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the InternalRel of n ` is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
( the InternalRel of n `) \ (id the carrier of n) is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n) is Relation-like set
the InternalRel of (ComplRelStr R) \/ the InternalRel of (ComplRelStr n) is Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Function-like one-to-one V25( the carrier of (sum_of (R,n))) V29( the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n))) V30( the carrier of (sum_of (R,n))) V31( the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is non empty set
id ( the carrier of R \/ the carrier of n) is Relation-like the carrier of R \/ the carrier of n -defined the carrier of R \/ the carrier of n -valued Function-like one-to-one V25( the carrier of R \/ the carrier of n) V29( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) V30( the carrier of R \/ the carrier of n) V31( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):]
bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is non empty set
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
(id the carrier of R) \/ (id the carrier of n) is Relation-like set
the carrier of R /\ the carrier of n is set
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:] is Relation-like set
(( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
the carrier of R /\ the carrier of n is set
the carrier of R /\ the carrier of n is set
the carrier of R /\ the carrier of n is set
[: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:] is Relation-like set
([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:] is Relation-like set
[: the carrier of R, the carrier of R:] \/ (([: the carrier of R, the carrier of n:] \/ [: the carrier of n, the carrier of R:]) \/ [: the carrier of n, the carrier of n:]) is Relation-like set
[: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] \ the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
the InternalRel of (sum_of (R,n)) ` is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
( the InternalRel of (sum_of (R,n)) `) \ (id the carrier of (sum_of (R,n))) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of n ` is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
( the InternalRel of n `) \ (id the carrier of n) is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
id the carrier of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Function-like one-to-one V25( the carrier of (sum_of (R,n))) V29( the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n))) V30( the carrier of (sum_of (R,n))) V31( the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] is non empty set
id ( the carrier of R \/ the carrier of n) is Relation-like the carrier of R \/ the carrier of n -defined the carrier of R \/ the carrier of n -valued Function-like one-to-one V25( the carrier of R \/ the carrier of n) V29( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) V30( the carrier of R \/ the carrier of n) V31( the carrier of R \/ the carrier of n, the carrier of R \/ the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):]
bool [:( the carrier of R \/ the carrier of n),( the carrier of R \/ the carrier of n):] is non empty set
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
(id the carrier of R) \/ (id the carrier of n) is Relation-like set
the carrier of R /\ the carrier of n is set
[: the carrier of n, the carrier of n:] \ the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R \/ the InternalRel of n is Relation-like set
( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:] is Relation-like set
(( the InternalRel of R \/ the InternalRel of n) \/ [: the carrier of R, the carrier of n:]) \/ [: the carrier of n, the carrier of R:] is Relation-like set
the carrier of R /\ the carrier of n is set
the carrier of R /\ the carrier of n is set
the carrier of R /\ the carrier of n is set
[: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):] \ the InternalRel of (sum_of (R,n)) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
the InternalRel of (sum_of (R,n)) ` is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
( the InternalRel of (sum_of (R,n)) `) \ (id the carrier of (sum_of (R,n))) is Relation-like the carrier of (sum_of (R,n)) -defined the carrier of (sum_of (R,n)) -valued Element of bool [: the carrier of (sum_of (R,n)), the carrier of (sum_of (R,n)):]
the carrier of (ComplRelStr R) \/ the carrier of (ComplRelStr n) is set
the carrier of R \/ the carrier of (ComplRelStr n) is set
R is RelStr
ComplRelStr R is strict irreflexive RelStr
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
n is full SubRelStr of R
ComplRelStr n is strict irreflexive RelStr
the InternalRel of (ComplRelStr n) is Relation-like the carrier of (ComplRelStr n) -defined the carrier of (ComplRelStr n) -valued Element of bool [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):]
the carrier of (ComplRelStr n) is set
[: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):] is Relation-like set
bool [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):] is non empty set
the InternalRel of (ComplRelStr R) |_2 the carrier of (ComplRelStr n) is Relation-like set
the InternalRel of (ComplRelStr R) /\ [: the carrier of (ComplRelStr n), the carrier of (ComplRelStr n):] is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the carrier of n is set
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of n ` is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
id the carrier of n is Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
( the InternalRel of n `) \ (id the carrier of n) is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] \ the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
([: the carrier of n, the carrier of n:] \ the InternalRel of n) \ (id the carrier of n) is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ the InternalRel of R) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of (ComplRelStr R) |_2 the carrier of n is Relation-like set
the InternalRel of (ComplRelStr R) /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued set
([: the carrier of R, the carrier of R:] \ the InternalRel of R) /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
(([: the carrier of R, the carrier of R:] \ the InternalRel of R) /\ [: the carrier of n, the carrier of n:]) \ ((id the carrier of R) /\ [: the carrier of n, the carrier of n:]) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:] is Relation-like set
the InternalRel of R /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:]) \ ( the InternalRel of R /\ [: the carrier of n, the carrier of n:]) is Relation-like Element of bool ([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:])
bool ([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:]) is non empty set
(([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:]) \ ( the InternalRel of R /\ [: the carrier of n, the carrier of n:])) \ ((id the carrier of R) /\ [: the carrier of n, the carrier of n:]) is Relation-like Element of bool ([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:])
(id the carrier of R) | the carrier of n is Relation-like the carrier of n -defined the carrier of R -defined the carrier of R -valued Function-like Element of bool [: the carrier of R, the carrier of R:]
(([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:]) \ ( the InternalRel of R /\ [: the carrier of n, the carrier of n:])) \ ((id the carrier of R) | the carrier of n) is Relation-like Element of bool ([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:])
the InternalRel of R |_2 the carrier of n is Relation-like set
the InternalRel of R /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued set
([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:]) \ ( the InternalRel of R |_2 the carrier of n) is Relation-like Element of bool ([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:])
(([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:]) \ ( the InternalRel of R |_2 the carrier of n)) \ (id the carrier of n) is Relation-like Element of bool ([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:])
([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:]) \ the InternalRel of n is Relation-like Element of bool ([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:])
(([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:]) \ the InternalRel of n) \ (id the carrier of n) is Relation-like Element of bool ([: the carrier of R, the carrier of R:] /\ [: the carrier of n, the carrier of n:])
the carrier of R /\ the carrier of n is set
[:( the carrier of R /\ the carrier of n),( the carrier of R /\ the carrier of n):] is Relation-like set
[:( the carrier of R /\ the carrier of n),( the carrier of R /\ the carrier of n):] \ the InternalRel of n is Relation-like the carrier of R /\ the carrier of n -defined the carrier of R /\ the carrier of n -valued Element of bool [:( the carrier of R /\ the carrier of n),( the carrier of R /\ the carrier of n):]
bool [:( the carrier of R /\ the carrier of n),( the carrier of R /\ the carrier of n):] is non empty set
([:( the carrier of R /\ the carrier of n),( the carrier of R /\ the carrier of n):] \ the InternalRel of n) \ (id the carrier of n) is Relation-like the carrier of R /\ the carrier of n -defined the carrier of R /\ the carrier of n -valued Element of bool [:( the carrier of R /\ the carrier of n),( the carrier of R /\ the carrier of n):]
[: the carrier of n,( the carrier of R /\ the carrier of n):] is Relation-like set
[: the carrier of n,( the carrier of R /\ the carrier of n):] \ the InternalRel of n is Relation-like the carrier of n -defined the carrier of R /\ the carrier of n -valued Element of bool [: the carrier of n,( the carrier of R /\ the carrier of n):]
bool [: the carrier of n,( the carrier of R /\ the carrier of n):] is non empty set
([: the carrier of n,( the carrier of R /\ the carrier of n):] \ the InternalRel of n) \ (id the carrier of n) is Relation-like the carrier of n -defined the carrier of R /\ the carrier of n -valued Element of bool [: the carrier of n,( the carrier of R /\ the carrier of n):]
R is non empty irreflexive RelStr
the carrier of R is non empty set
ComplRelStr R is non empty strict irreflexive RelStr
the carrier of (ComplRelStr R) is non empty set
[#] R is non empty non proper Element of bool the carrier of R
bool the carrier of R is non empty set
[#] (ComplRelStr R) is non empty non proper Element of bool the carrier of (ComplRelStr R)
bool the carrier of (ComplRelStr R) is non empty set
n is Element of the carrier of R
{n} is non empty trivial finite 1 -element Element of bool the carrier of R
([#] R) \ {n} is Element of bool the carrier of R
subrelstr (([#] R) \ {n}) is strict full irreflexive SubRelStr of R
ComplRelStr (subrelstr (([#] R) \ {n})) is strict irreflexive RelStr
G is Element of the carrier of (ComplRelStr R)
{G} is non empty trivial finite 1 -element Element of bool the carrier of (ComplRelStr R)
([#] (ComplRelStr R)) \ {G} is Element of bool the carrier of (ComplRelStr R)
subrelstr (([#] (ComplRelStr R)) \ {G}) is strict full irreflexive SubRelStr of ComplRelStr R
the carrier of (subrelstr (([#] R) \ {n})) is set
the carrier of R \ {n} is Element of bool the carrier of R
[:( the carrier of R \ {n}),( the carrier of R \ {n}):] is Relation-like set
[: the carrier of (subrelstr (([#] R) \ {n})),(([#] R) \ {n}):] is Relation-like set
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] is Relation-like set
the InternalRel of (subrelstr (([#] (ComplRelStr R)) \ {G})) is Relation-like the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})) -defined the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})) -valued Element of bool [: the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})), the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})):]
the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})) is set
[: the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})), the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})):] is Relation-like set
bool [: the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})), the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})):] is non empty set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
the InternalRel of (ComplRelStr R) |_2 the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})) is Relation-like set
the InternalRel of (ComplRelStr R) /\ [: the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})), the carrier of (subrelstr (([#] (ComplRelStr R)) \ {G})):] is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued set
the InternalRel of (ComplRelStr R) |_2 ( the carrier of R \ {n}) is Relation-like set
the InternalRel of (ComplRelStr R) /\ [:( the carrier of R \ {n}),( the carrier of R \ {n}):] is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued set
[: the carrier of R, the carrier of R:] is non empty Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
(( the InternalRel of R `) \ (id the carrier of R)) /\ [:( the carrier of R \ {n}),( the carrier of R \ {n}):] is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ ( the InternalRel of R `) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ ( the InternalRel of R `)) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ ([: the carrier of R, the carrier of R:] \ the InternalRel of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ ([: the carrier of R, the carrier of R:] \ the InternalRel of R)) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ [: the carrier of R, the carrier of R:] is Relation-like set
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ [: the carrier of R, the carrier of R:]) \ the InternalRel of R is Relation-like Element of bool ([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ [: the carrier of R, the carrier of R:])
bool ([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ [: the carrier of R, the carrier of R:]) is non empty set
(([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ [: the carrier of R, the carrier of R:]) \ the InternalRel of R) \ (id the carrier of R) is Relation-like Element of bool ([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] /\ [: the carrier of R, the carrier of R:])
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] is non empty set
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R) \ (id the carrier of R) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
the InternalRel of (ComplRelStr (subrelstr (([#] R) \ {n}))) is Relation-like the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))) -defined the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))) -valued Element of bool [: the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))), the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))):]
the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))) is set
[: the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))), the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))):] is Relation-like set
bool [: the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))), the carrier of (ComplRelStr (subrelstr (([#] R) \ {n}))):] is non empty set
the InternalRel of (subrelstr (([#] R) \ {n})) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
the InternalRel of (subrelstr (([#] R) \ {n})) ` is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
id the carrier of (subrelstr (([#] R) \ {n})) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Function-like one-to-one V25( the carrier of (subrelstr (([#] R) \ {n}))) V29( the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n}))) V30( the carrier of (subrelstr (([#] R) \ {n}))) V31( the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n}))) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
( the InternalRel of (subrelstr (([#] R) \ {n})) `) \ (id the carrier of (subrelstr (([#] R) \ {n}))) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of (subrelstr (([#] R) \ {n})) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of (subrelstr (([#] R) \ {n}))) \ (id the carrier of (subrelstr (([#] R) \ {n}))) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
the InternalRel of R |_2 the carrier of (subrelstr (([#] R) \ {n})) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] is Relation-like the carrier of R -defined the carrier of R -valued set
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ ( the InternalRel of R |_2 the carrier of (subrelstr (([#] R) \ {n}))) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ ( the InternalRel of R |_2 the carrier of (subrelstr (([#] R) \ {n})))) \ (id the carrier of (subrelstr (([#] R) \ {n}))) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R) \/ ([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
(([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R) \/ ([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):])) \ (id the carrier of (subrelstr (([#] R) \ {n}))) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R) \/ {} is Relation-like set
(([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R) \/ {}) \ (id the carrier of (subrelstr (([#] R) \ {n}))) is Relation-like Element of bool (([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R) \/ {})
bool (([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R) \/ {}) is non empty set
([: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] \ the InternalRel of R) \ (id the carrier of (subrelstr (([#] R) \ {n}))) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
[:([#] R),(([#] R) \ {n}):] is Relation-like set
[:{n},(([#] R) \ {n}):] is Relation-like set
[:([#] R),(([#] R) \ {n}):] \ [:{n},(([#] R) \ {n}):] is Relation-like [#] R -defined ([#] R) \ {n} -valued Element of bool [:([#] R),(([#] R) \ {n}):]
bool [:([#] R),(([#] R) \ {n}):] is non empty set
[:([#] R),([#] R):] is non empty Relation-like set
[:([#] R),{n}:] is non empty Relation-like set
[:([#] R),([#] R):] \ [:([#] R),{n}:] is Relation-like [#] R -defined [#] R -valued Element of bool [:([#] R),([#] R):]
bool [:([#] R),([#] R):] is non empty set
([:([#] R),([#] R):] \ [:([#] R),{n}:]) \ [:{n},(([#] R) \ {n}):] is Relation-like [#] R -defined [#] R -valued Element of bool [:([#] R),([#] R):]
[: the carrier of R,{n}:] is non empty Relation-like set
[: the carrier of R, the carrier of R:] \ [: the carrier of R,{n}:] is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[:{n}, the carrier of R:] is non empty Relation-like set
[:{n},{n}:] is non empty Relation-like finite set
[:{n}, the carrier of R:] \ [:{n},{n}:] is Relation-like {n} -defined the carrier of R -valued Element of bool [:{n}, the carrier of R:]
bool [:{n}, the carrier of R:] is non empty set
([: the carrier of R, the carrier of R:] \ [: the carrier of R,{n}:]) \ ([:{n}, the carrier of R:] \ [:{n},{n}:]) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ [: the carrier of R,{n}:]) \ [:{n}, the carrier of R:] is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ [: the carrier of R,{n}:]) /\ [:{n},{n}:] is Relation-like the carrier of R -defined the carrier of R -valued finite Element of bool [: the carrier of R, the carrier of R:]
(([: the carrier of R, the carrier of R:] \ [: the carrier of R,{n}:]) \ [:{n}, the carrier of R:]) \/ (([: the carrier of R, the carrier of R:] \ [: the carrier of R,{n}:]) /\ [:{n},{n}:]) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R,{n}:] \/ [:{n}, the carrier of R:] is non empty Relation-like set
[: the carrier of R, the carrier of R:] \ ([: the carrier of R,{n}:] \/ [:{n}, the carrier of R:]) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
([: the carrier of R, the carrier of R:] \ ([: the carrier of R,{n}:] \/ [:{n}, the carrier of R:])) \/ (([: the carrier of R, the carrier of R:] \ [: the carrier of R,{n}:]) /\ [:{n},{n}:]) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
A is set
A is set
R is set
[A,R] is non empty set
{A,R} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,R},{A}} is non empty finite V54() set
A is set
id ( the carrier of R \ {n}) is Relation-like the carrier of R \ {n} -defined the carrier of R \ {n} -valued Function-like one-to-one V25( the carrier of R \ {n}) V29( the carrier of R \ {n}, the carrier of R \ {n}) V30( the carrier of R \ {n}) V31( the carrier of R \ {n}, the carrier of R \ {n}) reflexive symmetric antisymmetric transitive Element of bool [:( the carrier of R \ {n}),( the carrier of R \ {n}):]
bool [:( the carrier of R \ {n}),( the carrier of R \ {n}):] is non empty set
id {n} is non empty trivial Relation-like {n} -defined {n} -valued Function-like one-to-one constant V25({n}) V29({n},{n}) V30({n}) V31({n},{n}) reflexive symmetric antisymmetric strongly_connected transitive finite 1 -element Element of bool [:{n},{n}:]
bool [:{n},{n}:] is non empty finite V54() set
(id the carrier of R) \ (id {n}) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[n,n] is non empty Element of [: the carrier of R, the carrier of R:]
{n,n} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,n},{n}} is non empty finite V54() set
{[n,n]} is non empty trivial Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one constant finite 1 -element Element of bool [: the carrier of R, the carrier of R:]
n is non empty RelStr
the carrier of n is non empty set
G is set
{G} is non empty trivial finite 1 -element set
[: the carrier of (Necklace 4), the carrier of n:] is non empty Relation-like set
bool [: the carrier of (Necklace 4), the carrier of n:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is non empty Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
CG is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of n -valued Function-like V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of n) finite Element of bool [: the carrier of (Necklace 4), the carrier of n:]
dom CG is non empty finite Element of bool the carrier of (Necklace 4)
bool the carrier of (Necklace 4) is non empty finite V54() set
{0,1,2,3} is non empty finite Element of bool NAT
CG . 1 is set
CG . 0 is set
R is V199() reflexive antisymmetric RelStr
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued V25( the carrier of R) V29( the carrier of R, the carrier of R) reflexive antisymmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
n is RelStr
the carrier of n is set
[: the carrier of R, the carrier of n:] is Relation-like set
bool [: the carrier of R, the carrier of n:] is non empty set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
G is Relation-like the carrier of R -defined the carrier of n -valued Function-like V29( the carrier of R, the carrier of n) Element of bool [: the carrier of R, the carrier of n:]
G is Relation-like the carrier of R -defined the carrier of n -valued Function-like V29( the carrier of R, the carrier of n) Element of bool [: the carrier of R, the carrier of n:]
dom G is Element of bool the carrier of R
bool the carrier of R is non empty set
CG is set
x is set
G . CG is set
G . x is set
A is Element of the carrier of R
[A,A] is non empty set
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V54() set
G . A is set
x is Element of the carrier of R
G . x is set
[(G . A),(G . x)] is non empty set
{(G . A),(G . x)} is non empty finite set
{(G . A)} is non empty trivial finite 1 -element set
{{(G . A),(G . x)},{(G . A)}} is non empty finite V54() set
[A,x] is non empty set
{A,x} is non empty finite set
{{A,x},{A}} is non empty finite V54() set
[x,x] is non empty set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V54() set
[(G . x),(G . A)] is non empty set
{(G . x),(G . A)} is non empty finite set
{(G . x)} is non empty trivial finite 1 -element set
{{(G . x),(G . A)},{(G . x)}} is non empty finite V54() set
[x,A] is non empty set
{x,A} is non empty finite set
{{x,A},{x}} is non empty finite V54() set
G is Relation-like the carrier of R -defined the carrier of n -valued Function-like V29( the carrier of R, the carrier of n) Element of bool [: the carrier of R, the carrier of n:]
x is Relation-like the carrier of R -defined the carrier of n -valued Function-like V29( the carrier of R, the carrier of n) Element of bool [: the carrier of R, the carrier of n:]
G is Relation-like the carrier of R -defined the carrier of n -valued Function-like V29( the carrier of R, the carrier of n) Element of bool [: the carrier of R, the carrier of n:]
x is Relation-like the carrier of R -defined the carrier of n -valued Function-like V29( the carrier of R, the carrier of n) Element of bool [: the carrier of R, the carrier of n:]
R is non empty RelStr
n is non empty full SubRelStr of R
the carrier of n is non empty set
[: the carrier of n, the carrier of n:] is non empty Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
id the carrier of n is non empty Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one V25( the carrier of n) V29( the carrier of n, the carrier of n) V30( the carrier of n) V31( the carrier of n, the carrier of n) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of n, the carrier of n:]
G is non empty Relation-like the carrier of n -defined the carrier of n -valued Function-like V25( the carrier of n) V29( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
dom G is non empty Element of bool the carrier of n
bool the carrier of n is non empty set
the carrier of R is non empty set
CG is set
G . CG is set
[: the carrier of n, the carrier of R:] is non empty Relation-like set
bool [: the carrier of n, the carrier of R:] is non empty set
CG is non empty Relation-like the carrier of n -defined the carrier of R -valued Function-like V25( the carrier of n) V29( the carrier of n, the carrier of R) Element of bool [: the carrier of n, the carrier of R:]
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
x is non empty Relation-like the carrier of n -defined the carrier of R -valued Function-like V25( the carrier of n) V29( the carrier of n, the carrier of R) Element of bool [: the carrier of n, the carrier of R:]
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
R is Element of the carrier of n
R is Element of the carrier of n
[R,R] is non empty Element of [: the carrier of n, the carrier of n:]
{R,R} is non empty finite set
{R} is non empty trivial finite 1 -element set
{{R,R},{R}} is non empty finite V54() set
x . R is Element of the carrier of R
x . R is Element of the carrier of R
[(x . R),(x . R)] is non empty Element of [: the carrier of R, the carrier of R:]
{(x . R),(x . R)} is non empty finite set
{(x . R)} is non empty trivial finite 1 -element set
{{(x . R),(x . R)},{(x . R)}} is non empty finite V54() set
the InternalRel of R |_2 the carrier of n is Relation-like set
the InternalRel of R /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R |_2 the carrier of n is Relation-like set
the InternalRel of R /\ [: the carrier of n, the carrier of n:] is Relation-like the carrier of R -defined the carrier of R -valued set
R is non empty RelStr
n is non empty full SubRelStr of R
R is non empty irreflexive RelStr
ComplRelStr R is non empty strict irreflexive RelStr
the carrier of (ComplRelStr R) is non empty set
the carrier of R is non empty set
{0,1,2,3} is non empty finite Element of bool NAT
[: the carrier of (ComplRelStr (Necklace 4)), the carrier of (Necklace 4):] is non empty Relation-like set
bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (Necklace 4):] is non empty set
x is non empty Relation-like the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued Function-like V25( the carrier of (ComplRelStr (Necklace 4))) V29( the carrier of (ComplRelStr (Necklace 4)), the carrier of (Necklace 4)) Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (Necklace 4):]
[: the carrier of (Necklace 4), the carrier of R:] is non empty Relation-like set
bool [: the carrier of (Necklace 4), the carrier of R:] is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
x is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of R -valued Function-like V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of R) finite Element of bool [: the carrier of (Necklace 4), the carrier of R:]
[: the carrier of (ComplRelStr (Necklace 4)), the carrier of R:] is non empty Relation-like set
bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of R:] is non empty set
x * x is non empty Relation-like the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of R -valued Function-like V25( the carrier of (ComplRelStr (Necklace 4))) V29( the carrier of (ComplRelStr (Necklace 4)), the carrier of R) Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of R:]
A is non empty Relation-like the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of R -valued Function-like V25( the carrier of (ComplRelStr (Necklace 4))) V29( the carrier of (ComplRelStr (Necklace 4)), the carrier of R) Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of R:]
A is Element of the carrier of (ComplRelStr (Necklace 4))
R is Element of the carrier of (ComplRelStr (Necklace 4))
[A,R] is non empty Element of [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
{A,R} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,R},{A}} is non empty finite V54() set
A . A is Element of the carrier of R
A . R is Element of the carrier of R
[(A . A),(A . R)] is non empty Element of [: the carrier of R, the carrier of R:]
{(A . A),(A . R)} is non empty finite set
{(A . A)} is non empty trivial finite 1 -element set
{{(A . A),(A . R)},{(A . A)}} is non empty finite V54() set
x . A is Element of the carrier of (Necklace 4)
x . R is Element of the carrier of (Necklace 4)
[(x . A),(x . R)] is non empty Element of [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
{(x . A),(x . R)} is non empty finite set
{(x . A)} is non empty trivial finite 1 -element set
{{(x . A),(x . R)},{(x . A)}} is non empty finite V54() set
x . (x . A) is Element of the carrier of R
x . (x . R) is Element of the carrier of R
[(x . (x . A)),(x . (x . R))] is non empty Element of [: the carrier of R, the carrier of R:]
{(x . (x . A)),(x . (x . R))} is non empty finite set
{(x . (x . A))} is non empty trivial finite 1 -element set
{{(x . (x . A)),(x . (x . R))},{(x . (x . A))}} is non empty finite V54() set
(x * x) . A is Element of the carrier of R
[((x * x) . A),(x . (x . R))] is non empty Element of [: the carrier of R, the carrier of R:]
{((x * x) . A),(x . (x . R))} is non empty finite set
{((x * x) . A)} is non empty trivial finite 1 -element set
{{((x * x) . A),(x . (x . R))},{((x * x) . A)}} is non empty finite V54() set
x . A is Element of the carrier of (Necklace 4)
x . (x . A) is Element of the carrier of R
[(x . (x . A)),(A . R)] is non empty Element of [: the carrier of R, the carrier of R:]
{(x . (x . A)),(A . R)} is non empty finite set
{(x . (x . A))} is non empty trivial finite 1 -element set
{{(x . (x . A)),(A . R)},{(x . (x . A))}} is non empty finite V54() set
x . R is Element of the carrier of (Necklace 4)
x . (x . R) is Element of the carrier of R
[(x . (x . A)),(x . (x . R))] is non empty Element of [: the carrier of R, the carrier of R:]
{(x . (x . A)),(x . (x . R))} is non empty finite set
{{(x . (x . A)),(x . (x . R))},{(x . (x . A))}} is non empty finite V54() set
[(x . A),(x . R)] is non empty Element of [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
{(x . A),(x . R)} is non empty finite set
{(x . A)} is non empty trivial finite 1 -element set
{{(x . A),(x . R)},{(x . A)}} is non empty finite V54() set
dom A is non empty Element of bool the carrier of (ComplRelStr (Necklace 4))
bool the carrier of (ComplRelStr (Necklace 4)) is non empty set
A . 0 is set
A . 1 is set
[(A . 0),(A . 1)] is non empty set
{(A . 0),(A . 1)} is non empty finite set
{(A . 0)} is non empty trivial finite 1 -element set
{{(A . 0),(A . 1)},{(A . 0)}} is non empty finite V54() set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
[0,1] is non empty Element of [:NAT,NAT:]
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
A . 2 is set
[(A . 1),(A . 2)] is non empty set
{(A . 1),(A . 2)} is non empty finite set
{(A . 1)} is non empty trivial finite 1 -element set
{{(A . 1),(A . 2)},{(A . 1)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
[1,2] is non empty Element of [:NAT,NAT:]
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
A . 3 is set
[(A . 2),(A . 3)] is non empty set
{(A . 2),(A . 3)} is non empty finite set
{(A . 2)} is non empty trivial finite 1 -element set
{{(A . 2),(A . 3)},{(A . 2)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
[2,3] is non empty Element of [:NAT,NAT:]
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
[(A . 3),(A . 1)] is non empty set
{(A . 3),(A . 1)} is non empty finite set
{(A . 3)} is non empty trivial finite 1 -element set
{{(A . 3),(A . 1)},{(A . 3)}} is non empty finite V54() set
[(A . 1),(A . 3)] is non empty set
{(A . 1),(A . 3)} is non empty finite set
{{(A . 1),(A . 3)},{(A . 1)}} is non empty finite V54() set
[(A . 3),(A . 0)] is non empty set
{(A . 3),(A . 0)} is non empty finite set
{{(A . 3),(A . 0)},{(A . 3)}} is non empty finite V54() set
[(A . 0),(A . 3)] is non empty set
{(A . 0),(A . 3)} is non empty finite set
{{(A . 0),(A . 3)},{(A . 0)}} is non empty finite V54() set
[(A . 1),(A . 0)] is non empty set
{(A . 1),(A . 0)} is non empty finite set
{{(A . 1),(A . 0)},{(A . 1)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
[1,0] is non empty Element of [:NAT,NAT:]
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
[(A . 2),(A . 1)] is non empty set
{(A . 2),(A . 1)} is non empty finite set
{{(A . 2),(A . 1)},{(A . 2)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
[2,1] is non empty Element of [:NAT,NAT:]
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
[(A . 3),(A . 2)] is non empty set
{(A . 3),(A . 2)} is non empty finite set
{{(A . 3),(A . 2)},{(A . 3)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
[3,2] is non empty Element of [:NAT,NAT:]
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
[(A . 2),(A . 0)] is non empty set
{(A . 2),(A . 0)} is non empty finite set
{{(A . 2),(A . 0)},{(A . 2)}} is non empty finite V54() set
[(A . 0),(A . 2)] is non empty set
{(A . 0),(A . 2)} is non empty finite set
{{(A . 0),(A . 2)},{(A . 0)}} is non empty finite V54() set
A is Element of the carrier of (Necklace 4)
R is Element of the carrier of (Necklace 4)
[A,R] is non empty Element of [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
{A,R} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,R},{A}} is non empty finite V54() set
A . A is set
A . R is set
[(A . A),(A . R)] is non empty set
{(A . A),(A . R)} is non empty finite set
{(A . A)} is non empty trivial finite 1 -element set
{{(A . A),(A . R)},{(A . A)}} is non empty finite V54() set
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (Necklace 4), the carrier of (ComplRelStr R):] is non empty Relation-like set
bool [: the carrier of (Necklace 4), the carrier of (ComplRelStr R):] is non empty set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
x is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr R) -valued Function-like V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (ComplRelStr R)) finite Element of bool [: the carrier of (Necklace 4), the carrier of (ComplRelStr R):]
[: the carrier of (Necklace 4), the carrier of (ComplRelStr (Necklace 4)):] is non empty Relation-like set
bool [: the carrier of (Necklace 4), the carrier of (ComplRelStr (Necklace 4)):] is non empty set
x is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -valued Function-like V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of (ComplRelStr (Necklace 4))) finite Element of bool [: the carrier of (Necklace 4), the carrier of (ComplRelStr (Necklace 4)):]
dom x is non empty finite Element of bool the carrier of (Necklace 4)
bool the carrier of (Necklace 4) is non empty finite V54() set
x . 0 is set
x . 2 is set
[(x . 0),(x . 2)] is non empty set
{(x . 0),(x . 2)} is non empty finite set
{(x . 0)} is non empty trivial finite 1 -element set
{{(x . 0),(x . 2)},{(x . 0)}} is non empty finite V54() set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
x . 3 is set
[(x . 0),(x . 3)] is non empty set
{(x . 0),(x . 3)} is non empty finite set
{{(x . 0),(x . 3)},{(x . 0)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
x . 1 is set
[(x . 1),(x . 3)] is non empty set
{(x . 1),(x . 3)} is non empty finite set
{(x . 1)} is non empty trivial finite 1 -element set
{{(x . 1),(x . 3)},{(x . 1)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
[3,2] is non empty Element of [:NAT,NAT:]
[(x . 3),(x . 2)] is non empty set
{(x . 3),(x . 2)} is non empty finite set
{(x . 3)} is non empty trivial finite 1 -element set
{{(x . 3),(x . 2)},{(x . 3)}} is non empty finite V54() set
[2,3] is non empty Element of [:NAT,NAT:]
[(x . 2),(x . 3)] is non empty set
{(x . 2),(x . 3)} is non empty finite set
{(x . 2)} is non empty trivial finite 1 -element set
{{(x . 2),(x . 3)},{(x . 2)}} is non empty finite V54() set
[1,2] is non empty Element of [:NAT,NAT:]
[(x . 1),(x . 2)] is non empty set
{(x . 1),(x . 2)} is non empty finite set
{{(x . 1),(x . 2)},{(x . 1)}} is non empty finite V54() set
[1,0] is non empty Element of [:NAT,NAT:]
[(x . 1),(x . 0)] is non empty set
{(x . 1),(x . 0)} is non empty finite set
{{(x . 1),(x . 0)},{(x . 1)}} is non empty finite V54() set
[(x . 2),(x . 0)] is non empty set
{(x . 2),(x . 0)} is non empty finite set
{{(x . 2),(x . 0)},{(x . 2)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
[(x . 3),(x . 0)] is non empty set
{(x . 3),(x . 0)} is non empty finite set
{{(x . 3),(x . 0)},{(x . 3)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
[(x . 3),(x . 1)] is non empty set
{(x . 3),(x . 1)} is non empty finite set
{{(x . 3),(x . 1)},{(x . 3)}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
(id the carrier of R) \/ the InternalRel of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
((id the carrier of R) \/ the InternalRel of R) \/ the InternalRel of (ComplRelStr R) is non empty Relation-like set
the InternalRel of (Necklace 4) /\ the InternalRel of (ComplRelStr (Necklace 4)) is Relation-like the carrier of (Necklace 4) -defined the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of (Necklace 4) -valued the carrier of (ComplRelStr (Necklace 4)) -valued finite Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
[2,1] is non empty Element of [:NAT,NAT:]
[(x . 2),(x . 1)] is non empty set
{(x . 2),(x . 1)} is non empty finite set
{{(x . 2),(x . 1)},{(x . 2)}} is non empty finite V54() set
[0,1] is non empty Element of [:NAT,NAT:]
[(x . 0),(x . 1)] is non empty set
{(x . 0),(x . 1)} is non empty finite set
{{(x . 0),(x . 1)},{(x . 0)}} is non empty finite V54() set
A is Element of the carrier of (ComplRelStr (Necklace 4))
A is Element of the carrier of (ComplRelStr (Necklace 4))
[A,A] is non empty Element of [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
{A,A} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,A},{A}} is non empty finite V54() set
x . A is set
x . A is set
[(x . A),(x . A)] is non empty set
{(x . A),(x . A)} is non empty finite set
{(x . A)} is non empty trivial finite 1 -element set
{{(x . A),(x . A)},{(x . A)}} is non empty finite V54() set
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr (Necklace 4)), the carrier of R:] is non empty Relation-like set
bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of R:] is non empty set
[: the carrier of (Necklace 4), the carrier of R:] is non empty Relation-like set
bool [: the carrier of (Necklace 4), the carrier of R:] is non empty set
A is non empty Relation-like the carrier of (ComplRelStr (Necklace 4)) -defined the carrier of R -valued Function-like V25( the carrier of (ComplRelStr (Necklace 4))) V29( the carrier of (ComplRelStr (Necklace 4)), the carrier of R) Element of bool [: the carrier of (ComplRelStr (Necklace 4)), the carrier of R:]
A * x is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of R -valued Function-like V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of R) finite Element of bool [: the carrier of (Necklace 4), the carrier of R:]
A is non empty Relation-like the carrier of (Necklace 4) -defined the carrier of R -valued Function-like V25( the carrier of (Necklace 4)) V29( the carrier of (Necklace 4), the carrier of R) finite Element of bool [: the carrier of (Necklace 4), the carrier of R:]
R is Element of the carrier of (Necklace 4)
R is Element of the carrier of (Necklace 4)
[R,R] is non empty Element of [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
{R,R} is non empty finite set
{R} is non empty trivial finite 1 -element set
{{R,R},{R}} is non empty finite V54() set
A . R is Element of the carrier of R
A . R is Element of the carrier of R
[(A . R),(A . R)] is non empty Element of [: the carrier of R, the carrier of R:]
{(A . R),(A . R)} is non empty finite set
{(A . R)} is non empty trivial finite 1 -element set
{{(A . R),(A . R)},{(A . R)}} is non empty finite V54() set
x . R is Element of the carrier of (ComplRelStr (Necklace 4))
x . R is Element of the carrier of (ComplRelStr (Necklace 4))
[(x . R),(x . R)] is non empty Element of [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
{(x . R),(x . R)} is non empty finite set
{(x . R)} is non empty trivial finite 1 -element set
{{(x . R),(x . R)},{(x . R)}} is non empty finite V54() set
A . (x . R) is Element of the carrier of R
A . (x . R) is Element of the carrier of R
[(A . (x . R)),(A . (x . R))] is non empty Element of [: the carrier of R, the carrier of R:]
{(A . (x . R)),(A . (x . R))} is non empty finite set
{(A . (x . R))} is non empty trivial finite 1 -element set
{{(A . (x . R)),(A . (x . R))},{(A . (x . R))}} is non empty finite V54() set
(A * x) . R is Element of the carrier of R
[((A * x) . R),(A . (x . R))] is non empty Element of [: the carrier of R, the carrier of R:]
{((A * x) . R),(A . (x . R))} is non empty finite set
{((A * x) . R)} is non empty trivial finite 1 -element set
{{((A * x) . R),(A . (x . R))},{((A * x) . R)}} is non empty finite V54() set
x . R is Element of the carrier of (ComplRelStr (Necklace 4))
A . (x . R) is Element of the carrier of R
[(A . (x . R)),(A . R)] is non empty Element of [: the carrier of R, the carrier of R:]
{(A . (x . R)),(A . R)} is non empty finite set
{(A . (x . R))} is non empty trivial finite 1 -element set
{{(A . (x . R)),(A . R)},{(A . (x . R))}} is non empty finite V54() set
x . R is Element of the carrier of (ComplRelStr (Necklace 4))
A . (x . R) is Element of the carrier of R
[(A . (x . R)),(A . (x . R))] is non empty Element of [: the carrier of R, the carrier of R:]
{(A . (x . R)),(A . (x . R))} is non empty finite set
{{(A . (x . R)),(A . (x . R))},{(A . (x . R))}} is non empty finite V54() set
[(x . R),(x . R)] is non empty Element of [: the carrier of (ComplRelStr (Necklace 4)), the carrier of (ComplRelStr (Necklace 4)):]
{(x . R),(x . R)} is non empty finite set
{(x . R)} is non empty trivial finite 1 -element set
{{(x . R),(x . R)},{(x . R)}} is non empty finite V54() set
R is non empty irreflexive RelStr
ComplRelStr R is non empty strict irreflexive RelStr
R is RelStr
n is set
the carrier of R is set
G is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
R is non empty RelStr
the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
CG is set
x is set
x is Element of the carrier of R
A is Element of the carrier of R
[x,A] is non empty Element of [: the carrier of R, the carrier of R:]
{x,A} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,A},{x}} is non empty finite V54() set
<*x,A*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
len <*x,A*> is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
<*x,A*> . 1 is set
<*x,A*> . 2 is set
[A,x] is non empty Element of [: the carrier of R, the carrier of R:]
{A,x} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,x},{A}} is non empty finite V54() set
<*A,x*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
len <*A,x*> is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
<*A,x*> . 1 is set
<*A,x*> . 2 is set
[x,A] is non empty Element of [: the carrier of R, the carrier of R:]
{x,A} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,A},{x}} is non empty finite V54() set
[A,x] is non empty Element of [: the carrier of R, the carrier of R:]
{A,x} is non empty finite set
{A} is non empty trivial finite 1 -element set
{{A,x},{A}} is non empty finite V54() set
R is non empty V199() reflexive transitive RelStr
the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued V25( the carrier of R) V29( the carrier of R, the carrier of R) reflexive transitive Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
n is Element of the carrier of R
G is Element of the carrier of R
[n,G] is non empty Element of [: the carrier of R, the carrier of R:]
{n,G} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,G},{n}} is non empty finite V54() set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like RedSequence of the InternalRel of R
x . 1 is set
len x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
x . (len x) is set
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom A is finite Element of bool NAT
A . 1 is set
A is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
A . A is set
[(A . 1),(A . A)] is non empty set
{(A . 1),(A . A)} is non empty finite set
{(A . 1)} is non empty trivial finite 1 -element set
{{(A . 1),(A . A)},{(A . 1)}} is non empty finite V54() set
A + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
A . (A + 1) is set
[(A . 1),(A . (A + 1))] is non empty set
{(A . 1),(A . (A + 1))} is non empty finite set
{{(A . 1),(A . (A + 1))},{(A . 1)}} is non empty finite V54() set
len A is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
0 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
[(A . A),(A . (A + 1))] is non empty set
{(A . A),(A . (A + 1))} is non empty finite set
{(A . A)} is non empty trivial finite 1 -element set
{{(A . A),(A . (A + 1))},{(A . A)}} is non empty finite V54() set
[(A . 1),(A . 1)] is non empty set
{(A . 1),(A . 1)} is non empty finite set
{(A . 1)} is non empty trivial finite 1 -element set
{{(A . 1),(A . 1)},{(A . 1)}} is non empty finite V54() set
len A is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
0 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
R is non empty V199() reflexive transitive RelStr
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued V25( the carrier of R) V29( the carrier of R, the carrier of R) reflexive transitive Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is non empty set
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
G is Element of the carrier of R
CG is Element of the carrier of R
[G,CG] is non empty Element of [: the carrier of R, the carrier of R:]
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,G] is non empty Element of [: the carrier of R, the carrier of R:]
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
R is symmetric RelStr
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
G is set
CG is set
the InternalRel of R ~ is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like RedSequence of the InternalRel of R
x . 1 is set
len x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
x . (len x) is set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Rev x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
(Rev x) . (len x) is set
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like RedSequence of the InternalRel of R
A . 1 is set
len A is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
A . (len A) is set
R is symmetric RelStr
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
CG is set
x is set
CG is set
x is set
R is RelStr
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
EqCl the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued V25( the carrier of R) V29( the carrier of R, the carrier of R) reflexive symmetric transitive Element of bool [: the carrier of R, the carrier of R:]
n is Element of the carrier of R
Class ((EqCl the InternalRel of R),n) is Element of bool the carrier of R
bool the carrier of R is non empty set
R is non empty RelStr
the carrier of R is non empty set
n is Element of the carrier of R
(R,n) is Element of bool the carrier of R
bool the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
EqCl the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued V25( the carrier of R) V29( the carrier of R, the carrier of R) reflexive symmetric transitive Element of bool [: the carrier of R, the carrier of R:]
Class ((EqCl the InternalRel of R),n) is Element of bool the carrier of R
R is RelStr
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
EqCl the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued V25( the carrier of R) V29( the carrier of R, the carrier of R) reflexive symmetric transitive Element of bool [: the carrier of R, the carrier of R:]
n is Element of the carrier of R
(R,n) is Element of bool the carrier of R
bool the carrier of R is non empty set
Class ((EqCl the InternalRel of R),n) is Element of bool the carrier of R
G is set
[n,G] is non empty set
{n,G} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,G},{n}} is non empty finite V54() set
[G,n] is non empty set
{G,n} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,n},{G}} is non empty finite V54() set
R is RelStr
the carrier of R is set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
EqCl the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued V25( the carrier of R) V29( the carrier of R, the carrier of R) reflexive symmetric transitive Element of bool [: the carrier of R, the carrier of R:]
n is Element of the carrier of R
(R,n) is Element of bool the carrier of R
bool the carrier of R is non empty set
Class ((EqCl the InternalRel of R),n) is Element of bool the carrier of R
G is set
x is set
[x,n] is non empty set
{x,n} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,n},{x}} is non empty finite V54() set
[n,x] is non empty set
{n,x} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,x},{n}} is non empty finite V54() set
x is set
[n,x] is non empty set
{n,x} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,x},{n}} is non empty finite V54() set
[x,n] is non empty set
{x,n} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,n},{x}} is non empty finite V54() set
x is set
[n,x] is non empty set
{n,x} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,x},{n}} is non empty finite V54() set
[x,n] is non empty set
{x,n} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,n},{x}} is non empty finite V54() set
x is set
[n,x] is non empty set
{n,x} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,x},{n}} is non empty finite V54() set
x is set
[n,x] is non empty set
{n,x} is non empty finite set
{{n,x},{n}} is non empty finite V54() set
A is set
[n,A] is non empty set
{n,A} is non empty finite set
{{n,A},{n}} is non empty finite V54() set
A is set
[n,A] is non empty set
{n,A} is non empty finite set
{{n,A},{n}} is non empty finite V54() set
R is non empty symmetric irreflexive RelStr
the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
RelStr(# the carrier of R, the InternalRel of R #) is non empty strict RelStr
CG is set
x is set
x is Element of the carrier of R
(R,x) is non empty Element of bool the carrier of R
bool the carrier of R is non empty set
EqCl the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued V25( the carrier of R) V29( the carrier of R, the carrier of R) reflexive symmetric transitive Element of bool [: the carrier of R, the carrier of R:]
Class ((EqCl the InternalRel of R),x) is Element of bool the carrier of R
the carrier of R \ (R,x) is Element of bool the carrier of R
subrelstr (R,x) is strict full symmetric irreflexive SubRelStr of R
R is Element of bool the carrier of R
subrelstr R is strict full symmetric irreflexive SubRelStr of R
the carrier of (subrelstr R) is set
(R,x) \/ R is non empty Element of bool the carrier of R
R22 is set
the carrier of (subrelstr (R,x)) is set
the InternalRel of (subrelstr (R,x)) is Relation-like the carrier of (subrelstr (R,x)) -defined the carrier of (subrelstr (R,x)) -valued symmetric Element of bool [: the carrier of (subrelstr (R,x)), the carrier of (subrelstr (R,x)):]
[: the carrier of (subrelstr (R,x)), the carrier of (subrelstr (R,x)):] is Relation-like set
bool [: the carrier of (subrelstr (R,x)), the carrier of (subrelstr (R,x)):] is non empty set
the InternalRel of (subrelstr R) is Relation-like the carrier of (subrelstr R) -defined the carrier of (subrelstr R) -valued symmetric Element of bool [: the carrier of (subrelstr R), the carrier of (subrelstr R):]
[: the carrier of (subrelstr R), the carrier of (subrelstr R):] is Relation-like set
bool [: the carrier of (subrelstr R), the carrier of (subrelstr R):] is non empty set
the InternalRel of (subrelstr (R,x)) /\ the InternalRel of (subrelstr R) is Relation-like the carrier of (subrelstr R) -defined the carrier of (subrelstr (R,x)) -defined the carrier of (subrelstr R) -valued the carrier of (subrelstr (R,x)) -valued Element of bool [: the carrier of (subrelstr R), the carrier of (subrelstr R):]
G9 is set
x9 is set
H is set
[x9,H] is non empty set
{x9,H} is non empty finite set
{x9} is non empty trivial finite 1 -element set
{{x9,H},{x9}} is non empty finite V54() set
H is set
u is set
[H,u] is non empty set
{H,u} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,u},{H}} is non empty finite V54() set
(R,x) /\ R is Element of bool the carrier of R
the InternalRel of R \ the InternalRel of (subrelstr (R,x)) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
G9 is set
x9 is set
H is set
[x9,H] is non empty set
{x9,H} is non empty finite set
{x9} is non empty trivial finite 1 -element set
{{x9,H},{x9}} is non empty finite V54() set
H is Element of the carrier of (subrelstr R)
u is Element of the carrier of (subrelstr R)
the InternalRel of (subrelstr (R,x)) /\ the InternalRel of (subrelstr R) is Relation-like the carrier of (subrelstr R) -defined the carrier of (subrelstr (R,x)) -defined the carrier of (subrelstr R) -valued the carrier of (subrelstr (R,x)) -valued Element of bool [: the carrier of (subrelstr R), the carrier of (subrelstr R):]
v is Element of the carrier of R
w is Element of the carrier of R
G9 is set
x9 is set
H is set
[x9,H] is non empty set
{x9,H} is non empty finite set
{x9} is non empty trivial finite 1 -element set
{{x9,H},{x9}} is non empty finite V54() set
H is Element of the carrier of R
u is Element of the carrier of R
w is Element of the carrier of (subrelstr (R,x))
v is Element of the carrier of (subrelstr (R,x))
[:(R,x),R:] is Relation-like set
[:(R,x),R:] /\ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
v is set
w is set
Z is set
[w,Z] is non empty set
{w,Z} is non empty finite set
{w} is non empty trivial finite 1 -element set
{{w,Z},{w}} is non empty finite V54() set
H is Element of the carrier of R
[x,H] is non empty Element of [: the carrier of R, the carrier of R:]
{x,H} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,H},{x}} is non empty finite V54() set
Z is Element of the carrier of R
[x,Z] is non empty Element of [: the carrier of R, the carrier of R:]
{x,Z} is non empty finite set
{{x,Z},{x}} is non empty finite V54() set
(R,x) /\ R is Element of bool the carrier of R
[:(R,x),R:] /\ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[:R,(R,x):] is Relation-like set
[:R,(R,x):] /\ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
v is set
w is set
Z is set
[w,Z] is non empty set
{w,Z} is non empty finite set
{w} is non empty trivial finite 1 -element set
{{w,Z},{w}} is non empty finite V54() set
H is Element of the carrier of R
[x,H] is non empty Element of [: the carrier of R, the carrier of R:]
{x,H} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,H},{x}} is non empty finite V54() set
Z is Element of the carrier of R
[H,Z] is non empty Element of [: the carrier of R, the carrier of R:]
{H,Z} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,Z},{H}} is non empty finite V54() set
[x,Z] is non empty Element of [: the carrier of R, the carrier of R:]
{x,Z} is non empty finite set
{{x,Z},{x}} is non empty finite V54() set
(R,x) /\ R is Element of bool the carrier of R
[:R,(R,x):] /\ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
w is Element of the carrier of (subrelstr R)
v is Element of the carrier of (subrelstr R)
the InternalRel of (subrelstr (R,x)) \/ the InternalRel of (subrelstr R) is Relation-like set
G9 is set
G9 is set
x9 is set
H is set
[x9,H] is non empty set
{x9,H} is non empty finite set
{x9} is non empty trivial finite 1 -element set
{{x9,H},{x9}} is non empty finite V54() set
H is Element of the carrier of (subrelstr (R,x))
u is Element of the carrier of (subrelstr (R,x))
v is Element of the carrier of R
w is Element of the carrier of R
x9 is set
H is set
[x9,H] is non empty set
{x9,H} is non empty finite set
{x9} is non empty trivial finite 1 -element set
{{x9,H},{x9}} is non empty finite V54() set
H is Element of the carrier of (subrelstr R)
u is Element of the carrier of (subrelstr R)
v is Element of the carrier of R
w is Element of the carrier of R
union_of ((subrelstr (R,x)),(subrelstr R)) is strict symmetric irreflexive RelStr
the InternalRel of (union_of ((subrelstr (R,x)),(subrelstr R))) is Relation-like the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))) -defined the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))) -valued symmetric Element of bool [: the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))), the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))):]
the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))) is set
[: the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))), the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))):] is Relation-like set
bool [: the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))), the carrier of (union_of ((subrelstr (R,x)),(subrelstr R))):] is non empty set
the InternalRel of R ~ is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R \/ ( the InternalRel of R ~) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
A is Element of the carrier of R
[x,A] is non empty Element of [: the carrier of R, the carrier of R:]
{x,A} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,A},{x}} is non empty finite V54() set
R is non empty symmetric irreflexive RelStr
ComplRelStr R is non empty strict symmetric irreflexive RelStr
the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
RelStr(# the carrier of R, the InternalRel of R #) is non empty strict RelStr
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued symmetric Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is non empty set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
A is set
A is set
R is Element of the carrier of (ComplRelStr R)
((ComplRelStr R),R) is non empty Element of bool the carrier of (ComplRelStr R)
bool the carrier of (ComplRelStr R) is non empty set
EqCl the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued V25( the carrier of (ComplRelStr R)) V29( the carrier of (ComplRelStr R), the carrier of (ComplRelStr R)) reflexive symmetric transitive Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
Class ((EqCl the InternalRel of (ComplRelStr R)),R) is Element of bool the carrier of (ComplRelStr R)
the carrier of R \ ((ComplRelStr R),R) is Element of bool the carrier of R
bool the carrier of R is non empty set
the InternalRel of (ComplRelStr R) ~ is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the InternalRel of (ComplRelStr R) \/ ( the InternalRel of (ComplRelStr R) ~) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
R is Element of the carrier of (ComplRelStr R)
[R,R] is non empty Element of [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
{R,R} is non empty finite set
{R} is non empty trivial finite 1 -element set
{{R,R},{R}} is non empty finite V54() set
R22 is Element of bool the carrier of R
subrelstr R22 is strict full symmetric irreflexive SubRelStr of R
R11 is Element of bool the carrier of R
subrelstr R11 is strict full symmetric irreflexive SubRelStr of R
the carrier of (subrelstr R22) is set
the InternalRel of (subrelstr R22) is Relation-like the carrier of (subrelstr R22) -defined the carrier of (subrelstr R22) -valued symmetric Element of bool [: the carrier of (subrelstr R22), the carrier of (subrelstr R22):]
[: the carrier of (subrelstr R22), the carrier of (subrelstr R22):] is Relation-like set
bool [: the carrier of (subrelstr R22), the carrier of (subrelstr R22):] is non empty set
the InternalRel of (subrelstr R11) is Relation-like the carrier of (subrelstr R11) -defined the carrier of (subrelstr R11) -valued symmetric Element of bool [: the carrier of (subrelstr R11), the carrier of (subrelstr R11):]
the carrier of (subrelstr R11) is set
[: the carrier of (subrelstr R11), the carrier of (subrelstr R11):] is Relation-like set
bool [: the carrier of (subrelstr R11), the carrier of (subrelstr R11):] is non empty set
[: the carrier of (subrelstr R22), the carrier of (subrelstr R11):] is Relation-like set
[: the carrier of (subrelstr R11), the carrier of (subrelstr R22):] is Relation-like set
R22 \/ R11 is Element of bool the carrier of R
w is set
w is set
the InternalRel of (subrelstr R22) /\ the InternalRel of (subrelstr R11) is Relation-like the carrier of (subrelstr R22) -defined the carrier of (subrelstr R11) -defined the carrier of (subrelstr R22) -valued the carrier of (subrelstr R11) -valued Element of bool [: the carrier of (subrelstr R11), the carrier of (subrelstr R11):]
w is set
Z is set
Z is set
[Z,Z] is non empty set
{Z,Z} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,Z},{Z}} is non empty finite V54() set
H is set
w is set
[H,w] is non empty set
{H,w} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,w},{H}} is non empty finite V54() set
R22 /\ R11 is Element of bool the carrier of R
the InternalRel of R \ the InternalRel of (subrelstr R22) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R \ the InternalRel of (subrelstr R22)) \ [: the carrier of (subrelstr R22), the carrier of (subrelstr R11):] is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
(( the InternalRel of R \ the InternalRel of (subrelstr R22)) \ [: the carrier of (subrelstr R22), the carrier of (subrelstr R11):]) \ [: the carrier of (subrelstr R11), the carrier of (subrelstr R22):] is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
w is set
Z is set
Z is set
[Z,Z] is non empty set
{Z,Z} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,Z},{Z}} is non empty finite V54() set
H is Element of the carrier of (subrelstr R11)
w is Element of the carrier of (subrelstr R11)
the InternalRel of (subrelstr R22) /\ the InternalRel of (subrelstr R11) is Relation-like the carrier of (subrelstr R22) -defined the carrier of (subrelstr R11) -defined the carrier of (subrelstr R22) -valued the carrier of (subrelstr R11) -valued Element of bool [: the carrier of (subrelstr R11), the carrier of (subrelstr R11):]
R22 /\ R11 is Element of bool the carrier of R
R22 /\ R11 is Element of bool the carrier of R
u is Element of the carrier of R
v is Element of the carrier of R
w is set
Z is set
Z is set
[Z,Z] is non empty set
{Z,Z} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,Z},{Z}} is non empty finite V54() set
H is Element of the carrier of R
w is Element of the carrier of R
v is Element of the carrier of (subrelstr R22)
u is Element of the carrier of (subrelstr R22)
u is Element of the carrier of (subrelstr R11)
v is Element of the carrier of (subrelstr R11)
the InternalRel of (subrelstr R22) \/ the InternalRel of (subrelstr R11) is Relation-like set
( the InternalRel of (subrelstr R22) \/ the InternalRel of (subrelstr R11)) \/ [: the carrier of (subrelstr R22), the carrier of (subrelstr R11):] is Relation-like set
(( the InternalRel of (subrelstr R22) \/ the InternalRel of (subrelstr R11)) \/ [: the carrier of (subrelstr R22), the carrier of (subrelstr R11):]) \/ [: the carrier of (subrelstr R11), the carrier of (subrelstr R22):] is Relation-like set
Z is set
Z is set
H is set
w is set
[H,w] is non empty set
{H,w} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,w},{H}} is non empty finite V54() set
u is Element of the carrier of (subrelstr R22)
v is Element of the carrier of (subrelstr R22)
y1 is Element of the carrier of R
u is Element of the carrier of R
H is set
w is set
[H,w] is non empty set
{H,w} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,w},{H}} is non empty finite V54() set
u is Element of the carrier of (subrelstr R11)
v is Element of the carrier of (subrelstr R11)
y1 is Element of the carrier of R
u is Element of the carrier of R
H is set
w is set
[H,w] is non empty set
{H,w} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,w},{H}} is non empty finite V54() set
u is Element of the carrier of (ComplRelStr R)
v is Element of the carrier of (ComplRelStr R)
R22 /\ R11 is Element of bool the carrier of R
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[u,v] is non empty Element of [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
{u,v} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,v},{u}} is non empty finite V54() set
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[R,u] is non empty Element of [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
{R,u} is non empty finite set
{{R,u},{R}} is non empty finite V54() set
[R,v] is non empty Element of [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
{R,v} is non empty finite set
{{R,v},{R}} is non empty finite V54() set
R22 /\ R11 is Element of bool the carrier of R
H is set
w is set
[H,w] is non empty set
{H,w} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,w},{H}} is non empty finite V54() set
u is Element of the carrier of (ComplRelStr R)
v is Element of the carrier of (ComplRelStr R)
R22 /\ R11 is Element of bool the carrier of R
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
[u,v] is non empty Element of [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
{u,v} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,v},{u}} is non empty finite V54() set
[: the carrier of R, the carrier of R:] \ the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of R ` is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
( the InternalRel of R `) \ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[v,u] is non empty Element of [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
{v,u} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,u},{v}} is non empty finite V54() set
[R,v] is non empty Element of [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
{R,v} is non empty finite set
{{R,v},{R}} is non empty finite V54() set
[R,u] is non empty Element of [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
{R,u} is non empty finite set
{{R,u},{R}} is non empty finite V54() set
R22 /\ R11 is Element of bool the carrier of R
sum_of ((subrelstr R22),(subrelstr R11)) is strict symmetric RelStr
the InternalRel of (sum_of ((subrelstr R22),(subrelstr R11))) is Relation-like the carrier of (sum_of ((subrelstr R22),(subrelstr R11))) -defined the carrier of (sum_of ((subrelstr R22),(subrelstr R11))) -valued symmetric Element of bool [: the carrier of (sum_of ((subrelstr R22),(subrelstr R11))), the carrier of (sum_of ((subrelstr R22),(subrelstr R11))):]
the carrier of (sum_of ((subrelstr R22),(subrelstr R11))) is set
[: the carrier of (sum_of ((subrelstr R22),(subrelstr R11))), the carrier of (sum_of ((subrelstr R22),(subrelstr R11))):] is Relation-like set
bool [: the carrier of (sum_of ((subrelstr R22),(subrelstr R11))), the carrier of (sum_of ((subrelstr R22),(subrelstr R11))):] is non empty set
R is non empty finite set
card R is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
n is non empty set
G is non empty set
n \/ G is non empty set
card n is non empty V4() V5() V6() cardinal set
card G is non empty V4() V5() V6() cardinal set
x is finite set
card x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
x is finite set
card x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
(card x) + (card x) is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
(card R) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
R is irreflexive RelStr
ComplRelStr R is strict irreflexive RelStr
n is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
G is irreflexive RelStr
the carrier of G is set
card the carrier of G is V4() V5() V6() cardinal set
ComplRelStr G is strict irreflexive RelStr
CG is strict RelStr
the carrier of CG is set
x is strict RelStr
the carrier of x is set
union_of (CG,x) is strict RelStr
sum_of (CG,x) is strict RelStr
CG is strict RelStr
the carrier of CG is set
x is strict RelStr
the carrier of x is set
union_of (CG,x) is strict RelStr
sum_of (CG,x) is strict RelStr
card the carrier of x is V4() V5() V6() cardinal set
card the carrier of CG is V4() V5() V6() cardinal set
R is irreflexive RelStr
the carrier of R is set
A is irreflexive RelStr
the carrier of A is set
the carrier of R \/ the carrier of A is set
R is non empty finite set
card R is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
R1 is non empty finite set
card R1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
(card R) + (card R1) is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
A is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
A + x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
n + 0 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
ComplRelStr A is strict irreflexive RelStr
ComplRelStr R is strict irreflexive RelStr
the carrier of (ComplRelStr R) is set
the carrier of (ComplRelStr A) is set
x + A is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
n + 0 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
sum_of ((ComplRelStr R),(ComplRelStr A)) is strict RelStr
R is irreflexive RelStr
the carrier of R is set
A is irreflexive RelStr
the carrier of A is set
the carrier of R \/ the carrier of A is set
R is non empty finite set
card R is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
R1 is non empty finite set
card R1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
(card R) + (card R1) is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
A is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
A + x is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
n + 0 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
ComplRelStr A is strict irreflexive RelStr
ComplRelStr R is strict irreflexive RelStr
the carrier of (ComplRelStr R) is set
the carrier of (ComplRelStr A) is set
x + A is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
n + 0 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
union_of ((ComplRelStr R),(ComplRelStr A)) is strict irreflexive RelStr
the carrier of R is set
card the carrier of R is V4() V5() V6() cardinal set
R is symmetric irreflexive RelStr
the carrier of R is set
card the carrier of R is V4() V5() V6() cardinal set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
RelStr(# the carrier of R, the InternalRel of R #) is strict RelStr
n is set
G is set
{n,G} is non empty finite set
[n,G] is non empty set
{n} is non empty trivial finite 1 -element set
{{n,G},{n}} is non empty finite V54() set
[G,n] is non empty set
{G,n} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,n},{G}} is non empty finite V54() set
{[n,G],[G,n]} is non empty Relation-like finite set
x is set
x is set
bool the carrier of R is non empty set
A is Element of bool the carrier of R
subrelstr A is strict full symmetric irreflexive SubRelStr of R
x is Element of bool the carrier of R
subrelstr x is strict full symmetric irreflexive SubRelStr of R
R is non empty strict symmetric irreflexive RelStr
the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
[:{G},{G}:] is non empty Relation-like finite set
[G,G] is non empty set
{G,G} is non empty finite set
{{G,G},{G}} is non empty finite V54() set
{[G,G]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
R1 is non empty strict symmetric irreflexive RelStr
the carrier of R1 is non empty set
the carrier of R1 \/ the carrier of R is non empty set
the InternalRel of R1 is Relation-like the carrier of R1 -defined the carrier of R1 -valued symmetric Element of bool [: the carrier of R1, the carrier of R1:]
[: the carrier of R1, the carrier of R1:] is non empty Relation-like set
bool [: the carrier of R1, the carrier of R1:] is non empty set
[:{n},{n}:] is non empty Relation-like finite set
[n,n] is non empty set
{n,n} is non empty finite set
{{n,n},{n}} is non empty finite V54() set
{[n,n]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
sum_of (R1,R) is non empty strict symmetric RelStr
the InternalRel of (sum_of (R1,R)) is Relation-like the carrier of (sum_of (R1,R)) -defined the carrier of (sum_of (R1,R)) -valued symmetric Element of bool [: the carrier of (sum_of (R1,R)), the carrier of (sum_of (R1,R)):]
the carrier of (sum_of (R1,R)) is non empty set
[: the carrier of (sum_of (R1,R)), the carrier of (sum_of (R1,R)):] is non empty Relation-like set
bool [: the carrier of (sum_of (R1,R)), the carrier of (sum_of (R1,R)):] is non empty set
the InternalRel of R1 \/ the InternalRel of R is Relation-like set
[:A,x:] is Relation-like set
( the InternalRel of R1 \/ the InternalRel of R) \/ [:A,x:] is Relation-like set
[:x,A:] is Relation-like set
(( the InternalRel of R1 \/ the InternalRel of R) \/ [:A,x:]) \/ [:x,A:] is Relation-like set
{[n,G]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
[:{G},{n}:] is non empty Relation-like finite set
{[n,G]} \/ [:{G},{n}:] is non empty Relation-like finite set
{[G,n]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
{[n,G]} \/ {[G,n]} is non empty Relation-like finite set
union_of (R1,R) is non empty strict symmetric irreflexive RelStr
the InternalRel of (union_of (R1,R)) is Relation-like the carrier of (union_of (R1,R)) -defined the carrier of (union_of (R1,R)) -valued symmetric Element of bool [: the carrier of (union_of (R1,R)), the carrier of (union_of (R1,R)):]
the carrier of (union_of (R1,R)) is non empty set
[: the carrier of (union_of (R1,R)), the carrier of (union_of (R1,R)):] is non empty Relation-like set
bool [: the carrier of (union_of (R1,R)), the carrier of (union_of (R1,R)):] is non empty set
the InternalRel of R1 \/ the InternalRel of R is Relation-like set
R is RelStr
the carrier of R is set
n is set
G is set
[n,G] is non empty set
{n,G} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,G},{n}} is non empty finite V54() set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
[G,n] is non empty set
{G,n} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,n},{G}} is non empty finite V54() set
the carrier of R is set
n is set
{n} is non empty trivial finite 1 -element set
n is set
{n} is non empty trivial finite 1 -element set
[: the carrier of R, the carrier of R:] is Relation-like set
[n,n] is non empty set
{n,n} is non empty finite set
{{n,n},{n}} is non empty finite V54() set
{[n,n]} is non empty trivial Relation-like Function-like one-to-one constant finite 1 -element set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
G is set
CG is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,G] is non empty set
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
G is set
CG is set
[G,CG] is non empty set
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,G] is non empty set
{CG,G} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,G},{CG}} is non empty finite V54() set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the carrier of R is set
n is non empty RelStr
the carrier of n is non empty set
card the carrier of n is non empty V4() V5() V6() cardinal set
G is strict RelStr
the carrier of G is set
G is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
G + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
x is non empty RelStr
the carrier of x is non empty set
card the carrier of x is non empty V4() V5() V6() cardinal set
x is strict RelStr
the carrier of x is set
A is strict RelStr
the carrier of A is set
union_of (x,A) is strict RelStr
sum_of (x,A) is strict RelStr
R is strict RelStr
the carrier of R is set
R is finite set
card R is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
CG is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
CG + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
card (CG + 1) is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
the carrier of x \/ the carrier of A is set
card ( the carrier of x \/ the carrier of A) is V4() V5() V6() cardinal set
R22 is strict RelStr
the carrier of R22 is set
R11 is strict RelStr
the carrier of R11 is set
R22 is finite set
card R22 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
R2 is finite set
card R2 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
(card R22) + (card R2) is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
card CG is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
card G is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
the set is set
{ the set } is non empty trivial finite 1 -element set
card { the set } is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
G9 is set
{G9} is non empty trivial finite 1 -element set
the InternalRel of x is Relation-like the carrier of x -defined the carrier of x -valued Element of bool [: the carrier of x, the carrier of x:]
[: the carrier of x, the carrier of x:] is Relation-like set
bool [: the carrier of x, the carrier of x:] is non empty set
R11 is set
{R11} is non empty trivial finite 1 -element set
the InternalRel of A is Relation-like the carrier of A -defined the carrier of A -valued Element of bool [: the carrier of A, the carrier of A:]
[: the carrier of A, the carrier of A:] is Relation-like set
bool [: the carrier of A, the carrier of A:] is non empty set
G9 is set
{G9} is non empty trivial finite 1 -element set
R11 is symmetric RelStr
G9 is symmetric RelStr
union_of (R11,G9) is strict symmetric RelStr
the InternalRel of x is Relation-like the carrier of x -defined the carrier of x -valued Element of bool [: the carrier of x, the carrier of x:]
[: the carrier of x, the carrier of x:] is Relation-like set
bool [: the carrier of x, the carrier of x:] is non empty set
R11 is set
{R11} is non empty trivial finite 1 -element set
R11 is symmetric RelStr
G9 is symmetric RelStr
union_of (R11,G9) is strict symmetric RelStr
the InternalRel of A is Relation-like the carrier of A -defined the carrier of A -valued Element of bool [: the carrier of A, the carrier of A:]
[: the carrier of A, the carrier of A:] is Relation-like set
bool [: the carrier of A, the carrier of A:] is non empty set
R11 is set
{R11} is non empty trivial finite 1 -element set
G9 is symmetric RelStr
R11 is symmetric RelStr
union_of (G9,R11) is strict symmetric RelStr
(G + 1) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
card CG is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
card G is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
(G + 1) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
G9 is symmetric RelStr
R11 is symmetric RelStr
union_of (G9,R11) is strict symmetric RelStr
G is non empty RelStr
the carrier of G is non empty set
card the carrier of G is non empty V4() V5() V6() cardinal set
R is RelStr
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
n is non empty RelStr
the carrier of n is non empty set
G is non empty RelStr
the carrier of G is non empty set
union_of (n,G) is non empty strict RelStr
CG is Element of the carrier of n
x is Element of the carrier of G
[CG,x] is non empty Element of [: the carrier of n, the carrier of G:]
[: the carrier of n, the carrier of G:] is non empty Relation-like set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is non empty Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
the InternalRel of n \/ the InternalRel of G is Relation-like set
the carrier of n /\ the carrier of G is set
the carrier of n /\ the carrier of G is set
R is RelStr
ComplRelStr R is strict irreflexive RelStr
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
the carrier of (ComplRelStr R) is set
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
n is non empty RelStr
the carrier of n is non empty set
G is non empty RelStr
the carrier of G is non empty set
sum_of (n,G) is non empty strict RelStr
CG is Element of the carrier of n
x is Element of the carrier of G
[CG,x] is non empty Element of [: the carrier of n, the carrier of G:]
[: the carrier of n, the carrier of G:] is non empty Relation-like set
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
the InternalRel of n is Relation-like the carrier of n -defined the carrier of n -valued Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is non empty Relation-like set
bool [: the carrier of n, the carrier of n:] is non empty set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
[: the carrier of G, the carrier of n:] is non empty Relation-like set
[: the carrier of n, the carrier of G:] \/ [: the carrier of G, the carrier of n:] is non empty Relation-like set
the InternalRel of G \/ ([: the carrier of n, the carrier of G:] \/ [: the carrier of G, the carrier of n:]) is non empty Relation-like set
the InternalRel of n \/ ( the InternalRel of G \/ ([: the carrier of n, the carrier of G:] \/ [: the carrier of G, the carrier of n:])) is non empty Relation-like set
the InternalRel of G \/ [: the carrier of n, the carrier of G:] is non empty Relation-like set
( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is non empty Relation-like set
the InternalRel of n \/ (( the InternalRel of G \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:]) is non empty Relation-like set
the InternalRel of n \/ the InternalRel of G is Relation-like set
( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:] is non empty Relation-like set
(( the InternalRel of n \/ the InternalRel of G) \/ [: the carrier of n, the carrier of G:]) \/ [: the carrier of G, the carrier of n:] is non empty Relation-like set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued Element of bool [: the carrier of R, the carrier of R:]
the carrier of R is set
[: the carrier of R, the carrier of R:] is Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of R /\ the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of R -defined the carrier of (ComplRelStr R) -valued the carrier of R -valued Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
R is non empty symmetric RelStr
the carrier of R is non empty set
[#] R is non empty non proper Element of bool the carrier of R
bool the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
n is Element of the carrier of R
{n} is non empty trivial finite 1 -element Element of bool the carrier of R
([#] R) \ {n} is Element of bool the carrier of R
subrelstr (([#] R) \ {n}) is strict full symmetric SubRelStr of R
G is non empty RelStr
the carrier of G is non empty set
CG is non empty RelStr
the carrier of CG is non empty set
union_of (G,CG) is non empty strict RelStr
the carrier of (subrelstr (([#] R) \ {n})) is set
the carrier of G \/ the carrier of CG is non empty set
the Element of the carrier of G is Element of the carrier of G
the carrier of R \ {n} is Element of bool the carrier of R
A is Element of bool the carrier of R
R is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len R is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
R . 1 is set
R . (len R) is set
dom R is finite Element of bool NAT
R is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
R . R is set
R is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
R . R is set
R is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
R . R is set
Seg (len R) is finite len R -element Element of bool NAT
R1 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
R1 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
Seg (len R) is finite len R -element Element of bool NAT
R2 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
R . R2 is set
R2 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
R . R2 is set
the carrier of (subrelstr (([#] R) \ {n})) \/ {n} is non empty set
R2 is set
R2 is set
R . R1 is set
R . (R1 + 1) is set
[(R . R1),(R . (R1 + 1))] is non empty set
{(R . R1),(R . (R1 + 1))} is non empty finite set
{(R . R1)} is non empty trivial finite 1 -element set
{{(R . R1),(R . (R1 + 1))},{(R . R1)}} is non empty finite V54() set
[(R . R1),(R . R)] is non empty set
{(R . R1),(R . R)} is non empty finite set
{{(R . R1),(R . R)},{(R . R1)}} is non empty finite V54() set
[: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] is Relation-like set
the InternalRel of R |_2 the carrier of (subrelstr (([#] R) \ {n})) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] is Relation-like the carrier of R -defined the carrier of R -valued set
R11 is Element of the carrier of CG
G9 is Element of the carrier of G
[R11,G9] is non empty Element of [: the carrier of CG, the carrier of G:]
[: the carrier of CG, the carrier of G:] is non empty Relation-like set
{R11,G9} is non empty finite set
{R11} is non empty trivial finite 1 -element set
{{R11,G9},{R11}} is non empty finite V54() set
the InternalRel of (subrelstr (([#] R) \ {n})) is Relation-like the carrier of (subrelstr (([#] R) \ {n})) -defined the carrier of (subrelstr (([#] R) \ {n})) -valued symmetric Element of bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):]
bool [: the carrier of (subrelstr (([#] R) \ {n})), the carrier of (subrelstr (([#] R) \ {n})):] is non empty set
[G9,R11] is non empty Element of [: the carrier of G, the carrier of CG:]
[: the carrier of G, the carrier of CG:] is non empty Relation-like set
{G9,R11} is non empty finite set
{G9} is non empty trivial finite 1 -element set
{{G9,R11},{G9}} is non empty finite V54() set
R22 is Element of the carrier of G
[R22,n] is non empty Element of [: the carrier of G, the carrier of R:]
[: the carrier of G, the carrier of R:] is non empty Relation-like set
{R22,n} is non empty finite set
{R22} is non empty trivial finite 1 -element set
{{R22,n},{R22}} is non empty finite V54() set
R is non empty symmetric irreflexive RelStr
the carrier of R is non empty set
bool the carrier of R is non empty set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
n is Element of the carrier of R
G is Element of the carrier of R
CG is Element of the carrier of R
x is Element of the carrier of R
{n,G,CG,x} is non empty finite Element of bool the carrier of R
[n,G] is non empty Element of [: the carrier of R, the carrier of R:]
{n,G} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,G},{n}} is non empty finite V54() set
[G,CG] is non empty Element of [: the carrier of R, the carrier of R:]
{G,CG} is non empty finite set
{G} is non empty trivial finite 1 -element set
{{G,CG},{G}} is non empty finite V54() set
[CG,x] is non empty Element of [: the carrier of R, the carrier of R:]
{CG,x} is non empty finite set
{CG} is non empty trivial finite 1 -element set
{{CG,x},{CG}} is non empty finite V54() set
[n,CG] is non empty Element of [: the carrier of R, the carrier of R:]
{n,CG} is non empty finite set
{{n,CG},{n}} is non empty finite V54() set
[n,x] is non empty Element of [: the carrier of R, the carrier of R:]
{n,x} is non empty finite set
{{n,x},{n}} is non empty finite V54() set
[G,x] is non empty Element of [: the carrier of R, the carrier of R:]
{G,x} is non empty finite set
{{G,x},{G}} is non empty finite V54() set
x is Element of bool the carrier of R
subrelstr x is strict full symmetric irreflexive SubRelStr of R
(0,1) --> (n,G) is non empty Relation-like NAT -defined {0,1} -defined the carrier of R -valued Function-like V25({0,1}) V29({0,1}, the carrier of R) finite Element of bool [:{0,1}, the carrier of R:]
[:{0,1}, the carrier of R:] is non empty Relation-like set
bool [:{0,1}, the carrier of R:] is non empty set
(2,3) --> (CG,x) is non empty Relation-like NAT -defined {2,3} -defined the carrier of R -valued Function-like V25({2,3}) V29({2,3}, the carrier of R) finite Element of bool [:{2,3}, the carrier of R:]
[:{2,3}, the carrier of R:] is non empty Relation-like set
bool [:{2,3}, the carrier of R:] is non empty set
((0,1) --> (n,G)) +* ((2,3) --> (CG,x)) is non empty Relation-like NAT -defined the carrier of R -valued Function-like finite set
rng ((2,3) --> (CG,x)) is non empty finite set
{CG,x} is non empty finite Element of bool the carrier of R
0 .--> n is trivial Relation-like NAT -defined {0} -defined the carrier of R -valued Function-like one-to-one constant finite set
{0} --> n is non empty trivial Relation-like {0} -defined the carrier of R -valued {n} -valued Function-like one-to-one constant V25({0}) V29({0},{n}) finite 1 -element Element of bool [:{0},{n}:]
[:{0},{n}:] is non empty Relation-like finite set
bool [:{0},{n}:] is non empty finite V54() set
rng (0 .--> n) is trivial finite set
1 .--> G is trivial Relation-like NAT -defined {1} -defined the carrier of R -valued Function-like one-to-one constant finite set
{1} --> G is non empty trivial Relation-like {1} -defined the carrier of R -valued {G} -valued Function-like one-to-one constant V25({1}) V29({1},{G}) finite 1 -element Element of bool [:{1},{G}:]
[:{1},{G}:] is non empty Relation-like finite set
bool [:{1},{G}:] is non empty finite V54() set
rng (1 .--> G) is trivial finite set
R is set
{n} is non empty trivial finite 1 -element Element of bool the carrier of R
{G} is non empty trivial finite 1 -element Element of bool the carrier of R
the InternalRel of (subrelstr x) is Relation-like the carrier of (subrelstr x) -defined the carrier of (subrelstr x) -valued symmetric Element of bool [: the carrier of (subrelstr x), the carrier of (subrelstr x):]
the carrier of (subrelstr x) is set
[: the carrier of (subrelstr x), the carrier of (subrelstr x):] is Relation-like set
bool [: the carrier of (subrelstr x), the carrier of (subrelstr x):] is non empty set
[n,n] is non empty Element of [: the carrier of R, the carrier of R:]
{n,n} is non empty finite set
{{n,n},{n}} is non empty finite V54() set
[G,n] is non empty Element of [: the carrier of R, the carrier of R:]
{G,n} is non empty finite set
{{G,n},{G}} is non empty finite V54() set
[G,G] is non empty Element of [: the carrier of R, the carrier of R:]
{G,G} is non empty finite set
{{G,G},{G}} is non empty finite V54() set
{[n,n],[n,G],[G,n],[G,G],[n,CG],[n,x],[G,CG],[G,x]} is non empty Relation-like the carrier of R -defined the carrier of R -valued finite Element of bool [: the carrier of R, the carrier of R:]
[CG,n] is non empty Element of [: the carrier of R, the carrier of R:]
{CG,n} is non empty finite set
{{CG,n},{CG}} is non empty finite V54() set
[CG,G] is non empty Element of [: the carrier of R, the carrier of R:]
{CG,G} is non empty finite set
{{CG,G},{CG}} is non empty finite V54() set
[x,n] is non empty Element of [: the carrier of R, the carrier of R:]
{x,n} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,n},{x}} is non empty finite V54() set
[x,G] is non empty Element of [: the carrier of R, the carrier of R:]
{x,G} is non empty finite set
{{x,G},{x}} is non empty finite V54() set
[CG,CG] is non empty Element of [: the carrier of R, the carrier of R:]
{CG,CG} is non empty finite set
{{CG,CG},{CG}} is non empty finite V54() set
[x,CG] is non empty Element of [: the carrier of R, the carrier of R:]
{x,CG} is non empty finite set
{{x,CG},{x}} is non empty finite V54() set
[x,x] is non empty Element of [: the carrier of R, the carrier of R:]
{x,x} is non empty finite set
{{x,x},{x}} is non empty finite V54() set
{[CG,n],[CG,G],[x,n],[x,G],[CG,CG],[CG,x],[x,CG],[x,x]} is non empty Relation-like the carrier of R -defined the carrier of R -valued finite Element of bool [: the carrier of R, the carrier of R:]
2 .--> CG is trivial Relation-like NAT -defined {2} -defined the carrier of R -valued Function-like one-to-one constant finite set
{2} --> CG is non empty trivial Relation-like {2} -defined the carrier of R -valued {CG} -valued Function-like one-to-one constant V25({2}) V29({2},{CG}) finite 1 -element Element of bool [:{2},{CG}:]
[:{2},{CG}:] is non empty Relation-like finite set
bool [:{2},{CG}:] is non empty finite V54() set
3 .--> x is trivial Relation-like NAT -defined {3} -defined the carrier of R -valued Function-like one-to-one constant finite set
{3} --> x is non empty trivial Relation-like {3} -defined the carrier of R -valued {x} -valued Function-like one-to-one constant V25({3}) V29({3},{x}) finite 1 -element Element of bool [:{3},{x}:]
[:{3},{x}:] is non empty Relation-like finite set
bool [:{3},{x}:] is non empty finite V54() set
(2 .--> CG) +* (3 .--> x) is Relation-like NAT -defined the carrier of R -valued Function-like finite set
rng (2 .--> CG) is trivial finite set
rng (3 .--> x) is trivial finite set
H is set
{CG} is non empty trivial finite 1 -element Element of bool the carrier of R
{x} is non empty trivial finite 1 -element Element of bool the carrier of R
rng ((0,1) --> (n,G)) is non empty finite set
{n,G} is non empty finite Element of bool the carrier of R
H is set
dom (((0,1) --> (n,G)) +* ((2,3) --> (CG,x))) is non empty finite set
dom ((0,1) --> (n,G)) is non empty finite V54() Element of bool {0,1}
bool {0,1} is non empty finite V54() set
dom ((2,3) --> (CG,x)) is non empty finite V54() Element of bool {2,3}
bool {2,3} is non empty finite V54() set
(dom ((0,1) --> (n,G))) \/ (dom ((2,3) --> (CG,x))) is non empty finite V54() set
{0,1} is non empty finite V54() Element of bool NAT
{0,1} \/ (dom ((2,3) --> (CG,x))) is non empty finite V54() set
{2,3} is non empty finite V54() Element of bool NAT
{0,1} \/ {2,3} is non empty finite V54() Element of bool NAT
{0,1,2,3} is non empty finite Element of bool NAT
H is set
rng (((0,1) --> (n,G)) +* ((2,3) --> (CG,x))) is non empty finite set
(rng ((0,1) --> (n,G))) \/ (rng ((2,3) --> (CG,x))) is non empty finite set
[: the carrier of (Necklace 4), the carrier of (subrelstr x):] is Relation-like set
bool [: the carrier of (Necklace 4), the carrier of (subrelstr x):] is non empty set
(0 .--> n) +* (1 .--> G) is Relation-like NAT -defined the carrier of R -valued Function-like finite set
H is Relation-like the carrier of (Necklace 4) -defined the carrier of (subrelstr x) -valued Function-like V29( the carrier of (Necklace 4), the carrier of (subrelstr x)) finite Element of bool [: the carrier of (Necklace 4), the carrier of (subrelstr x):]
{[n,G],[G,n],[G,CG],[CG,G],[CG,x],[x,CG]} is non empty Relation-like the carrier of R -defined the carrier of R -valued finite Element of bool [: the carrier of R, the carrier of R:]
H is set
the InternalRel of R |_2 the carrier of (subrelstr x) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr x), the carrier of (subrelstr x):] is Relation-like the carrier of R -defined the carrier of R -valued set
{[n,n],[n,G],[G,n],[G,G],[n,CG],[n,x],[G,CG],[G,x]} \/ {[CG,n],[CG,G],[x,n],[x,G],[CG,CG],[CG,x],[x,CG],[x,x]} is non empty Relation-like the carrier of R -defined the carrier of R -valued finite Element of bool [: the carrier of R, the carrier of R:]
H is set
the InternalRel of R |_2 the carrier of (subrelstr x) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr x), the carrier of (subrelstr x):] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R |_2 the carrier of (subrelstr x) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr x), the carrier of (subrelstr x):] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R |_2 the carrier of (subrelstr x) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr x), the carrier of (subrelstr x):] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R |_2 the carrier of (subrelstr x) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr x), the carrier of (subrelstr x):] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R |_2 the carrier of (subrelstr x) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr x), the carrier of (subrelstr x):] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R |_2 the carrier of (subrelstr x) is Relation-like set
the InternalRel of R /\ [: the carrier of (subrelstr x), the carrier of (subrelstr x):] is Relation-like the carrier of R -defined the carrier of R -valued set
H is Element of the carrier of (Necklace 4)
u is Element of the carrier of (Necklace 4)
[H,u] is non empty Element of [: the carrier of (Necklace 4), the carrier of (Necklace 4):]
{H,u} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,u},{H}} is non empty finite V54() set
H . H is Element of the carrier of (subrelstr x)
H . u is Element of the carrier of (subrelstr x)
[(H . H),(H . u)] is non empty set
{(H . H),(H . u)} is non empty finite set
{(H . H)} is non empty trivial finite 1 -element set
{{(H . H),(H . u)},{(H . H)}} is non empty finite V54() set
[0,1] is non empty Element of [:NAT,NAT:]
((0,1) --> (n,G)) . 1 is set
((0,1) --> (n,G)) . 0 is set
[1,0] is non empty Element of [:NAT,NAT:]
((0,1) --> (n,G)) . 0 is set
((0,1) --> (n,G)) . 1 is set
[1,2] is non empty Element of [:NAT,NAT:]
((0,1) --> (n,G)) . 1 is set
((2,3) --> (CG,x)) +* ((0,1) --> (n,G)) is non empty Relation-like NAT -defined the carrier of R -valued Function-like finite set
((2,3) --> (CG,x)) . 2 is set
[2,1] is non empty Element of [:NAT,NAT:]
((0,1) --> (n,G)) . 1 is set
((2,3) --> (CG,x)) +* ((0,1) --> (n,G)) is non empty Relation-like NAT -defined the carrier of R -valued Function-like finite set
((2,3) --> (CG,x)) . 2 is set
[2,3] is non empty Element of [:NAT,NAT:]
((2,3) --> (CG,x)) +* ((0,1) --> (n,G)) is non empty Relation-like NAT -defined the carrier of R -valued Function-like finite set
((2,3) --> (CG,x)) . 3 is set
((2,3) --> (CG,x)) . 2 is set
[3,2] is non empty Element of [:NAT,NAT:]
((2,3) --> (CG,x)) +* ((0,1) --> (n,G)) is non empty Relation-like NAT -defined the carrier of R -valued Function-like finite set
{3,2} is non empty finite V54() Element of bool NAT
((2,3) --> (CG,x)) . 2 is set
((2,3) --> (CG,x)) . 3 is set
[0,1] is non empty Element of [:NAT,NAT:]
[1,0] is non empty Element of [:NAT,NAT:]
[1,2] is non empty Element of [:NAT,NAT:]
[2,1] is non empty Element of [:NAT,NAT:]
[2,3] is non empty Element of [:NAT,NAT:]
[3,2] is non empty Element of [:NAT,NAT:]
[: the carrier of (subrelstr x), the carrier of (Necklace 4):] is Relation-like set
bool [: the carrier of (subrelstr x), the carrier of (Necklace 4):] is non empty set
H " is Relation-like Function-like set
[:{0,1},{n,G}:] is non empty Relation-like finite set
bool [:{0,1},{n,G}:] is non empty finite V54() set
[:{n,G},{0,1}:] is non empty Relation-like finite set
bool [:{n,G},{0,1}:] is non empty finite V54() set
w is non empty Relation-like {0,1} -defined {n,G} -valued Function-like V25({0,1}) V29({0,1},{n,G}) finite Element of bool [:{0,1},{n,G}:]
w " is Relation-like Function-like set
[:{2,3},{CG,x}:] is non empty Relation-like finite set
bool [:{2,3},{CG,x}:] is non empty finite V54() set
[:{CG,x},{2,3}:] is non empty Relation-like finite set
bool [:{CG,x},{2,3}:] is non empty finite V54() set
Z is non empty Relation-like {2,3} -defined {CG,x} -valued Function-like V25({2,3}) V29({2,3},{CG,x}) finite Element of bool [:{2,3},{CG,x}:]
Z " is Relation-like Function-like set
H is non empty Relation-like {CG,x} -defined {2,3} -valued Function-like V25({CG,x}) V29({CG,x},{2,3}) finite Element of bool [:{CG,x},{2,3}:]
dom H is non empty finite Element of bool {CG,x}
bool {CG,x} is non empty finite V54() set
(CG,x) --> (2,3) is non empty Relation-like the carrier of R -defined {CG,x} -defined NAT -valued Function-like V25({CG,x}) V29({CG,x}, NAT ) finite Element of bool [:{CG,x},NAT:]
[:{CG,x},NAT:] is non empty non trivial Relation-like non finite set
bool [:{CG,x},NAT:] is non empty non trivial non finite set
v is Relation-like the carrier of (subrelstr x) -defined the carrier of (Necklace 4) -valued Function-like V25( the carrier of (subrelstr x)) V29( the carrier of (subrelstr x), the carrier of (Necklace 4)) Element of bool [: the carrier of (subrelstr x), the carrier of (Necklace 4):]
Z is non empty Relation-like {n,G} -defined {0,1} -valued Function-like V25({n,G}) V29({n,G},{0,1}) finite Element of bool [:{n,G},{0,1}:]
Z +* H is non empty Relation-like Function-like finite set
(n,G) --> (0,1) is non empty Relation-like the carrier of R -defined {n,G} -defined NAT -valued Function-like V25({n,G}) V29({n,G}, NAT ) finite Element of bool [:{n,G},NAT:]
[:{n,G},NAT:] is non empty non trivial Relation-like non finite set
bool [:{n,G},NAT:] is non empty non trivial non finite set
dom Z is non empty finite Element of bool {n,G}
bool {n,G} is non empty finite V54() set
H +* Z is non empty Relation-like Function-like finite set
v . (H . H) is set
Z . n is set
v . (H . u) is set
Z . G is set
v . (H . u) is set
Z . n is set
v . (H . H) is set
Z . G is set
v . (H . H) is set
Z . G is set
v . (H . u) is set
H . CG is set
v . (H . u) is set
Z . G is set
v . (H . H) is set
H . CG is set
v . (H . H) is set
H . CG is set
v . (H . u) is set
H . x is set
v . (H . u) is set
H . CG is set
v . (H . H) is set
H . x is set
R is non empty symmetric irreflexive RelStr
the carrier of R is non empty set
[#] R is non empty non proper Element of bool the carrier of R
bool the carrier of R is non empty set
ComplRelStr R is non empty strict symmetric irreflexive RelStr
n is Element of the carrier of R
{n} is non empty trivial finite 1 -element Element of bool the carrier of R
([#] R) \ {n} is Element of bool the carrier of R
subrelstr (([#] R) \ {n}) is strict full symmetric irreflexive SubRelStr of R
G is non empty RelStr
the carrier of G is non empty set
CG is non empty RelStr
the carrier of CG is non empty set
union_of (G,CG) is non empty strict RelStr
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
x is Element of the carrier of G
[x,n] is non empty Element of [: the carrier of G, the carrier of R:]
[: the carrier of G, the carrier of R:] is non empty Relation-like set
{x,n} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,n},{x}} is non empty finite V54() set
the carrier of R \ {n} is Element of bool the carrier of R
A is Element of bool the carrier of R
subrelstr A is strict full symmetric irreflexive SubRelStr of R
R is non empty symmetric irreflexive RelStr
union_of (CG,G) is non empty strict RelStr
R1 is Element of the carrier of CG
[R1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
[: the carrier of CG, the carrier of R:] is non empty Relation-like set
{R1,n} is non empty finite set
{R1} is non empty trivial finite 1 -element set
{{R1,n},{R1}} is non empty finite V54() set
{ b1 where b1 is Element of the carrier of G : [b1,n] in the InternalRel of R } is set
{ b1 where b1 is Element of the carrier of G : not [b1,n] in the InternalRel of R } is set
{ b1 where b1 is Element of the carrier of CG : [b1,n] in the InternalRel of R } is set
{ b1 where b1 is Element of the carrier of CG : not [b1,n] in the InternalRel of R } is set
x9 is Element of bool the carrier of R
subrelstr x9 is strict full symmetric irreflexive SubRelStr of R
R2 is set
R22 is set
H is set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
v is Element of the carrier of G
[v,n] is non empty Element of [: the carrier of G, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
R2 \/ R22 is set
H is set
[H,n] is non empty set
{H,n} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,n},{H}} is non empty finite V54() set
[H,n] is non empty set
{H,n} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,n},{H}} is non empty finite V54() set
[H,n] is non empty set
{H,n} is non empty finite set
{H} is non empty trivial finite 1 -element set
{{H,n},{H}} is non empty finite V54() set
H is set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
R11 is set
G9 is set
H is set
u is Element of the carrier of CG
[u,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
v is Element of the carrier of CG
[v,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
the carrier of (subrelstr x9) is set
the carrier of R is non empty set
the carrier of (subrelstr x9) /\ the carrier of R is set
x9 /\ the carrier of R is Element of bool the carrier of R
x9 /\ A is Element of bool the carrier of R
H is set
the carrier of R \/ {n} is non empty set
u is set
u is set
R11 \/ G9 is set
u is set
[u,n] is non empty set
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
[u,n] is non empty set
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
[u,n] is non empty set
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
u is set
v is Element of the carrier of CG
[v,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
v is Element of the carrier of CG
[v,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
R22 \/ G9 is set
u is Element of the carrier of R
[u,n] is non empty Element of [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
v is Element of the carrier of G
[v,n] is non empty Element of [: the carrier of G, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
v is Element of the carrier of CG
[v,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
H is non empty symmetric irreflexive RelStr
the carrier of H is non empty set
the carrier of R /\ the carrier of H is set
the carrier of G \/ the carrier of CG is non empty set
the carrier of (ComplRelStr R) is non empty set
the InternalRel of (ComplRelStr R) is Relation-like the carrier of (ComplRelStr R) -defined the carrier of (ComplRelStr R) -valued symmetric Element of bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):]
[: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty Relation-like set
bool [: the carrier of (ComplRelStr R), the carrier of (ComplRelStr R):] is non empty set
u is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len u is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
u . 1 is set
u . (len u) is set
dom u is finite Element of bool NAT
0 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
1 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
u . (1 + 1) is set
[(u . 1),(u . (1 + 1))] is non empty set
{(u . 1),(u . (1 + 1))} is non empty finite set
{(u . 1)} is non empty trivial finite 1 -element set
{{(u . 1),(u . (1 + 1))},{(u . 1)}} is non empty finite V54() set
u . 2 is set
[n,n] is non empty Element of [: the carrier of R, the carrier of R:]
{n,n} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,n},{n}} is non empty finite V54() set
id the carrier of R is non empty Relation-like the carrier of R -defined the carrier of R -valued Function-like one-to-one V25( the carrier of R) V29( the carrier of R, the carrier of R) V30( the carrier of R) V31( the carrier of R, the carrier of R) reflexive symmetric antisymmetric transitive Element of bool [: the carrier of R, the carrier of R:]
the InternalRel of (ComplRelStr R) /\ (id the carrier of R) is Relation-like the carrier of R -defined the carrier of (ComplRelStr R) -defined the carrier of R -valued the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of R, the carrier of R:]
[(u . 2),n] is non empty set
{(u . 2),n} is non empty finite set
{(u . 2)} is non empty trivial finite 1 -element set
{{(u . 2),n},{(u . 2)}} is non empty finite V54() set
[(u . (1 + 1)),(u . 1)] is non empty set
{(u . (1 + 1)),(u . 1)} is non empty finite set
{(u . (1 + 1))} is non empty trivial finite 1 -element set
{{(u . (1 + 1)),(u . 1)},{(u . (1 + 1))}} is non empty finite V54() set
the InternalRel of (ComplRelStr R) /\ the InternalRel of R is Relation-like the carrier of R -defined the carrier of (ComplRelStr R) -defined the carrier of R -valued the carrier of (ComplRelStr R) -valued Element of bool [: the carrier of R, the carrier of R:]
the Element of R22 is Element of R22
the carrier of G \/ the carrier of CG is non empty set
v is Element of the carrier of G
[v,n] is non empty Element of [: the carrier of G, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
v is Element of the carrier of R
w is Element of the carrier of R
R2 /\ R22 is set
Z is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
Z . 1 is set
Z . (len Z) is set
dom Z is finite Element of bool NAT
Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . Z is set
Seg (len Z) is finite len Z -element Element of bool NAT
Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . Z is set
Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . Z is set
Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . Z is set
Seg (len Z) is finite len Z -element Element of bool NAT
H is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
H + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
R2 /\ R22 is set
Seg (len Z) is finite len Z -element Element of bool NAT
Z . H is set
Z . (H + 1) is set
[(Z . H),(Z . (H + 1))] is non empty set
{(Z . H),(Z . (H + 1))} is non empty finite set
{(Z . H)} is non empty trivial finite 1 -element set
{{(Z . H),(Z . (H + 1))},{(Z . H)}} is non empty finite V54() set
[(Z . Z),(Z . H)] is non empty set
{(Z . Z),(Z . H)} is non empty finite set
{(Z . Z)} is non empty trivial finite 1 -element set
{{(Z . Z),(Z . H)},{(Z . Z)}} is non empty finite V54() set
w is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . w is set
w is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . w is set
u is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . u is set
w is Element of R2
u is Element of R22
[w,u] is non empty set
{w,u} is non empty finite set
{w} is non empty trivial finite 1 -element set
{{w,u},{w}} is non empty finite V54() set
[u,w] is non empty set
{u,w} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,w},{u}} is non empty finite V54() set
w is Element of the carrier of CG
u is Element of the carrier of G
[u,w] is non empty Element of [: the carrier of G, the carrier of CG:]
[: the carrier of G, the carrier of CG:] is non empty Relation-like set
{u,w} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,w},{u}} is non empty finite V54() set
[: the carrier of R, the carrier of R:] is non empty Relation-like set
the InternalRel of R |_2 the carrier of R is Relation-like set
the InternalRel of R /\ [: the carrier of R, the carrier of R:] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
w is Element of the carrier of G
[w,n] is non empty Element of [: the carrier of G, the carrier of R:]
{w,n} is non empty finite set
{w} is non empty trivial finite 1 -element set
{{w,n},{w}} is non empty finite V54() set
u is Element of R22
v is Element of R2
[u,v] is non empty set
{u,v} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,v},{u}} is non empty finite V54() set
u is Element of R22
v is Element of R2
[u,v] is non empty set
{u,v} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,v},{u}} is non empty finite V54() set
the Element of R11 is Element of R11
{u,v,n, the Element of R11} is non empty finite set
the carrier of G \/ the carrier of CG is non empty set
Z is Element of the carrier of CG
[Z,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{Z,n} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,n},{Z}} is non empty finite V54() set
Z is Element of the carrier of G
[Z,n] is non empty Element of [: the carrier of G, the carrier of R:]
{Z,n} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,n},{Z}} is non empty finite V54() set
Z is set
Z is Element of bool the carrier of R
subrelstr Z is strict full symmetric irreflexive SubRelStr of R
u is Element of the carrier of CG
[u,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
w is Element of the carrier of R
[n,w] is non empty Element of [: the carrier of R, the carrier of R:]
{n,w} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,w},{n}} is non empty finite V54() set
u is Element of the carrier of CG
[u,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
v is Element of the carrier of R
[v,n] is non empty Element of [: the carrier of R, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of R
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
[u,n] is non empty Element of [: the carrier of R, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
[v,w] is non empty Element of [: the carrier of R, the carrier of R:]
{v,w} is non empty finite set
{{v,w},{v}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
u is Element of the carrier of R
y1 is Element of the carrier of R
[u,y1] is non empty Element of [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
{u,y1} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,y1},{u}} is non empty finite V54() set
the InternalRel of R |_2 the carrier of R is Relation-like set
the InternalRel of R /\ [: the carrier of R, the carrier of R:] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
the InternalRel of CG is Relation-like the carrier of CG -defined the carrier of CG -valued Element of bool [: the carrier of CG, the carrier of CG:]
[: the carrier of CG, the carrier of CG:] is non empty Relation-like set
bool [: the carrier of CG, the carrier of CG:] is non empty set
the InternalRel of G \/ the InternalRel of CG is Relation-like set
the carrier of G /\ the carrier of CG is set
c30 is Element of the carrier of CG
[c30,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{c30,n} is non empty finite set
{c30} is non empty trivial finite 1 -element set
{{c30,n},{c30}} is non empty finite V54() set
the carrier of G /\ the carrier of CG is set
c30 is Element of the carrier of G
[c30,n] is non empty Element of [: the carrier of G, the carrier of R:]
{c30,n} is non empty finite set
{c30} is non empty trivial finite 1 -element set
{{c30,n},{c30}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
[u,w] is non empty Element of [: the carrier of R, the carrier of R:]
{u,w} is non empty finite set
{{u,w},{u}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
u is Element of the carrier of R
y1 is Element of the carrier of R
[u,y1] is non empty Element of [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
{u,y1} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,y1},{u}} is non empty finite V54() set
the InternalRel of R |_2 the carrier of R is Relation-like set
the InternalRel of R /\ [: the carrier of R, the carrier of R:] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
the InternalRel of CG is Relation-like the carrier of CG -defined the carrier of CG -valued Element of bool [: the carrier of CG, the carrier of CG:]
[: the carrier of CG, the carrier of CG:] is non empty Relation-like set
bool [: the carrier of CG, the carrier of CG:] is non empty set
the InternalRel of G \/ the InternalRel of CG is Relation-like set
the carrier of G /\ the carrier of CG is set
c30 is Element of the carrier of CG
[c30,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{c30,n} is non empty finite set
{c30} is non empty trivial finite 1 -element set
{{c30,n},{c30}} is non empty finite V54() set
the carrier of G /\ the carrier of CG is set
c30 is Element of the carrier of G
[c30,n] is non empty Element of [: the carrier of G, the carrier of R:]
{c30,n} is non empty finite set
{c30} is non empty trivial finite 1 -element set
{{c30,n},{c30}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
the carrier of G /\ the carrier of CG is set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
H is non empty full symmetric irreflexive SubRelStr of R
the Element of G9 is Element of G9
the carrier of G \/ the carrier of CG is non empty set
v is Element of the carrier of CG
[v,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
v is Element of the carrier of R
w is Element of the carrier of R
R11 /\ G9 is set
Z is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
Z . 1 is set
Z . (len Z) is set
dom Z is finite Element of bool NAT
Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . Z is set
Seg (len Z) is finite len Z -element Element of bool NAT
Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . Z is set
Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . Z is set
Z is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . Z is set
Seg (len Z) is finite len Z -element Element of bool NAT
H is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
H + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() set
R11 /\ G9 is set
Seg (len Z) is finite len Z -element Element of bool NAT
Z . H is set
Z . (H + 1) is set
[(Z . H),(Z . (H + 1))] is non empty set
{(Z . H),(Z . (H + 1))} is non empty finite set
{(Z . H)} is non empty trivial finite 1 -element set
{{(Z . H),(Z . (H + 1))},{(Z . H)}} is non empty finite V54() set
[(Z . Z),(Z . H)] is non empty set
{(Z . Z),(Z . H)} is non empty finite set
{(Z . Z)} is non empty trivial finite 1 -element set
{{(Z . Z),(Z . H)},{(Z . Z)}} is non empty finite V54() set
w is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . w is set
w is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . w is set
u is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
Z . u is set
w is Element of R11
u is Element of G9
[w,u] is non empty set
{w,u} is non empty finite set
{w} is non empty trivial finite 1 -element set
{{w,u},{w}} is non empty finite V54() set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
bool [: the carrier of R, the carrier of R:] is non empty set
w is Element of the carrier of G
u is Element of the carrier of CG
[u,w] is non empty Element of [: the carrier of CG, the carrier of G:]
[: the carrier of CG, the carrier of G:] is non empty Relation-like set
{u,w} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,w},{u}} is non empty finite V54() set
the InternalRel of R |_2 the carrier of R is Relation-like set
the InternalRel of R /\ [: the carrier of R, the carrier of R:] is Relation-like the carrier of R -defined the carrier of R -valued set
[w,u] is non empty Element of [: the carrier of G, the carrier of CG:]
[: the carrier of G, the carrier of CG:] is non empty Relation-like set
{w,u} is non empty finite set
{w} is non empty trivial finite 1 -element set
{{w,u},{w}} is non empty finite V54() set
w is Element of the carrier of CG
[w,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{w,n} is non empty finite set
{w} is non empty trivial finite 1 -element set
{{w,n},{w}} is non empty finite V54() set
u is Element of G9
v is Element of R11
[u,v] is non empty set
{u,v} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,v},{u}} is non empty finite V54() set
u is Element of G9
v is Element of R11
[u,v] is non empty set
{u,v} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,v},{u}} is non empty finite V54() set
the Element of R2 is Element of R2
{u,v,n, the Element of R2} is non empty finite set
the carrier of G \/ the carrier of CG is non empty set
Z is Element of the carrier of G
[Z,n] is non empty Element of [: the carrier of G, the carrier of R:]
{Z,n} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,n},{Z}} is non empty finite V54() set
Z is Element of the carrier of CG
[Z,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{Z,n} is non empty finite set
{Z} is non empty trivial finite 1 -element set
{{Z,n},{Z}} is non empty finite V54() set
Z is set
Z is Element of bool the carrier of R
subrelstr Z is strict full symmetric irreflexive SubRelStr of R
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
w is Element of the carrier of R
[n,w] is non empty Element of [: the carrier of R, the carrier of R:]
{n,w} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,w},{n}} is non empty finite V54() set
u is Element of the carrier of G
[u,n] is non empty Element of [: the carrier of G, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
v is Element of the carrier of R
[v,n] is non empty Element of [: the carrier of R, the carrier of R:]
{v,n} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,n},{v}} is non empty finite V54() set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of R
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of CG
[u,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
[u,n] is non empty Element of [: the carrier of R, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
[v,w] is non empty Element of [: the carrier of R, the carrier of R:]
{v,w} is non empty finite set
{{v,w},{v}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of CG
[u,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
u is Element of the carrier of R
y1 is Element of the carrier of R
[u,y1] is non empty Element of [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
{u,y1} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,y1},{u}} is non empty finite V54() set
the InternalRel of R |_2 the carrier of R is Relation-like set
the InternalRel of R /\ [: the carrier of R, the carrier of R:] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
the InternalRel of CG is Relation-like the carrier of CG -defined the carrier of CG -valued Element of bool [: the carrier of CG, the carrier of CG:]
[: the carrier of CG, the carrier of CG:] is non empty Relation-like set
bool [: the carrier of CG, the carrier of CG:] is non empty set
the InternalRel of G \/ the InternalRel of CG is Relation-like set
the carrier of G /\ the carrier of CG is set
c30 is Element of the carrier of CG
[c30,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{c30,n} is non empty finite set
{c30} is non empty trivial finite 1 -element set
{{c30,n},{c30}} is non empty finite V54() set
the carrier of G /\ the carrier of CG is set
c30 is Element of the carrier of G
[c30,n] is non empty Element of [: the carrier of G, the carrier of R:]
{c30,n} is non empty finite set
{c30} is non empty trivial finite 1 -element set
{{c30,n},{c30}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
[u,w] is non empty Element of [: the carrier of R, the carrier of R:]
{u,w} is non empty finite set
{{u,w},{u}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of CG
[u,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
u is Element of the carrier of R
y1 is Element of the carrier of R
[u,y1] is non empty Element of [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like set
{u,y1} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,y1},{u}} is non empty finite V54() set
the InternalRel of R |_2 the carrier of R is Relation-like set
the InternalRel of R /\ [: the carrier of R, the carrier of R:] is Relation-like the carrier of R -defined the carrier of R -valued set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric Element of bool [: the carrier of R, the carrier of R:]
bool [: the carrier of R, the carrier of R:] is non empty set
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty Relation-like set
bool [: the carrier of G, the carrier of G:] is non empty set
the InternalRel of CG is Relation-like the carrier of CG -defined the carrier of CG -valued Element of bool [: the carrier of CG, the carrier of CG:]
[: the carrier of CG, the carrier of CG:] is non empty Relation-like set
bool [: the carrier of CG, the carrier of CG:] is non empty set
the InternalRel of G \/ the InternalRel of CG is Relation-like set
the carrier of G /\ the carrier of CG is set
c30 is Element of the carrier of CG
[c30,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{c30,n} is non empty finite set
{c30} is non empty trivial finite 1 -element set
{{c30,n},{c30}} is non empty finite V54() set
the carrier of G /\ the carrier of CG is set
c30 is Element of the carrier of G
[c30,n] is non empty Element of [: the carrier of G, the carrier of R:]
{c30,n} is non empty finite set
{c30} is non empty trivial finite 1 -element set
{{c30,n},{c30}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
y1 is Element of the carrier of G
[y1,n] is non empty Element of [: the carrier of G, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
the carrier of G /\ the carrier of CG is set
u is Element of the carrier of CG
[u,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
the carrier of G \/ the carrier of CG is non empty set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
y1 is Element of the carrier of CG
[y1,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{y1,n} is non empty finite set
{y1} is non empty trivial finite 1 -element set
{{y1,n},{y1}} is non empty finite V54() set
u is Element of the carrier of CG
[u,n] is non empty Element of [: the carrier of CG, the carrier of R:]
{u,n} is non empty finite set
{u} is non empty trivial finite 1 -element set
{{u,n},{u}} is non empty finite V54() set
H is non empty full symmetric irreflexive SubRelStr of R
R is non empty finite strict symmetric irreflexive RelStr
the carrier of R is non empty finite set
the InternalRel of R is Relation-like the carrier of R -defined the carrier of R -valued symmetric finite Element of bool [: the carrier of R, the carrier of R:]
[: the carrier of R, the carrier of R:] is non empty Relation-like finite set
bool [: the carrier of R, the carrier of R:] is non empty finite V54() set
RelStr(# the carrier of R, the InternalRel of R #) is non empty strict RelStr
n is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() set
G is non empty finite strict symmetric irreflexive RelStr
the carrier of G is non empty finite set
card the carrier of G is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
the InternalRel of G is Relation-like the carrier of G -defined the carrier of G -valued symmetric finite Element of bool [: the carrier of G, the carrier of G:]
[: the carrier of G, the carrier of G:] is non empty Relation-like finite set
bool [: the carrier of G, the carrier of G:] is non empty finite V54() set
RelStr(# the carrier of G, the InternalRel of G #) is non empty strict RelStr
ComplRelStr G is non empty strict symmetric irreflexive RelStr
x is non empty trivial finite 1 -element RelStr
the carrier of x is non empty trivial finite 1 -element set
the InternalRel of x is trivial Relation-like the carrier of x -defined the carrier of x -valued reflexive symmetric strongly_connected transitive finite Element of bool [: the carrier of x, the carrier of x:]
[: the carrier of x, the carrier of x:] is non empty Relation-like finite set
bool [: the carrier of x, the carrier of x:] is non empty finite V54() set
RelStr(# the carrier of x, the InternalRel of x #) is non empty strict RelStr
x is non empty strict symmetric irreflexive RelStr
the carrier of x is non empty set
x is non empty strict symmetric irreflexive RelStr
the carrier of x is non empty set
union_of (x,x) is non empty strict symmetric irreflexive RelStr
the carrier of RelStr(# the carrier of G, the InternalRel of G #) is non empty set
the carrier of x \/ the carrier of x is non empty set
card the carrier of x is non empty V4() V5() V6() cardinal set
card the carrier of RelStr(# the carrier of G, the InternalRel of G #) is non empty V4() V5() V6() cardinal set
card the carrier of x is non empty V4() V5() V6() cardinal set
R2 is finite set
card R2 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
R11 is finite set
card R11 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
R22 is non empty finite strict symmetric irreflexive RelStr
the carrier of R22 is non empty finite set
R1 is non empty finite strict symmetric irreflexive RelStr
G9 is finite set
card G9 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
the carrier of R1 is non empty finite set
x is non empty strict symmetric irreflexive RelStr
the carrier of x is non empty set
x is non empty strict symmetric irreflexive RelStr
the carrier of x is non empty set
sum_of (x,x) is non empty strict symmetric RelStr
the carrier of RelStr(# the carrier of G, the InternalRel of G #) is non empty set
the carrier of x \/ the carrier of x is non empty set
card the carrier of x is non empty V4() V5() V6() cardinal set
card the carrier of RelStr(# the carrier of G, the InternalRel of G #) is non empty V4() V5() V6() cardinal set
card the carrier of x is non empty V4() V5() V6() cardinal set
R2 is finite set
card R2 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
R11 is finite set
card R11 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
R22 is non empty finite strict symmetric irreflexive RelStr
the carrier of R22 is non empty finite set
R1 is non empty finite strict symmetric irreflexive RelStr
G9 is finite set
card G9 is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
the carrier of R1 is non empty finite set
x is set
x is Element of the carrier of G
{x} is non empty trivial finite 1 -element Element of bool the carrier of G
bool the carrier of G is non empty finite V54() set
the carrier of G \ {x} is finite Element of bool the carrier of G
A is finite Element of bool the carrier of G
subrelstr A is strict full symmetric irreflexive SubRelStr of G
R is non empty finite symmetric irreflexive RelStr
the carrier of R is non empty finite set
card A is V4() V5() V6() V10() V11() ext-real non negative finite cardinal V71() Element of NAT
card {x} is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
(card the carrier of G) - (card {x}) is V11() ext-real V71() set
n - 1 is V11() ext-real V71() set
(n - 1) + 1 is V11() ext-real V71() set
card the carrier of R is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT
R1 is set
{R1} is non empty trivial finite 1 -element set
the carrier of G \/ {x} is non empty finite set
R2 is set
R2 is set
{R1} \/ {x} is non empty finite set
{R1,x} is non empty finite set
R1 is strict RelStr
the carrier of R1 is set
R2 is strict RelStr
the carrier of R2 is set
union_of (R1,R2) is strict RelStr
sum_of (R1,R2) is strict RelStr
R1 is strict RelStr
the carrier of R1 is set
R2 is strict RelStr
the carrier of R2 is set
union_of (R1,R2) is strict RelStr
sum_of (R1,R2) is strict RelStr
[#] G is non empty non proper finite Element of bool the carrier of G
([#] G) \ {x} is finite Element of bool the carrier of G
subrelstr (([#] G) \ {x}) is strict full symmetric irreflexive SubRelStr of G
R11 is non empty SubRelStr of G
R22 is non empty SubRelStr of G
union_of (R11,R22) is non empty strict RelStr
ComplRelStr R2 is strict irreflexive RelStr
ComplRelStr R1 is strict irreflexive RelStr
G9 is non empty symmetric irreflexive RelStr
the carrier of G9 is non empty set
R11 is non empty RelStr
the carrier of R11 is non empty set
R22 is non empty RelStr
the carrier of R22 is non empty set
ComplRelStr R is non empty strict symmetric irreflexive RelStr
[#] G is non empty non proper finite Element of bool the carrier of G
([#] G) \ {x} is finite Element of bool the carrier of G
subrelstr (([#] G) \ {x}) is strict full symmetric irreflexive SubRelStr of G
ComplRelStr (subrelstr (([#] G) \ {x})) is strict symmetric irreflexive RelStr
[#] G9 is non empty non proper Element of bool the carrier of G9
bool the carrier of G9 is non empty set
x9 is Element of the carrier of G9
{x9} is non empty trivial finite 1 -element Element of bool the carrier of G9
([#] G9) \ {x9} is Element of bool the carrier of G9
subrelstr (([#] G9) \ {x9}) is strict full symmetric irreflexive SubRelStr of G9
ComplRelStr G9 is non empty strict symmetric irreflexive RelStr
union_of ((ComplRelStr R1),(ComplRelStr R2)) is strict irreflexive RelStr
card the carrier of R is non empty V4() V5() V6() V10() V11() ext-real positive non negative finite cardinal V71() Element of NAT